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Article

# Identifying Design Requirements for Wireless Routing Link Metrics

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## Abstract

In this paper, we identify and analyze the requirements to design a new routing link metric for wireless multihop networks. Considering these requirements, when a link metric is proposed, then both the design and implementation of the link metric with a routing protocol become easy. Secondly, the underlying network issues can easily be tackled. Thirdly, an appreciable performance of the network is guaranteed. Along with the existing implementation of three link metrics Expected Transmission Count (ETX), Minimum Delay (MD), and Minimum Loss (ML), we implement inverse ETX; invETX with Optimized Link State Routing (OLSR) using NS-2.34. The simulation results show that how the computational burden of a metric degrades the performance of the respective protocol and how a metric has to trade-off between different performance parameters.

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... For example, a metric may/can produce computational overhead and it may also pay cost in terms of other performance metric(s) like achieving minimized end-to-end delay at the cost lower throughput or higher routing overhead. Thus, we analyze/investigate almost all possible design requirements given in [7]. In this paper, we present a mathematical framework for a proposed quality link metric; Bandwidth adjusted Inverse ETX (BIETX). ...
... d exp firstly detects and then handles asymmetry by incorporating loss ratios in forward and reverse directions. Computation of d exp , by taking the product of delivery ratios same as in [7] and [12] leads to avoidance of computational overhead that is generated due to ETX which firstly calculates inverse of all expected delivery ratios and then adds them up. There are two techniques to measure L cap i.e., packet-pair with different size and back-to-back probes with equal size. ...
... From [7], we conclude that routing load is an important issue in SWMhNs and this issue becomes critical whenever the network load increases with increase in either the number of packets or the number of nodes. In OLSR, shortest interval has been used for exchanging topological information in comparison to Destination Sequence Distance Vector (DSDV) and Fish-eye State Routing (FSR) [14] i.e., IntraScopeInterval in FSR and 'full-dump-period' in DSDV are equal to 15s, and, T C IN T ERV AL = 5s in OLSR, resulting in the generation of more routing overhead. ...
Conference Paper
In this work, we propose a novel quality link metric; Bandwidth adjusted Inverse ETX (BIETX) for Static Wireless Multi-hop Networks (SWMhNs). The proposed metric considers two path selection parameters into account i.e., packet delivery ratio and link capacity. For computing packet delivery ratios in BIETX, the mechanism of Expected Transmission Count (ETX) is adopted. On the other hand, we take two methods of computing link capacity in BIETX. These methods are based upon the size of pair probes; equal size and different size. We also enhance Optimized Link State Routing (OLSR) protocol while using BIETX. A comparative analysis of proposed metric with equal size and different size pair probe; BIETX-1 and BIETX-2, with two existing quality metrics (ETX and Expected Transmission Time (ETT)) in SWMhNs is also a part of this work. From simulation results, we conclude that BIETX-2 outperforms rest of the metrics because of low routing load in ad-hoc probes, and low routing latencies due to enhancements of routing update frequencies and window size in OLSR.
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . ...
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . While, ETX, IBETX, and ELP are implemented with Destination Sequenced Distance Vector (DSDV) [10] based on distance vector routing algorithm. ...
... Previouse implementation of QLMs in routing protocols have not considered routing load for performance measurements. We, in our previous work [8] have considered routing load while analyzing the performance of OLSR which is a link state based proactive routing protocol. Now, in the same way, we are evaluating the performance of those link metrics along with ETT in this paper. ...
Article
Full-text available
In this paper, we compare and analyze performance of five quality link metrics forWireless Multi-hop Networks (WMhNs). The metrics are based on loss probability measurements; ETX, ETT, InvETX, ML and MD, in a distance vector routing protocol; DSDV. Among these selected metrics, we have implemented ML, MD, InvETX and ETT in DSDV which are previously implemented with different protocols; ML, MD, InvETX are implemented with OLSR, while ETT is implemented in MR-LQSR. For our comparison, we have selected Throughput, Normalized Routing Load (NRL) and End-to-End Delay (E2ED) as performance parameters. Finally, we deduce that InvETX due to low computational burden and link asymmetry measurement outperforms among all metrics.
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . ...
... Several QLMs have been proposed, like, Expected Transmission Count (ETX)[2], Expected Transmission Time (ETT) [3], Interference and Bandwidth Adjusted ETX (IBETX) [4], Expected Link Performance (ELP) [5], Minimum Loss (ML) [6], Minimum Delay (MD)[7] and Inverse ETX (InvETX) [8]. The metrics, ETX, ML, MD and InvETX have already been implemented [8] with a proactive routing protocol, Optimized Link State Routing (OLSR) [9] using Link State routing technique . While, ETX, IBETX, and ELP are implemented with Destination Sequenced Distance Vector (DSDV) [10] based on distance vector routing algorithm. ...
... Previouse implementation of QLMs in routing protocols have not considered routing load for performance measurements. We, in our previous work [8] have considered routing load while analyzing the performance of OLSR which is a link state based proactive routing protocol. Now, in the same way, we are evaluating the performance of those link metrics along with ETT in this paper. ...
Data
Full-text available
... An efficiently designed QLM better helps a routing protocol to achieve appreciable performance by dealing with these issues. In our previous work[1], design requirements of QLM are discussed in detail. Moreover, a new QLM; InvETX, is also compared with Expected Transmission Count (ETX)[2], Minimum Loss (ML) and Minimum Delay (MD)[4]in Optimized Link State Routing (OLSR)[5]protocol. ...
... For example, a routing protocol achieves higher throughput at the cost of end-to-end delay or routing overhead. Therefore, we analyze possible design requirements in[1]. Further, in our previous work, we implement three existing link metrics; ETX, MD,and ML, and one newly proposed metric; InvETX OLSR using NS-2.34. ...
... As a result, InvET X achieves higher throughputs than M L and ET X. Similarly, M L performs better than ET X. From[1], we analyze that routing load is a critical issue in SWMhNs when network load increases either with increase in number of nodes or with increase in number of packets. As, OLSR uses the shortest interval for exchanging topological information as compared to DSDV, i.e., 'full-dump-period' in DSDV, whereas, in OLSR T C IN T ERV AL = 5s, therefore, it causes more routing overhead. ...
Article
In this paper, we propose a new Quality Link Metric (QLM), Inverse Expected Transmission Count (InvETX)'' in Optimized Link State Routing (OLSR) protocol. Then we compare performance of three existing QLMs which are based on loss probability measurements; Expected Transmission Count (ETX), Minimum Delay (MD), Minimum Loss (ML) in Static Wireless Multi-hop Networks (SWMhNs). A novel contribution of this paper is enhancement in conventional OLSR to achieve high efficiency in terms of optimized routing load and routing latency. For this purpose, first we present a mathematical framework, and then to validate this frame work, we select three performance parameters to simulate default and enhanced versions of OLSR. Three chosen performance parameters are; throughput, Normalized Routing Load and End-to-End Delay. From simulation results, we conclude that adjusting the frequencies of topological information exchange results in high efficiency.
... This issue is especially challenging as these networks are built to work in specific scenarios. For example, a monitoring network can require a reasonable level of Packet Delivery Ratio (PDR) [8,9]. On the other hand, when the goal is to enable a VoIP (Voice over Internet Protocol) content, the network needs to keep under control the Endto-End Delay (E2ED) [8,9]. ...
... For example, a monitoring network can require a reasonable level of Packet Delivery Ratio (PDR) [8,9]. On the other hand, when the goal is to enable a VoIP (Voice over Internet Protocol) content, the network needs to keep under control the Endto-End Delay (E2ED) [8,9]. Therefore, distinct applications can demand different Quality of Service (QoS) guarantees [6,[10][11][12]. ...
... In this light, the routing protocols should also consider the different applications can have conflicting quality requirements. As a result, future routing mechanisms must support two or more QoS requirements and take into account the trade-off between them, since state-of-the-art protocols do not have these features natively [9,13]. ...
Article
Full-text available
Ad hoc wireless networks have aroused much interest of the scientific community in the last two decades. The provision of Quality of Service (QoS) is a prominent challenge in this research field, since these networks are prone to suffer from instabilities related to wireless medium and mobility. Depending on application, the protocol needs to consider two or more QoS criteria when solving the routing problem. In this context, this work proposes a multicriteria and adaptive framework for proactive routing in order to generate promising compromise solutions by considering critical network quality indicators. Two new methods are proposed—one based on weighted sum method and another based on compromise method ($$\varepsilon$$-constraint)—and compared with the standard weighted sum method. Aiming to map a single final solution, a utility function is proposed to support the definition of the parameters (weights and constraints) of each method. The results show the framework, jointly with the proposed methods, were efficient in promoting significant improvements in the quality indicators investigated in static and mobile scenarios.
... An efficiently designed QLM better helps a routing protocol to achieve appreciable performance by dealing with these issues. In our previous work [1], design requirements of QLM are discussed in detail. Moreover, a new QLM, Inverse Expected Transmission Count (InvETX), is also compared with Expected Transmission Count (ETX) [2], Minimum Loss (ML) [3], and Minimum Delay (MD) [4] in Optimized Link State Routing (OLSR) [5] protocol. ...
... achieving high packet delivery ratio on the cost of increased end-to-end delay). Therefore, we analyze almost all possible design requirements in [1]. Further, in our previous work, we implement three existing link metrics, ETX, MD,and ML, and one newly proposed metric, InvETX OLSR, using NS-2.34. ...
Data
Full-text available
In this paper, we propose a new Quality Link Metric (QLM), “Inverse Expected Transmission Count (InvETX),” in Optimized Link State Routing (OLSR) protocol. Then, we compare performance of three existing QLMs which are based on loss probability measurements: Expected Transmission Count (ETX), Minimum Delay (MD), and Minimum Loss (ML) in Static Wireless Multihop Networks (SWMhNs). A novel contribution of this paper is enhancement in conventional OLSR to achieve high efficiency in terms of optimized routing load and routing latency. For this purpose, first we present a mathematical framework, and then to validate this frame work, we select three performance parameters to simulate default and enhanced versions of OLSR. The three chosen performance parameters are throughput, Normalized Routing Load, and End-to-End Delay. From the simulation results, we conclude that adjusting the frequencies of topological information exchange results in high efficiency.
... Besides the evaluating the performance of DSDV, OLSR and DYMO we also made some modifications to these routing protocols and observed their performance at the end we came up with the result that with minor. In future, we are interested to apply the same analysis on quality link metrics proposed in9101112 and at MAC layer as [13, 14]. ...
Article
In this paper, we present path loss model for VANETs and simulate three routing protocols; Destination Sequenced Distance Vector (DSDV), Optimized Link State Routing (OLSR) and Dynamic MANET On-demand (DYMO) to evaluate and compare their performance using NS-2. The main contribution of this work is enhancement of existing techniques to achieve high efficiency of the underlying networks. After extensive simulations in NS-2, we conclude that DSDV best performs with 802.11p while DYMO gives outstanding performance with 802.11.
... On the other hand in MOD DSR due to reduction in the size of route. In future work, we are interested to implement Expected Transmission Count (ETX) link metric with mathematical modeling, as demonstrated in111213. ...
Article
In this paper, a framework is presented for node distribution with respect to density, network connectivity and communication time. According to modeled framework we evaluate and compare the performance of three routing protocols; Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fisheye State Routing (FSR) in MANETs and VANETs using two Mac-layer protocols; 802.11 and 802.11p. We have further modified these protocols by changing their routing information exchange intervals; MOD AODV, MOD DSR and MOD FSR. A comprehensive simulation work is performed in NS-2 for the comparison of these routing protocols for varying mobilities and scalabilities of nodes. To evaluate their efficiency; throughput, End-to-End Delay (E2ED) and Normalized Routing Load (NRL) of these protocols are taken into account as performance parameters. After extensive simulations, we observe that AODV outperforms both with MANETs and VANETs.
... In future, we will implement different performance metrics of AM-DisCNT, as authors have done in [17], [18], [19] and [20]. ...
Article
The nodes in wireless sensor networks (WSNs) contain limited energy resources, which are needed to transmit data to base station (BS). Routing protocols are designed to reduce the energy consumption. Clustering algorithms are best in this aspect. Such clustering algorithms increase the stability and lifetime of the network. However, every routing protocol is not suitable for heterogeneous environments. AM-DisCNT is proposed and evaluated as a new energy efficient protocol for wireless sensor networks. AM-DisCNT uses circular deployment for even consumption of energy in entire wireless sensor network. Cluster-head selection is on the basis of energy. Highest energy node becomes CH for that round. Energy is again compared in the next round to check the highest energy node of that round. The simulation results show that AM-DisCNT performs better than the existing heterogeneous protocols on the basis of network lifetime, throughput and stability of the system.
... Future work focuses on estimating the delay in propagating data from body sensors to the destination node in DARE protocol and also to investigate mobility in patients body. Authors in [20][21][22][23], work on routing metrics based on ETX (Expected Transmission Count) which, shows better performance than minimum hop count metric, under the availability of link. In view of this, the plan focus to work on routing link metrics as well. ...
Article
In recent years, interests in the applications of Wireless Body Area Sensor Network (WBASN) is noticeably developed. WBASN is playing a significant role to get the real time and precise data with reduced level of energy consumption. It comprises of tiny, lightweight and energy restricted sensors, placed in/on the human body, to monitor any ambiguity in body organs and measure various biomedical parameters. In this study, a protocol named Distance Aware Relaying Energy-efficient (DARE) to monitor patients in multi-hop Body Area Sensor Networks (BASNs) is proposed. The protocol operates by investigating the ward of a hospital comprising of eight patients, under different topologies by positioning the sink at different locations or making it static or mobile. Seven sensors are attached to each patient, measuring different parameters of Electrocardiogram (ECG), pulse rate, heart rate, temperature level, glucose level, toxins level and motion. To reduce the energy consumption, these sensors communicate with the sink via an on-body relay, affixed on the chest of each patient. The body relay possesses higher energy resources as compared to the body sensors as, they perform aggregation and relaying of data to the sink node. A comparison is also conducted conducted with another protocol of BAN named, Mobility-supporting Adaptive Threshold-based Thermal-aware Energy-efficient Multi-hop ProTocol (M-ATTEMPT). The simulation results show that, the proposed protocol achieves increased network lifetime and efficiently reduces the energy consumption, in relative to M-ATTEMPT protocol.
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [21] and [22]. ...
Article
Full-text available
This paper evaluates and compares the performance of two routing protocols, one is reactive, Dynamic MANET On-Demand (DYMO) and other is proactive, Optimized Link State Routing (OLSR) in Mobile Ad-hoc Networks (MANETs) and Vehicular Ad-hoc Networks (VANETs). Performance of these protocols is analyzed using three performance metrics; Packet Delivery Ratio, Normalized Routing Overhead and End-to-End Delay against varying scalabilities of nodes. We perform these simulations with NS-2 using TwoRayGround propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. From the extensive simulations, we observe that DYMO performs better than OLSR for both VANETs and MANETs at the cost of delay. Moreover, DYMO performs better in VANETs as compared to MANETs.
... In future, Routing Link Matrices can also be applied on this proposed technique. Routing can be done by adapting many different approaches as done in [14], [15] and [16]. Application of Routing Link Matrices on the proposed scheme can be useful in achieving efficient consumption of energy in the network. ...
Article
In this paper, we propose Regional Energy Efficient Cluster Heads based on Maximum Energy (REECH-ME) Routing Protocol for Wireless Sensor Networks (WSNs) . The main purpose of this protocol is to improve the network lifetime and particularly the stability period of the network. In REECH-ME, the node with the maximum energy in a region becomes Cluster Head (CH) of that region for that particular round and the number of the cluster heads in each round remains the same. Our technique outperforms LEACH which uses probabilistic approach for the selection of CHs. We also implement the Uniform Random Distribution Model to find the packet drop to make this protocol more practical. We also calculate the confidence interval of all our results which helps us to visualize the possible deviation of our graphs from the mean value.
... In future, Routing Link Matrices can also be applied on this proposed technique. Routing can be done by adapting many different approaches as done in[14],[15]and[16]. Application of Routing Link Matrices on the proposed scheme can be useful in achieving efficient consumption of energy in the network. ...
Article
Full-text available
In this paper, we propose Regional Energy Efficient Cluster Heads based on Maximum Energy (REECH-ME) Routing Protocol for Wireless Sensor Networks (WSNs). The main purpose of this protocol is to improve the network lifetime and particularly the stability period of the network. In REECH-ME, the node with the maximum energy in a region becomes Cluster Head (CH) of that region for that particular round and the number of the cluster heads in each round remains the same. Our technique outperforms LEACH [1] which uses probabilistic approach for the selection of CHs. We also implement the Uniform Random Distribution Model to find the packet drop to make this protocol more practical. We also calculate the confidence interval of all our results which helps us to visualize the possible deviation of our graphs from the mean value.
... In this paper, the scenario we have presented is through the motivation of [24] and [25]. In [26], they have done evaluation of protocols through radio propagation model Nakagami which is well suited for all these models. ...
Article
Full-text available
In this paper, a novel framework is presented through link and path duration for link availability of paths. Further, we evaluate and analyze our work by varying the number of nodes, pause time and speed in VANETs. We select three routing protocols namely Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fish-eye State Routing (FSR). Performance of these protocols is analyzed using Packet Delivery Ratio (PDR), Normalized Routing Overhead (NRO), End-to-End Delay (E2ED), Average Link Duration (ALD) and Average Path Duration (APD) against varying scalability, pause time and speed as performance metrices. We perform these simulations with NS-2 implementing Nakagami radio propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. To find link duration and path duration we also use MATLAB. From the extensive simulations, we observe that AODV and DSR outperform better among all three routing protocols.
... Hence, THE-FAME gives better results in both energy and delay profiles as compared to multi-hop routing scheme. In future work, we will implement Expected Transmission Count (ETX) link metrics as demonstrated in [21] [22] [23] [24]. ...
Article
Wireless Body Area Sensor Network (WBASN) is a technology employed mainly for patient health monitoring. New research is being done to take the technology to the next level i.e. player's fatigue monitoring in sports. Muscle fatigue is the main cause of player's performance degradation. This type of fatigue can be measured by sensing the accumulation of lactic acid in muscles. Excess of lactic acid makes muscles feel lethargic. Keeping this in mind we propose a protocol \underline{TH}reshold based \underline{E}nergy-efficient \underline{FA}tigue \underline{ME}asurement (THE-FAME) for soccer players using WBASN. In THE-FAME protocol, a composite parameter has been used that consists of a threshold parameter for lactic acid accumulation and a parameter for measuring distance covered by a particular player. When any parameters's value in this composite parameter shows an increase beyond threshold, the players is declared to be in a fatigue state. The size of battery and sensor should be very small for the sake of players' best performance. These sensor nodes, implanted inside player's body, are made energy efficient by using multiple sinks instead of a single sink. Matlab simulation results show the effectiveness of THE-FAME.
... Giving measurable QoS ensures a viable data transfer capacity. Similarly, on observing the patterns on how the Internet has transformed people lives by trading various types of data among countless customers, WSNs may sooner rather than later be similarly emerge to be critical players by providing data about the physical wonders of intrigue and eventually having the option to recognise and control them to develop increasingly precise models of the physical world [8][9][10]. This is due to the fact that WSNs are completely different from traditional systems in this regard. ...
Article
Full-text available
Quality of Service (QoS) in Wireless Sensor Networks (WSN) are contemplated as one on the major attributes in evaluating the overall efficiency of them. Some of the qualities of WSNs include incredibly asset compelled sensors, irregular arrangement of sensors in the scene of deployment, novel information driven correspondence conventions that presents remarkable challenges in the improvement of Quality of Service support in Wireless Sensor Networks. The appropriation of WSN by applications require complex tasks that extends from human services to mechanical checking that are necessary for a wide range of day-to-day and remote applications. WSN has increased a lot of consideration in the present exploration for supporting a wide assortment of utilizations including the interactive media applications. Interactive media applications that are proposed are viewed as delay-sensitive and time-critical applications and require enough vitality and correspondence assets. The proposed QoS-dependent and varied clustered routing (QoS–VCR) algorithm preserves the vitality in the system.
... Our simulation results shows that proposed routing scheme enhance the network stability time and packet delivered to sink. Path loss is also investigated in this protocol and in future work, we will implement Expected Transmission Count (ETX) link metrics as demonstrated in [22] [23] [24]. ...
Article
In this work, we propose a reliable, power efficient and high throughput routing protocol for Wireless Body Area Networks (WBANs). We use multi-hop topology to achieve minimum energy consumption and longer network lifetime. We propose a cost function to select parent node or forwarder. Proposed cost function selects a parent node which has high residual energy and minimum distance to sink. Residual energy parameter balances the energy consumption among the sensor nodes while distance parameter ensures successful packet delivery to sink. Simulation results show that our proposed protocol maximize the network stability period and nodes stay alive for longer period. Longer stability period contributes high packet delivery to sink which is major interest for continuous patient monitoring.
... These metrics trade-off between different performance parameters, the computational burden of some metrics also degrades the performance of the respective protocol [9]. Considering that the functionality of SG is dependent on the ability of different applications meeting certain performance requirements, proposing multiple metric implemented within the existing routing protocols can guarantee the QoS of the variety of traffic in SG AMI network. ...
Conference Paper
Full-text available
Routing in Neighbourhood Area Network (NAN) for Smart Grid's Advanced Metering Infrastructure (AMI) raises the need for Quality of Service (QoS)-Aware routing. This is due to the expanded list of applications that will result in the transmission of different types of traffic between NAN devices (i.e smart meters). In wireless mesh network (WMN) routing, a combination of multiple link metrics, though complex, has been identified as a possible solution for QoS routing. These complexities (i.e Np complete problem) can be resolved through the use of Analytical Hierarchy Process (AHP) algorithm and pruning techniques. With the assumption that smart meters transmit IP packets of different sizes at different interval to represent AMI traffic, a case study of the performance of three Optimised Link State Routing (OLSR) link metrics is carried out on a grid topology NAN based WMN in ns-2 network simulator. The best two performing metric were used to show the possibility of combining multiple metrics with OLSR through the AHP algorithm to fulfill the QoS routing requirements of targeted AMI application traffic in NANs.
... Koksal et al. [5] presented a modified ETX metric, which combined the average and the variability of the error probability to optimize the decision results. Javaid et al. [6] presented a comprehensive study on the design requirements for routing link metrics and an inverse ETX (invETX) link metric for wireless multi-hop networks. In Boushaba et al. [7], considered the packet loss, intraflow and interflow interference, and load at gateways to select the best paths to reach the selected gateways and present a novel source-based routing (SBR) metric method. ...
Article
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The routing protocol is one of the most important aspects of the wireless sensor network, determining network connectivity, delay, energy balancing, reliability and other factors. Furthermore, a minimum hop-count does not mean minimum delay and energy consumption. To overcome the routing protocol’s shortcomings, we proposed an energy-efficient expected transmission count routing decision strategy (E³TX) for wireless sensor networks. E³TX makes use of two physical parameters, received signal strength indicator (RSSI) and battery voltage, to obtain the final decision via our proposed decision strategy. In our strategy, the received signal strength indicator is used to predict the future packet reception rate (PRR), and the battery voltage is used to estimate the residual energy of network nodes to balance their load. In order to estimate the packet reception rate via the received signal strength indicator with greater accuracy, we performed multiple experiments to build the relationship model between RSSI and PRR. In this article, we use NS-2.35 to evaluate and compare the performance of E³TX with AODV, AOMDV and BIETX. Our simulation results show that our proposed E³TX performs well when compared to the previous studies, not only in terms of energy consumption, but also in reliable data transmission and end-to-end delay.
... On the other hand in MOD DSR due to reduction in the size of route cache improves overall performance in high speeds. In future, we are interested to apply the same analysis on quality link metrics proposed in101112 and at MAC layer as [13, 14]. a. MANET's NRL vs Scalibility b. ...
Article
This paper presents a framework for node distribution with respect to density, network connectivity and communication time. Using NS2, we evaluate and compare performance of three routing protocols; Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and Fisheye State Routing (FSR) both in MANETs (IEEE 802.11) and VANETs (IEEE 802.11p). We further enhanced these protocols by changing their routing information exchange intervals; MOD AODV, MOD DSR and MOD FSR. A comprehensive simulation work is performed for the comparison of these routing protocols for varying motilities and scalabilities of nodes. As a result, we can say that AODV outperforms DSR and FSR both in MANETs and VANETs.
... where En is the initial energy of any of the four energy levels, r is the node at a specific energy level, ET X p is the expected transmission count [42] of a path P , InvET X p is the inverse expected transmission count [43], and MLp is the minimum loss [44]. The P metric values for the hybrid, high, medium, and low energy level nodes are given by Eqs. 19, 20, 21, and 22, respectively. ...
Article
Wireless sensor networks (WSNs) have gained much attention in today’s research domain for supporting a wide variety of applications including the multimedia applications. Multimedia applications that are regarded as the quality-ofservice (QoS)-aware, delay sensitive, and bandwidth hungry applications, require enough energy and communication resources. WSNs being the energy-scarce network have now been designed in such a way that they can support these delay-sensitive and time-critical applications. In this paper, we propose an energyefficient routing protocol for heterogeneous WSNs to support the delay sensitive, bandwidth hungry, time-critical, and QoSaware applications. The proposed QoS-aware and heterogeneously clustered routing (QHCR) protocol not only conserves the energy in the network, but also provides the dedicated paths for the real-time and delay sensitive applications. The inclusion of different energy-levels for the heterogeneous WSNs also provide the stability in the networks while minimizing the delay for the delay-sensitive applications. Extensive simulations have been performed to validate the effectiveness of our proposed scheme. Our proposed routing scheme outperforms other state-of-the-art schemes in terms of the delay performances.
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [17] and [18]. ...
Article
Full-text available
Mobile Ad-hoc NETworks (MANETs) comprise on wireless mobile nodes that are communicating with each other without any infrastructure. Vehicular Ad-hoc NETwork (VANET) is a special type of MANETs in which vehicles with high mobility need to communicate with each other. In this paper, we present a novel framework for link availability of paths for static as well as dynamic networks. Moreover, we evaluate our frame work for routing protocols performance with different number of nodes in MANETs and in VANETs. We select three routing protocols namely Ad-hoc On-demand Distance Vector (AODV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). Furthermore, we have also modified default parameters of selected protocols to check their efficiencies. Performance of these protocols is analyzed using three performance metrics; Packet Delivery Ratio (PDR), Normalized Routing Overhead (NRO) and End-to-End Delay (E2ED) against varying scalabilities of nodes. We perform these simulations with NS-2 using TwoRayGround propagation model. The SUMO simulator is used to generate a random mobility pattern for VANETs. From the extensive simulations, we observe that AODV outperforms among all three protocols.
... Performance of the selected protocols are then analysed and compared using the proposed model. In [15], a new routing link metric is designed, and in [16], a new quality link metric called inverse expected transmission count (InvETX) is proposed. The main contribution of [16] is improvement of the optimized link state routing (OLSR) protocol in terms of optimized routing load and routing latency. ...
Article
... Because, a link metric provides all available end-to-end paths and the best path information to the respective protocol. So, in future, we are interested to develop a new link metric, like [41] and [42]. ...
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Mobile Ad-hoc NETworks (MANETs) are comprised of wireless mobile nodes that are communicating with each other without any infrastructure. Vehicular Ad-hoc NETwork (VANET) is a special type of MANETs in which vehicles with high mobility need to communicate with each other. In our project, a framework for link availability for static as well as dynamic network and also experimental parameters in which Packet Delivery Ratio (PDR), effect of link duration over End-to-End Delay (E2ED) and Normalized Routing Overhead (NRO) in terms of control packets is analyzed and modeled for MANETs and VANETs. Moreover, this project also contributes the performance comparison of three reactive routing potocols; Ad-hoc On-Demand Distance Vector (AODV), DYnamic Source Routing (DSR), DYnamic MANET On-Demand (DYMO) and three proactive protocols; Destination Sequenced Distance Vector (DSDV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). A novel contribution of this work is enhancement of efficiency of these protocols except DSDV. Three performance parameters; PDR, E2ED and NRO with varying scalabilities are measured to analyze performance of the selected protocols both with default and enhanced version. From extensive simulations, it is observed that DSR outperforms both in MANETs and in VANETs at the cost of delay. Moreover, DSR performs better in VANETs as compared to MANETs. The NS-2 is used for simulation with TwoRayGround propagation model. The Simulation of Urban MObility (SUMO) and Vehicular Ad-hoc Networks Mobility Simulator (VanetMobiSim) are used to generate the mobility pattern for VANETs.
... Our simulation results show that DSR performs better at the cost of delay both in MANETs and in VANETs. In future, we are interested to develop a new link metric, like [16] and [17]. ...
Article
Full-text available
In this paper, a framework for experimental parameters in which Packet Delivery Ratio (PDR), effect of link duration over End-to-End Delay (E2ED) and Normalized Routing Overhead (NRO) in terms of control packets is analyzed and modeled for Mobile Ad-Hoc NETworks (MANETs) and Vehicular Ad-Hoc NETworks (VANETs) with the assumption that nodes (vehicles) are sparsely moving in two different road. Moreover, this paper contributes the performance comparison of one Proactive Routing Protocol; Destination Sequenced Distance vector (DSDV) and two reactive protocols; DYnamic Source Routing (DSR) and DYnamic MANET On-Demand (DYMO). A novel contribution of this work is enhancements in default versions of selected routing protocols. Three performance parameters; PDR, E2ED and NRO with varying scalabilities are measured to analyze the performance of selected routing protocols with their original and enhanced versions. From extensive simulations, it is observed that DSR outperforms among all three protocols at the cost of delay. NS-2 simulator is used for simulation with TwoRayGround propagation model to evaluate analytical results.
... The outcome displays the improved performance as compared to the existing protocol. In future, one can modify this problem statement to implement various link metrics that like ETX link metrics [16,17]. ...
... For delay sensitive applications, DYMO in reactive protocols and OLSR in proactive protocols are the plausible choices. During all this evaluation, we come to realize that the most important component of a routing protocol is routing link metric, so, future we are interested to propose and implement a new ETX-based routing link metric with AODV and OLSR, as discussed in [14], [15], [16]. ...
Article
In this paper, we evaluate, analyze, and compare the impact of mobility on the behavior of three reactive protocols (AODV, DSR, DYMO) and three proactive protocols (DSDV, FSR, OLSR) in multi-hop wireless networks. We take into account throughput, end-to-end delay, and normalized routing load as performance parameters. Based upon the extensive simulation results in NS-2, we rank all of six protocols according to the performance parameters. Besides providing the interesting facts regarding the response of each protocol on varying mobilities and speeds, we also study the trade-offs, the routing protocols have to make. Such as, to achieve throughput, a protocol has to pay some cost in the form of increased end-to-end delay or routing overhead.
... The authors in [16] identify a diversity of possible requirements to be addressed in a MANET, such as: minimizing hop-count, minimizing delay, maximizing data delivery, minimizing energy consumption, minimizing computational overhead, maximizing route stability, balancing traffic load, among others. The work also relates these requirements to the main link evaluation metrics and points out the associated performance trade-offs. ...
Conference Paper
Full-text available
Ad-hoc Wireless Networks provide a major base for ubiquitous computing development. In such networks, the communication occurs by multiple hops in a shared medium. In order to meet the different requirements of the applications, routing solutions aware of Quality of Service (QoS) have been developing. However, single-criterion strategies are unable to cope with conflicting objectives that commonly appear in these networks. This work proposes a multicriteria approach that considers End-to-End Delay (E2ED) and Packet Delivery Probability (PDP) as vital criteria in the route discovery process. For this purpose, Optimized Link State Routing Protocol (OLSR) with a modified Dijkstra algorithm is applied, wherein the bi-objective problem is transformed into a mono-objective problem through the epsilon-constraint technique. Extensive simulations have demonstrated that the multicriteria method can provide efficient routing in mobile environments, and it has outperformed the best results of single-criterion methods in terms of Packet Loss Ratio (PLR) by nearly 5-35 %. The results also have shown the potential of the model in finding a proper trade-off in relation to the number of hops and End-to-End Delay.
... In this work, we study the three performance metrics: Network lifetime , Residual energy and throughput. In future, we will study ETX link metrics and we will implement this metric in our scheme as implemented and demonstrated in [21] [22] [23]. ...
Article
Full-text available
In this research work, we advise gateway based energy-efficient routing protocol (M-GEAR) for Wireless Sensor Networks (WSNs). We divide the sensor nodes into four logical regions on the basis of their location in the sensing field. We install Base Station (BS) out of the sensing area and a gateway node at the centre of the sensing area. If the distance of a sensor node from BS or gateway is less than predefined distance threshold, the node uses direct communication. We divide the rest of nodes into two equal regions whose distance is beyond the threshold distance. We select cluster heads (CHs)in each region which are independent of the other region. These CHs are selected on the basis of a probability. We compare performance of our protocol with LEACH (Low Energy Adaptive Clustering Hierarchy). Performance analysis and compared statistic results show that our proposed protocol perform well in terms of energy consumption and network lifetime.
Article
In this paper, we present a detailed framework consisting of modeling of routing overhead generated by three widely used proactive routing protocols; Destination-Sequenced Distance Vector (DSDV), Fish-eye State Routing (FSR) and Optimized Link State Routing (OLSR). The questions like, how these protocols differ from each other on the basis of implementing different routing strategies, how neighbor estimation errors affect broadcast of route requests, how reduction of broadcast overhead achieves bandwidth, how to cope with the problem of mobility and density, etc, are attempted to respond. In all of the above mentioned situations, routing overhead and delay generated by the chosen protocols can exactly be calculated from our modeled equations. Finally, we analyze the performance of selected routing protocols using our proposed framework in NS-2 by considering different performance parameters; Route REQuest (RREQ) packet generation, End-to-End Delay (E2ED) and Normalized Routing Load (NRL) with respect to varying rates of mobility and density of nodes in the underlying wireless network.
Conference Paper
Due to small size of sensor nodes deployed in Wireless Sensor Networks (WSNs), energy utilization is a key issue. Poor channel conditions lead to retransmissions and hence, result in energy wastage. Error control strategies are usually utilized to accommodate channel impairments like noise and fading in order to optimize energy consumption for network lifetime enhancement. Meanwhile, cooperative communication also emerges to be an appropriate candidate to combat the effects of channel fading. Energy efficiency of cooperative scheme when applied with Automatic Repeat Request (ARQ), Hybrid-ARQ (HARQ) and Forward Error Correction (FEC) is investigated in this work. Moreover, the expressions for energy efficiency of Direct Transmission, Single Relay Cooperation and Multi Relay Cooperation are also derived. In all, our work is focused towards energy optimal communication in WSNs. Our results show that error control strategies along with the cooperative scheme significantly enhances system performance in the form of energy optimization.
Article
Due to small size of sensor nodes deployed in Wireless Sensor Networks (WSNs), energy utilization is a key issue. Poor channel conditions lead to retransmissions and hence, result in energy wastage. Error control strategies are usually utilized to accommodate channel impairments like noise and fading in order to optimize energy consumption for network lifetime enhancement. Meanwhile, cooperative communication also emerges to be an appropriate candidate to combat the effects of channel fading. Energy efficiency of cooperative scheme when applied with Automatic Repeat Request (ARQ), Hybrid-ARQ (HARQ) and Forward Error Correction (FEC) is investigated in this work. Moreover, the expressions for energy efficiency of Direct Transmission, Single Relay Cooperation and Multi Relay Cooperation are also derived. In all, our work is focused towards energy optimal communication in WSNs. Our results show that error control strategies with cooperative schemes can significantly enhance system performance in form of energy optimization.
Article
Full-text available
Wireless ad-hoc networks are characterized by a collection of wireless mobile nodes that dynamically form a temporary network without the use of any pre-defined network infrastructure or centralized administration. They have attributes such multi-hop wireless connectivity, continuously changing topology and easy deployment. The increasing demands that are made by users pose a challenge in the improvement of the quality of wireless ad-hoc networks. The performance of wireless ad-hoc networks depend on the efficiency of routing protocols, especially the routing metric operating within it. In this paper, the performance of the recently proposed routing metric Interference Bandwidth Adjusted Expected transmission count (IBETX) metric is compared with two prominent existing metrics, the Expected transmission count (ETX) and the Inverse Expected Transmission count (InvETX) over the Destination Sequenced Distance Vector (DSDV) routing protocol. The performance differentials are analysed using varying packet rates and node densities. From the simulations results, IBETX metric outperforms the ETX and InvETX metric because it implements the bandwidth sharing mechanism and makes use of the information available at the MAC layer. It can also be noted that it is very sensitive to data traffic rate. It performs well in low and medium node densities.
Article
Book
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The Thirteenth International Conference on Wireless and Mobile Communications (ICWMC 2017), held between July 23 - 27, 2017 - Nice, France, followed on the previous events on advanced wireless technologies, wireless networking, and wireless applications. ICWMC 2017 addressed wireless related topics concerning integration of latest technological advances to realize mobile and ubiquitous service environments for advanced applications and services in wireless networks. Mobility and wireless, special services and lessons learnt from particular deployment complemented the traditional wireless topics. We take here the opportunity to warmly thank all the members of the ICWMC 2017 Technical Program Committee, as well as the numerous reviewers. The creation of such a high quality conference program would not have been possible without their involvement. We also kindly thank all the authors who dedicated much of their time and efforts to contribute to ICWMC 2017. We truly believe that, thanks to all these efforts, the final conference program consisted of top quality contributions. Also, this event could not have been a reality without the support of many individuals, organizations, and sponsors. We are grateful to the members of the ICWMC 2017 organizing committee for their help in handling the logistics and for their work to make this professional meeting a success. We hope that ICWMC 2017 was a successful international forum for the exchange of ideas and results between academia and industry and for the promotion of progress in the area of wireless and mobile communications. We are convinced that the participants found the event useful and communications very open. We also hope that Nice provided a pleasant environment during the conference and everyone saved some time for exploring this beautiful city.
Article
In this paper, we have modeled the routing over- head generated by three reactive routing protocols; Ad-hoc On-demand Distance Vector (AODV), Dynamic Source Routing (DSR) and DYnamic MANET On-deman (DYMO). Routing performed by reactive protocols consists of two phases; route discovery and route maintenance. Total cost paid by a protocol for efficient routing is sum of the cost paid in the form of energy consumed and time spent. These protocols majorly focus on the optimization performed by expanding ring search algorithm to control the flooding generated by the mechanism of blind flooding. So, we have modeled the energy consumed and time spent per packet both for route discovery and route maintenance. The proposed framework is evaluated in NS-2 to compare performance of the chosen routing protocols.
Article
Full-text available
This document describes the Optimized Link State Routing (OLSR) protocol for mobile ad hoc networks. The protocol is an optimization of the classical link state algorithm tailored to the requirements of a mobile wireless LAN. The key concept used in the protocol is that of multipoint relays (MPRs). MPRs are selected nodes which forward broadcast messages during the flooding process. This technique substantially reduces the message overhead as compared to a classical flooding mechanism, where every node retransmits each message when it receives the first copy of the message. In OLSR, link state information is generated only by nodes elected as MPRs. Thus, a second optimization is achieved by minimizing the number of control messages flooded in the network. As a third optimization, an MPR node may chose to report only links between itself and its MPR selectors. Hence, as contrary to the classic link state algorithm, partial link state information is distributed in the network. This information is then used for route calculation. OLSR provides optimal routes (in terms of number of hops). The protocol is particularly suitable for large and dense networks as the technique of MPRs works well in this context.
Article
Full-text available
This document describes the Optimized Link State Routing (OLSR) protocol for mobile ad hoc networks. The protocol is an optimization of the classical link state algorithm tailored to the requirements of a mobile wireless LAN. The key concept used in the protocol is that of multipoint relays (MPRs). MPRs are selected nodes which forward broadcast messages during the flooding process. This technique substantially reduces the message overhead as compared to a classical flooding mechanism, where every node retransmits each message when it receives the first copy of the message. In OLSR, link state information is generated only by nodes elected as MPRs. Thus, a second optimization is achieved by minimizing the number of control messages flooded in the network. As a third optimization, an MPR node may chose to report only links between itself and its MPR selectors. Hence, as contrary to the classic link state algorithm, partial link state information is distributed in the network. This information is then used for route calculation. OLSR provides optimal routes (in terms of number of hops). The protocol is particularly suitable for large and dense networks as the technique of MPRs works well in this context.
Article
Full-text available
This work is based on measurements of the ReMesh wireless mesh network deployed over the city of Niterói, Brazil. It uses a modified version of the OLSR ad hoc routing protocol. OLSR has the goal of maximizing throughput by minimizing the number of transmissions over the wireless shared medium selecting routes based on the sum of the expected transmission count (ETX) of each link from a source node towards a destination node. Because of routing instabilities and the high packet loss rates (PLR) observed with the original OLSR algorithm, this work uses an algorithm for selecting multi-hop paths based on minimum loss probability along the entire path. Test results show that the mesh network performance has been improved, leading to more stable routes, lower packet loss rates, shorter delays and in many cases a small increase in network throughput.
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Full-text available
Designing routing metrics is critical for perfor-mance in wireless mesh networks. The unique characteristics of mesh networks, such as static nodes and the shared nature of the wireless medium, invalidate existing solutions from both wired and wireless networks and impose unique requirements on designing routing metrics for mesh networks. In this paper, we focus on identifying these requirements. We first analyze the possible types of routing protocols that can be used and show that proactive hop-by-hop routing protocols are the most appropriate for mesh networks. Then, we examine the requirements for designing routing metrics according to the characteristics of mesh networks and the type of routing protocols used. Finally, we study several existing routing metrics, including hop count, ETX, ETT, WCETT and MIC in terms of their ability to satisfy these requirements. Our simulation results of the performance of these metrics confirm our analysis of these metrics.
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Full-text available
Wireless mesh networks (WMNs) can be used in many different ap-plications. However, they lack standards and, as a consequence, a number of issues must still be addressed to ensure the proper functioning of these networks. Amongst these issues, routing is this paper's main concern. Thus, we propose the use of multiple metrics with the proactive Optimized Link State Routing (OLSR) protocol, in order to provide quality of service routing. Even though it has already been proved that routing with multiple metrics is an NP-complete problem, we show how the techniques of Analytic Hierarchy Process (AHP) and Pruning may be combined to perform multiple-metric routing, offering the best available routes based on the considered metrics. A study on the performance of the metrics considered for the proposal is also carried out in the NS simulator.
Conference Paper
Full-text available
Multi-hop wireless mesh networks are increasingly being deployed for last-mile Internet access. Typically, network algorithms such as routing, channel assignment and topology control for such net- works rely heavily on metrics that intend to capture link "quality" across the network. However, the underlying dynamics of the pro- posed link metrics themselves have not yet been studied in detail. In this paper, we study the dynamics of the most popular link metrics in real network deployments. Using two wireless mesh testbeds, we measure a number of link metrics across different hardware plat- forms and network environments. The collected measurements al- low us to study the stability and sensitivity of the different metrics to various conditions. Our study provides several insights and fu- ture research directions on how network algorithms need to adapt to link dynamics as well as how popular and widely used link metrics can be improved.
Conference Paper
Full-text available
Routing protocols for wireless ad hoc networks have traditionally focused on finding paths with minimum hop count. However, such paths can include slow or lossy links, leading to poor throughput. A routing algorithm can select better paths by explicitly taking the quality of the wireless links into account. In this paper, we conduct a detailed, empirical evaluation of the performance of three link-quality metrics---ETX, per-hop RTT, and per-hop packet pair---and compare them against minimum hop count. We study these metrics using a DSR-based routing protocol running in a wireless testbed. We find that the ETX metric has the best performance when all nodes are stationary. We also find that the per-hop RTT and per-hop packet-pair metrics perform poorly due to self-interference. Interestingly, the hop-count metric outperforms all of the link-quality metrics in a scenario where the sender is mobile.
Conference Paper
Full-text available
One of the main problems faced by ad hoc networks is providing specific quality of service guarantees for multimedia applications, mainly due to factors such as radio signal fading and node mobility. Since mesh networks are a special type of ad hoc network, they inherit these networks' problems. This paper's main goal is to present OLSR-MD, an extension to OLSR (optimized link state routing), to provide quality of service based on link delay measurements. An evaluation of OLSR-MD in a mesh network to be deployed at the Federal University of Para, by means of ns2 (version 2.30) simulations, showed that this protocol performed better than other OLSR based alternatives studied in the simulations.
Conference Paper
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We present a new metric for routing in multi-radio, multi-hop wireless networks. We focus on wireless networks with stationary nodes, such as community wireless networks.The goal of the metric is to choose a high-throughput path between a source and a destination. Our metric assigns weights to individual links based on the Expected Transmission Time (ETT) of a packet over the link. The ETT is a function of the loss rate and the bandwidth of the link. The individual link weights are combined into a path metric called Weighted Cumulative ETT (WCETT) that explicitly accounts for the interference among links that use the same channel. The WCETT metric is incorporated into a routing protocol that we call Multi-Radio Link-Quality Source Routing.We studied the performance of our metric by implementing it in a wireless testbed consisting of 23 nodes, each equipped with two 802.11 wireless cards. We find that in a multi-radio environment, our metric significantly outperforms previously-proposed routing metrics by making judicious use of the second radio.
Conference Paper
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Many wireless sensor network applications must resolve the inherent conflict between energy efficient communication and the need to achieve desired quality of service such as end-to-end communication delay. To address this challenge, we propose the real-time power-aware routing (RPAR) protocol, which achieves application-specified communication delays at low energy cost by dynamically adapting transmission power and routing decisions. RPAR features a power-aware forwarding policy and an efficient neighborhood manager that are optimized for resource-constrained wireless sensors. Moreover, RPAR addresses important practical issues in wireless sensor networks, including lossy links, scalability, and severe memory and bandwidth constraints. Simulations based on a realistic radio model of MICA2 motes show that RPAR significantly reduces the number of deadlines missed and energy consumption compared to existing real-time and energy-efficient routing protocols
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Load balancing is critical for improving performance in wireless mesh networks. The unique characteristics of mesh networks, such as static nodes and the shared nature of the wireless medium, invalidate existing solutions from both wired and wireless networks and introduce new challenges for providing load balancing. In this paper, we focus on addressing these challenges. We first formulate the objective of load balancing in mesh networks and provide a theoretical solution to optimally achieve this objective. Then, we investigate some existing practical approaches to load balancing in mesh networks and show that none of them sufficiently address these challenges and some may even cause non-optimal paths and forwarding loops. In response, we propose a new path weight function, called MIC, and a novel routing scheme, called LIBRA, to provide interference-aware and multi-channel/multi-radio aware load balancing for mesh networks, while still ensuring routing optimality and loop-freedom. We use extensive simulations to evaluate our scheme by comparing it with both the theoretical optimal solution and existing practical solutions. The results show close-to-optimum performance and indicate that LIBRA is a good candidate for load balancing and routing in wireless mesh networks.
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Besides energy constraint, wireless sensor networks should also be able to provide bounded communication delay when they are used to support real-time applications. In this paper, a new routing metric is proposed. It takes into account both energy and delay constraints. It can be used in AODV. By mathematical analysis and simulations, we have shown the efficiency of this new routing metric.
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The lifetime of a mobile ad hoc network (MANET) depends on the durability of the battery resource of the mobile hosts. Earlier research has proposed several routing protocols specifically on MANET, but most studies have not focused on the limitations of battery resource. We propose a new energy-aware routing protocol, which can increase the durability of the energy resource and, therefore, the lifetime of the mobile hosts and the MANET. The proposed protocol can conserve energy by shortening the idle period of the mobile hosts without increasing the probability of packet loss or reducing routing fidelity. Simulation results indicate that this new energy-conserving protocol can extend the lifetime of a MANET
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A mobile, multi-hop wireless computer network, also termed an ad-hoc network, can be envisioned as a collection of routers, equipped with wireless transmitter/receiver, which are free to move about arbitrarily. The basic assumption in an ad-hoc network is that some nodes willing to communicate may be outside the wireless transmission range of each other but may be able to communicate if other nodes in the network are willing to forward packets from them. However, the successful operation of an ad-hoc network will be hampered if an intermediate node, participating in a communication between two nodes, moves out of range suddenly or switches itself off in between message transfer. The objective of this paper is to introduce a parameter, affinity that characterizes the strength of relationship between two nodes and to propose a distributed routing scheme between two nodes in order to find a set of paths between them which are more stable and less congested in a specific context. Thus, the communication in an ad-hoc wireless network can be effective by making the nodes in the system communication-aware in the sense that each node should know its affinity with its neighbors and should be aware of the impact of its movement on the communication structure of the underlying network
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An ad-hoc network is the cooperative engagement of a collection of Mobile Hosts without the required intervention of any centralized Access Point. In this paper we present an innovative design for the operation of such ad-hoc networks. The basic idea of the design is to operate each Mobile Host as a specialized router, which periodically advertises its view of the interconnection topology with other Mobile Hosts within the network. This amounts to a new sort of routing protocol. We have investigated modifications to the basic BellmanFord routing mechanisms, as specified by the Routing Information Protocol, making it suitable for a dynamic and self-starting network mechanism as is required by users wishing to utilize ad-hoc networks. Our modifications address some of the previous objections to the use of Bellman-Ford, related to the poor looping properties of such algorithms in the face of broken links and the resulting time dependent nature of the interconnection topology describing th...
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Next generation fixed wireless broadband networks are being increasingly deployed as mesh networks in order to provide and extend access to the internet. These networks are characterized by the use of multiple orthogonal channels and nodes with the ability to simultaneously communicate with many neighbors using multi- ple radios (interfaces) over orthogonal channels. Networks based on the IEEE 802.11a/b/g and 802.16 standards are examples of these systems. However, due to the limited number of available or- thogonal channels, interference is still a factor in such networks. Recent results have attempted to characterize the achievable ca- pacity of such networks, both in the deterministic(1) and asymp- totic(2) sense. In this paper, we build on these previous works and provide an experimental verification of asymptotic capacity result in (2) by using the deterministic model first proposed in (1). Our simulation results are based on a novel joint channel assignment and scheduling algorithm which is shown to achieve near-optimal capacity limits in random network topologies. The results in this paper are the first to provide an experimental verification of the- oretical results in (2) and give an insight into the behavior of the capacity region of a multi-hop multi-radio mesh network.
Article
Wireless technologies, such as IEEE 802.11a, that are used in ad hoc networks provide for multiple non-overlapping channels. Most ad hoc network protocols that are currently available are designed to use a single channel. However, the available network capacity can be increased by using multiple channels. This paper presents new protocols specifically designed to exploit multiple channels. Our protocols simplify the use of multiple channels by using multiple interfaces, although the number of interfaces per host is typically smaller than the number of channels. We propose a link layer protocol to manage multiple channels, and it can be implemented over existing IEEE 802.11 hardware. We also propose a new routing metric for multi-channel multi-interface networks, and the metric is incorporated into an on-demand routing protocol that operates over the link layer protocol. Simulation results demonstrate the effectiveness of the proposed approach in significantly increasing network capacity, by utilizing all the available channels, even when the number of interfaces per host is smaller than the number of channels.
Conference Paper
Being most popular and IETF standard metric, minimum hop count is appropriately used by ad hoc networks, as new paths must rapidly be found in the situations where quality paths could not be found in due time due to high node mobility. There always has been a tradeoff between throughput and energy consumption, but stationary topology of WMNs and high node density of WSN's benefit the algorithms to consider quality-aware routing to choose the best routes. In this paper, we analytically review ongoing research on wireless routing metrics which are based on ETX (expected transmission count) as it performs better than minimum hop count under link availability. Performances over ETX, target platforms and design requirements of these ETX based metrics are high-lighted. Consequences of the criteria being adopted (in addition to expected link layer transmissions & retransmissions) in the form of incremental: (1) performance overheads and computational complexity causing inefficient use of network resources and instability of the routing algorithm, (2) throughput gains achieved with better utilization of wireless medium resources have been elaborated.
Conference Paper
The use of Fish eye scoping has been introduced to reduce the overhead of the OLSR routing protocol. This simple method is based on reducing the scope (TTL) of some topology updates, thus giving routers a precise view of their close neighborhood and a more and more approximate view of farther nodes. Fish Eye OLSR (OFLSR) has been showed to have excellent scaling properties and low network overhead. However, if deployed in relatively sparse networks, this scoping limitation of topology updates can result in long living routing loops, thus limiting the potential applications of such mechanisms in some practical wireless mesh networks. In this paper, we address the transient mini-loop problem due to fisheye scoping. We first analyze the occurrence of mini-loops. We discuss potential solutions and propose a pragmatic and distributed off-line heuristic, which allows each router to compute ldquosaferdquo scope for topology updates. With our method, every mesh router calculates in advance the minimum TTL value that avoids mini-loops at the ldquoscoperdquo boundary - optimal scope that will be set for generating topology update message whenever a neighbor link lost is detected. Simulations show that the proposed algorithm drastically improves safety of Fish Eye OLSR while still retaining its scaling and performance properties.
Conference Paper
Finding a path with enough throughput in multihop wireless ad hoc networks is a critical task of QoS Routing. Previous studies on routing algorithms focused on networks with a single channel rate. The capability of supporting multiple channel rates, which is common in wireless systems, has not been carefully studied in routing algorithms. In this paper, we first carry out a comprehensive study on the impacts of multiple rates, interference and packet loss rate on the maximum end-to-end throughput or path capacity. A linear programming problem is formulated to determine the path capacity of any given path. This problem is also extended to a joint routing and link scheduling optimization problem to find a path with the largest path capacity. We show that interference clique transmission time is inversely proportional to the upper bound of the path capacity, and hence we propose to use it as a new routing metric. Moreover, we evaluate the capability of various routing metrics such as hop count, expected transmission times, end-to-end transmission delay or medium time, link rate, bandwidth distance product, and interference clique transmission time to discover a high throughput path. The results show that different routing metrics lead to paths with significantly different path capacity, and the interference clique transmission time tends to discover paths with higher throughput than other metrics.
Conference Paper
Next generation fixed wireless broadband networks are being increasingly deployed as mesh networks in order to provide and extend access to the internet. These networks are characterized by the use of multiple orthogonal channels and nodes with the ability to simultaneously communicate with many neighbors using multiple radios (interfaces) over orthogonal channels. Networks based on the IEEE 802.11a/b/g and 802.16 standards are examples of these systems. However, due to the limited number of available orthogonal channels, interference is still a factor in such networks. In this paper, we propose a network model that captures the key practical aspects of such systems and characterize the constraints binding their behavior. We provide necessary conditions to verify the feasibility of rate vectors in these networks, and use them to derive upper bounds on the capacity in terms of achievable throughput, using a fast primal-dual algorithm. We then develop two link channel assignment schemes, one static and the other dynamic, in order to derive lower bounds on the achievable throughput. We demonstrate through simulations that the dynamic link channel assignment scheme performs close to optimal on the average, while the static link channel assignment algorithm also performs very well. The methods proposed in this paper can be a valuable tool for network designers in planning network deployment and for optimizing different performance objectives.
Article
In this paper, we propose a new quality link metric, interference and bandwidth adjusted ETX (IBETX) for wireless multi-hop networks. As MAC layer affects the link performance and consequently the route quality, the metric therefore, tackles the issue by achieving twofold MAC-awareness. Firstly, interference is calculated using cross-layered approach by sending probes to MAC layer. Secondly, the nominal bit rate information is provided to all nodes in the same contention domain by considering the bandwidth sharing mechanism of 802.11. Like ETX, our metric also calculates link delivery ratios that directly affect throughput and selects those routes that bypass dense regions in the network. Simulation results by NS-2 show that IBETX gives 19% higher throughput than ETX and 10% higher than Expected Throughput (ETP). Our metric also succeeds to reduce average end-to-end delay up to 16% less than Expected Link Performance (ELP) and 24% less than ETX.
Article
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004. Vita. Includes bibliographical references (leaves 111-118). This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections. The expected transmission count (ETX) metric is a new route metric for finding high-throughput paths in multi-hop wireless networks. The ETX of a path is the expected total number of packet transmissions (including retransmissions) required to successfully deliver a packet along that path. For practical networks, paths with the minimum ETX have the highest throughput. The ETX metric incorporates the effects of link loss ratios, asymmetry in the loss ratios between the two directions of each link, and interference among the successive links of a path. Busy networks that use the ETX route metric will also maximize total network throughput. We describe the design and implementation of ETX as a metric for the DSDV and DSR routing protocols, as well as modifications to DSDV and DSR which make them work well with ETX. Measurements taken from a 29-node 802.11b test-bed show that using ETX improves performance significantly over the widely-used minimum hop-count metric. For long paths the throughput increase is often a factor of two or more, suggesting that ETX will become more useful as networks grow larger and paths become longer. We also present a simple model for predicting how packet delivery ratio varies with packet size, and detailed measurements which characterize the test-bed's distribution of link delivery ratios and route throughputs. by Douglas S.J. Couto. Ph.D.
Conference Paper
There has been increased interest recently from military, civil, and commercial sectors in networks capable of self-organization. Routing and channel assignment for multi-hop communications in these networks are complex problems, given the interactions between the various transmissions, all of which must share some fixed bandwidth, and by the lack of a central controller. By enforcing a “reuse distance” similar to the frequency reuse factor in AMPS cellular service, we can route and assign channels to (place) arriving calls in a peer-to-peer network so as to significantly reduce power requirements and interference


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# Inventory theory

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Material theory (or more formally the mathematical theory of inventory and production) is the sub-specialty within operations research and operations management that is concerned with the design of production/inventory systems to minimize costs: it studies the decisions faced by firms and the military in connection with manufacturing, warehousing, supply chains, spare part allocation and so on and provides the mathematical foundation for logistics. The inventory control problem is the problem faced by a firm that must decide how much to order in each time period to meet demand for its products. The problem can be modeled using mathematical techniques of optimal control, dynamic programming and network optimization. The study of such models is part of inventory theory.

Operations research, or operational research (OR) in British usage, is a discipline that deals with the application of advanced analytical methods to help make better decisions. Further, the term operational analysis is used in the British military as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness and Investment Appraisals, which support British defense capability acquisition decision-making.

Operations management is an area of management concerned with designing and controlling the process of production and redesigning business operations in the production of goods or services. It involves the responsibility of ensuring that business operations are efficient in terms of using as few resources as needed and effective in terms of meeting customer requirements. Operations management is primarily concerned with planning, organizing and supervising in the contexts of production, manufacturing or the provision of services.

Inventory or stock is the goods and materials that a business holds for the ultimate goal of resale.

## Issues

One issue is infrequent large orders vs. frequent small orders. Large orders will increase the amount of inventory on hand, which is costly, but may benefit from volume discounts. Frequent orders are costly to process, and the resulting small inventory levels may increase the probability of stockouts, leading to loss of customers. In principle all these factors can be calculated mathematically and the optimum found.

A stockout, or out-of-stock (OOS) event is an event that causes inventory to be exhausted. While out-of-stocks can occur along the entire supply chain, the most visible kind are retail out-of-stocks in the fast-moving consumer goods industry. Stockouts are the opposite of overstocks, where too much inventory is retained.

In sales, commerce and economics, a customer is the recipient of a good, service, product or an idea - obtained from a seller, vendor, or supplier via a financial transaction or exchange for money or some other valuable consideration.

A second issue is related to changes in demand (predictable or random) for the product. For example, having the needed merchandise on hand in order to make sales during the appropriate buying season(s). A classic example is a toy store before Christmas: if the items are not on the shelves, they cannot be sold. And the wholesale market is not perfect' there can be considerable delays, particularly with the most popular toys. So, the entrepreneur or business manager will buy speculatively. Another example is a furniture store. If there is a six-week, or more, delay for customers to receive merchandise, some sales will be lost. A further example is a restaurant, where a considerable percentage of the sales are the value-added aspects of food preparation and presentation, and so it is rational to buy and store somewhat more to reduce the chances of running out of key ingredients. The situation often comes down to two key questions: confidence in the merchandise selling, and the benefits accruing if it does?

A toy store or toy shop, is a retail business specializing in selling toys.

Christmas is an annual festival, commemorating the birth of Jesus Christ, observed primarily on December 25 as a religious and cultural celebration among billions of people around the world. A feast central to the Christian liturgical year, it is preceded by the season of Advent or the Nativity Fast and initiates the season of Christmastide, which historically in the West lasts twelve days and culminates on Twelfth Night; in some traditions, Christmastide includes an octave. Christmas Day is a public holiday in many of the world's nations, is celebrated religiously by a majority of Christians, as well as culturally by many non-Christians, and forms an integral part of the holiday season centered around it.

Furniture refers to movable objects intended to support various human activities such as seating, eating (tables), and sleeping. Furniture is also used to hold objects at a convenient height for work, or to store things. Furniture can be a product of design and is considered a form of decorative art. In addition to furniture's functional role, it can serve a symbolic or religious purpose. It can be made from many materials, including metal, plastic, and wood. Furniture can be made using a variety of woodworking joints which often reflect the local culture.

A third issue comes from the view that inventory also serves the function of decoupling two separate operations. For example, work in process inventory often accumulates between two departments because the consuming and the producing department do not coordinate their work. With improved coordination this buffer inventory could be eliminated. This leads to the whole philosophy of Just In Time, which argues that the costs of carrying inventory have typically been underestimated, both the direct, obvious costs of storage space and insurance, but also the harder-to-measure costs of increased variables and complexity, and thus decreased flexibility, for the business enterprise.

Work in process (WIP), work in progress (WIP), goods in process, or in-process inventory are a company's partially finished goods waiting for completion and eventual sale or the value of these items. These items are either just being fabricated or waiting for further processing in a queue or a buffer storage. The term is used in production and supply chain management.

## Inventory models

The mathematical approach is typically formulated as follows: a store has, at time ${\displaystyle k}$, ${\displaystyle x_{k}}$ items in stock. It then orders (and receives) ${\displaystyle u_{k}}$ items, and sells ${\displaystyle w_{k}}$ items, where ${\displaystyle w}$ follows a given probability distribution. Thus:

${\displaystyle x_{k+1}=x_{k}+u_{k}-w_{k}}$
${\displaystyle u_{k}\geq 0}$

Whether ${\displaystyle x_{k}}$ is allowed to go negative, corresponding to back-ordered items, will depend on the specific situation; if allowed there will usually be a penalty for back orders. The store has costs that are related to the number of items in store and the number of items ordered:

${\displaystyle c_{k}=c(x_{k},u_{k})}$. Often this will be in additive form: ${\displaystyle c_{k}=p(x_{k})+h(u_{k})}$

The store wants to select ${\displaystyle u_{k}}$ in an optimal way, i.e. to minimize

${\displaystyle \sum _{k=0}^{T}c_{k}.}$

Many other features can be added to the model, including multiple products (denoted ${\displaystyle x_{ik}}$), upper bounds on inventory and so on. Inventory models can be based on different assumptions: [1] [2]

Demand is the quantity of a good that consumers are willing and able to purchase at various prices during a given period of time.

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.

The word stochastic is an adjective in English that describes something that was randomly determined. The word first appeared in English to describe a mathematical object called a stochastic process, but now in mathematics the terms stochastic process and random process are considered interchangeable. The word, with its current definition meaning random, came from German, but it originally came from Greek στόχος (stókhos), meaning 'aim, guess'.

### Classic models

Although the number of models described in the literature is immense, the following is a list of classics:

## Related Research Articles

A statistical model is a mathematical model that embodies a set of statistical assumptions concerning the generation of sample data. A statistical model represents, often in considerably idealized form, the data-generating process.

Material requirements planning (MRP) is a production planning, scheduling, and inventory control system used to manage manufacturing processes. Most MRP systems are software-based, but it is possible to conduct MRP by hand as well.

In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. Whereas deterministic optimization problems are formulated with known parameters, real world problems almost invariably include some unknown parameters. When the parameters are known only within certain bounds, one approach to tackling such problems is called robust optimization. Here the goal is to find a solution which is feasible for all such data and optimal in some sense. Stochastic programming models are similar in style but take advantage of the fact that probability distributions governing the data are known or can be estimated. The goal here is to find some policy that is feasible for all the possible data instances and maximizes the expectation of some function of the decisions and the random variables. More generally, such models are formulated, solved analytically or numerically, and analyzed in order to provide useful information to a decision-maker.

In inventory management, economic order quantity (EOQ) is the order quantity that minimizes the total holding costs and ordering costs. It is one of the oldest classical production scheduling models. The model was developed by Ford W. Harris in 1913, but R. H. Wilson, a consultant who applied it extensively, and K. Andler are given credit for their in-depth analysis.

In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random and independent, and statistically identical over different time intervals of the same length. A Lévy process may thus be viewed as the continuous-time analog of a random walk.

A stochastic differential equation (SDE) is a differential equation in which one or more of the terms is a stochastic process, resulting in a solution which is also a stochastic process. SDEs are used to model various phenomena such as unstable stock prices or physical systems subject to thermal fluctuations. Typically, SDEs contain a variable which represents random white noise calculated as the derivative of Brownian motion or the Wiener process. However, other types of random behaviour are possible, such as jump processes.

The economic lot scheduling problem (ELSP) is a problem in operations management and inventory theory that has been studied by a large number of researchers for more than 50 years. The term was first used in 1958 by professor Jack D. Rogers of Berkeley, who extended the economic order quantity model to the case where there are several products to be produced on the same machine, so that one must decide both the lot size for each product and when each lot should be produced. The method illustrated by Jack D. Rogers draws on a 1956 paper from Welch, W. Evert. The ELSP is a mathematical model of a common issue for almost any company or industry: planning what to manufacture, when to manufacture and how much to manufacture.

The newsvendormodel is a mathematical model in operations management and applied economics used to determine optimal inventory levels. It is (typically) characterized by fixed prices and uncertain demand for a perishable product. If the inventory level is , each unit of demand above is lost in potential sales. This model is also known as the newsvendor problem or newsboy problem by analogy with the situation faced by a newspaper vendor who must decide how many copies of the day's paper to stock in the face of uncertain demand and knowing that unsold copies will be worthless at the end of the day.

The economic production quantity model determines the quantity a company or retailer should order to minimize the total inventory costs by balancing the inventory holding cost and average fixed ordering cost. The EPQ model was developed by E.W. Taft in 1918. This method is an extension of the economic order quantity model. The difference between these two methods is that the EPQ model assumes the company will produce its own quantity or the parts are going to be shipped to the company while they are being produced, therefore the orders are available or received in an incremental manner while the products are being produced. While the EOQ model assumes the order quantity arrives complete and immediately after ordering, meaning that the parts are produced by another company and are ready to be shipped when the order is placed.

Robust optimization is a field of optimization theory that deals with optimization problems in which a certain measure of robustness is sought against uncertainty that can be represented as deterministic variability in the value of the parameters of the problem itself and/or its solution.

In the theory of stochastic processes, the filtering problem is a mathematical model for a number of state estimation problems in signal processing and related fields. The general idea is to establish a "best estimate" for the true value of some system from an incomplete, potentially noisy set of observations on that system. The problem of optimal non-linear filtering was solved by Ruslan L. Stratonovich, see also Harold J. Kushner's work and Moshe Zakai's, who introduced a simplified dynamics for the unnormalized conditional law of the filter known as Zakai equation. The solution, however, is infinite-dimensional in the general case. Certain approximations and special cases are well understood: for example, the linear filters are optimal for Gaussian random variables, and are known as the Wiener filter and the Kalman-Bucy filter. More generally, as the solution is infinite dimensional, it requires finite dimensional approximations to be implemented in a computer with finite memory. A finite dimensional approximated nonlinear filter may be more based on heuristics, such as the Extended Kalman Filter or the Assumed Density Filters, or more methodologically oriented such as for example the Projection Filters, some sub-families of which are shown to coincide with the Assumed Density Filters.

In actuarial science and applied probability ruin theory uses mathematical models to describe an insurer's vulnerability to insolvency/ruin. In such models key quantities of interest are the probability of ruin, distribution of surplus immediately prior to ruin and deficit at time of ruin.

The dynamic lot-size model in inventory theory, is a generalization of the economic order quantity model that takes into account that demand for the product varies over time. The model was introduced by Harvey M. Wagner and Thomson M. Whitin in 1958.

In mathematics, the slow manifold of an equilibrium point of a dynamical system occurs as the most common example of a center manifold. One of the main methods of simplifying dynamical systems, is to reduce the dimension of the system to that of the slow manifold—center manifold theory rigorously justifies the modelling. For example, some global and regional models of the atmosphere or oceans resolve the so-called quasi-geostrophic flow dynamics on the slow manifold of the atmosphere/oceanic dynamics, and is thus crucial to forecasting with a climate model.

In queueing theory, a discipline within the mathematical theory of probability, a D/M/1 queue represents the queue length in a system having a single server, where arrivals occur at fixed regular intervals and job service requirements are random with an exponential distribution. The model name is written in Kendall's notation. Agner Krarup Erlang first published a solution to the stationary distribution of a D/M/1 and D/M/k queue, the model with k servers, in 1917 and 1920.

In queueing theory, a discipline within the mathematical theory of probability, an M/D/c queue represents the queue length in a system having c servers, where arrivals are determined by a Poisson process and job service times are fixed (deterministic). The model name is written in Kendall's notation. Agner Krarup Erlang first published on this model in 1909, starting the subject of queueing theory. The model is an extension of the M/D/1 queue which has only a single server.

In applied probability, an assemble-to-order system is a model of a warehouse operating a build to order policy where products are assembled from components only once an order has been made. The time to assemble a product from components is negligible, but the time to create components is significant.

The base stock model is a statistical model in inventory theory. In this model inventory is refilled one unit at a time and demand is random. If there is only one replenishment, then the problem can be solved with the newsvendor model.

Supersymmetric theory of stochastic dynamics or stochastics (STS) is an exact theory of stochastic (partial) differential equations (SDEs), the class of mathematical models with the widest applicability covering, in particular, all continuous time dynamical systems, with and without noise. The main utility of the theory from the physical point of view is a rigorous theoretical explanation of the ubiquitous spontaneous long-range dynamical behavior that manifests itself across disciplines via such phenomena as 1/f, flicker, and crackling noises and the power-law statistics, or Zipf's law, of instantonic processes like earthquakes and neuroavalanches. From the mathematical point of view, STS is interesting because it bridges the two major parts of mathematical physics – the dynamical systems theory and topological field theories. Besides these and related disciplines such as algebraic topology and supersymmetric field theories, STS is also connected with the traditional theory of stochastic differential equations and the theory of pseudo-Hermitian operators.

## References

1. Zipkin Paul H., Foundations of Inventory Management, Boston: McGraw Hill, 2000, ISBN   0-256-11379-3
2. W. Hopp, M. Spearman, Factory Physics, 3rd ed. Waveland Press, 2011
• International Journal of Inventory Research is an academic journal on inventory theory publishing current research.

Classic books that established the field are:

• Kenneth J. Arrow, Samuel Karlin, and Herbert E. Scarf: Studies in the Mathematical Theory of Inventory and Production, Stanford University Press, 1958
• Thomson M. Whitin, G. Hadley, Analysis of Inventory Systems, Englewood Cliffs: Prentice-Hall 1963

Many university courses in inventory theory use one or more of the following current textbooks:

• Axsaeter, Sven. Inventory Control. Norwell, MA: Kluwer, 2000. ISBN   0-387-33250-2
• Porteus, Evan L. Foundations of Stochastic Inventory Theory. Stanford, CA: Stanford University Press, 2002. ISBN   0-8047-4399-1
• Silver, Edward A., David F. Pyke, and Rein Peterson. Inventory Management and Production Planning and Scheduling, 3rd ed. Hoboken, NJ: Wiley, 1998. ISBN   0-471-11947-4
• Simchi-Levi, David, Xin Chen, and Julien Bramel. The Logic of Logistics: Theory, Algorithms, and Applications for Logistics Management, 2nd ed. New York: Springer Verlag, 2004. ISBN   0-387-22199-9
• Tempelmeier, Horst. Inventory Management in Supply Networks, 3rd. Edition, Norderstedt (Books on Demand) 2011, ISBN   3-8423-4677-8
• Zipkin, Paul H. Foundations of Inventory Management. Boston: McGraw Hill, 2000. ISBN   0-256-11379-3

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# Is huck poor?

Is Huck poor?

If so, not good, if not, that's finely great!!!!!!!!!!!!!!!!

He got $6,000 from the girls at the funeral. But gave it to Judge Thatcher for Pap not to take his money and spend it to be drunk. Huck had received$6,000 from the girls at the funeral. But gave it to Judge Thatcher for Pap not to take his money and spend it to be drunk.