Elsevier

Performance Evaluation

Volume 63, Issue 11, November 2006, Pages 1127-1156
Performance Evaluation

On the performance of ad hoc wireless LANs: A practical queuing theoretic model

https://doi.org/10.1016/j.peva.2006.05.011Get rights and content

Abstract

In this paper, two Markov chain queuing models have been developed to obtain closed-form solutions for packet delay and packet throughput distributions in a real-time wireless communication environment using IEEE 802.11 DCF. An M/G/1/K queuing model is incorporated in both models. In the first model results are based on arbitrary contention conditions, namely, collision probabilities, transmission probabilities and contention window sizes vary arbitrarily among nodes contending for channel access. In the second model, however, the contention condition is limited by the assumption that collision probabilities remain constant among contending nodes. Results are presented for the fully-connected case. Two models are compared and validated via simulation with statistical analysis. The main contributions are the analysis of DCF and the foundation for the sensitivity analysis.

Introduction

This article presents a novel queuing theoretic model for wireless LANs. The objective is to gain deeper insight into performance characterization as reflected by cross-layer interactions and local MAC operation. IEEE 802.11 DCF was chosen as the subject of the analysis. Selection of DCF was motivated by its support of both infrastructure and ad hoc modes, and, hence, to facilitate future extension to multi-hop environments. Substantial effort has been devoted to related performance analysis as evidenced by the vast literature. The most important, relevant contributions are discussed below. Discussion of related work also appears in context throughout the paper.

Although basic performance characteristics of 802.11 DCF are generally well understood, the aim of this paper is to address the need for more flexible and extensible models that can be engaged in real-time for dynamically adaptive control. Evaluation of a local queuing system without the need for information exchange would provide the most elegant and efficient solution. Analytical tractability was achieved by reducing the complexity normally encountered in queuing networks by effectively restoring the independence between service and packet inter-arrival times through DTMC formulation. Thus, direct steady-state analysis becomes possible using iterative techniques to estimate the model parameters for different traffic intensity levels. Moreover, observing that a node attempting to transmit responds equivalently to contention regardless of its source makes it feasible to adopt a single queuing system using a Markov Modulated General Service time distribution to account for all contention.

This paper is the first work the authors are aware of that presents a complete and generalized queuing model for a wireless LAN. The M/MMGI/1/K model represents a unique contribution on its own merits. Furthermore, it poses a fundamentally different strategy for understanding and improving the effectiveness of practical networks, facilitating cross-layer design through on-line estimation of performance metrics. Specific applications are beyond the scope of this paper, however they represent the “raison d’être” underlying this research. Moreover, the queuing model is readily adapted to alternative modes of operation, node parameterization and MAC protocols. The effect is limited to evaluation of the state probabilities and impact on the performance metrics.

Two analytical models based on the M/MMGI/1/K queue are presented, validated and analyzed in this paper. The arrival process is assumed to be Poisson and the distribution of service times are modeled as a Markov Modulated General Independent process. K represents the maximum queue length at each node. Another parameter N representing the number of potential contending nodes is used in the analysis. In the first model each of the N nodes may be in any state at a given time, namely, any node may be busy or idle and busy nodes may be at any back-off stage. In contrast to the commonly adopted assumptions found in much of the related analytical work, [4], [32], [29], [28], [9], [15] no limiting assumptions were made that force uniform collision probabilities, uniform distribution of back-off stage or saturation conditions. A second model based on [28] is presented for comparative purposes due to its overall simplicity. In the second model uniform collision probabilities are assumed for each contending node.

In principle this system is an example of a Phase-Type (PH) service. Hence, comprehensive analysis is well conformed to matrix-geometric techniques. The difficulty of this approach, however, is in finding an accurate parametric description of the PH service. For steady-state analysis a general service distribution could be adopted in which the service-times depend on local collision probabilities of the RTS/CTS frames and the distribution of the time to resolve them, which, itself is dependent on the number of busy nodes in contention for the channel.

It is necessary to know the node distribution for single-hop analysis and it is sufficient to determine the aforementioned values: a two-dimensional Discrete-Time Markov-Chain (DTMC) that characterizes the back-off stages and collision probabilities associated with each node effectively modulate the general process, thus facilitating the estimation of the needed parameters. The model introduced by Ozdemir and McDonald in [25] provides the first element underlying general queuing analysis here. The broader objective is to develop a methodology that is extensible to multi-hop ad hoc networks scenarios. The second model here is considered to be pursued in the multi-hop methodology because of its simplicity.

Throughput, delay and jitter are fundamental and major performance metrics that serve as the foundation of the design and real-time applications of ad hoc wireless networks. However, compared to the large volume of analysis for performance metrics of wireless networks at saturation, few advances have been made in the understanding performance metrics for generalized traffic loads [25], [15], [29]. Specifically, to the authors’ knowledge no analytical results have been reported for the transition regions. Thus, it is crucial to have validated analytical models for the generalized traffic conditions.

Performance metric measurements are shown using the analytical model over IEEE 802.11b wireless networks. The goals of these measurements are to assess whether there are significant issues with 802.11b wireless networks regarding real-time applications, as it is stated in several papers [4], [22], [35], [26]. With this information it is intended to obtain a better understanding of wireless networks’ suitability for real-time applications. Practical future applications include routing, admission control and scheduling in ad hoc networks.

It is well-known that the wireless channel is error-prone due to noise and interference in the channel. However, the impact of bit errors in the packet is not considered in the previous analytical models [4], [9], [28]. It is expected that when bit error rate is high, the good throughput of DCF access mechanism will degrade significantly. But it is not well-known how the bit error rate affects other performance measures such as MAC delay, jitter, blocking and dropping probabilities. Thus, the tradeoff of DCF performance metrics and packet reliability is investigated by extending the proposed model to error-prone channels.

The remainder of this paper is organized as follows: related work is discussed in Section 2. Section 3 describes the system model which encompasses models for the back-off algorithm, service time distribution and the M/G/1/K formulation. Performance measures are given in Section 4. Section 5 shows how to carry out the error analysis on top of the system model. Section 6 applies simulation and statistical analysis to validate the analytical results and Section 7 depicts some sensitivity analysis results. Finally, Section 8 presents conclusions and discusses future work.

Section snippets

Related work

Some prior research work analyzes the performance of IEEE 802.11 DCF [4], [3], [28], [23], [34], [21], [38], [7], [31], [13], [18], [11], [33], [20], [37]. Many approaches in the past tried to optimize the channel by adopting runtime estimation of system parameters to increase the MAC protocol performance. The most relevant parameter is the number of contending stations in the collision domain of a target receiver [5]. On the other hand, the estimation of the number of contending stations is

System model

This section describes the basic methodology and components of the M/MMGI/1/K queuing analysis. The main parameters are identified and applied to each of the system entities—the back-off algorithm, the service time distribution and, finally, the queuing model. In the present analysis the states of each node are considered independently and then coupled through an iterative process in order to evaluate the system state. Specifically, the MAC algorithm executes at each node leaving each in an

Performance

While 802.11b networks have proved their appropriateness for best effort traffic, i.e. e-mail, browsing, chat or file transfer, their lack of QoS support makes it questionable whether the use of real-time multimedia applications, such as voice communication, is possible in these wireless networks. For QoS applications, there are many system measures to be decided according to the application. The ones to be measured are MAC delay, jitter, delay, variance of waiting time, throughput, dropping

Error analysis

The ideal channel model is assumed in the analysis up to this point. However, during the previous research work, the impact of bit error rate on the performance of 802.11 DCF is not taken into consideration for the whole spectrum of traffic load. In [19] and [12], the saturation conditions are assumed to see the effects of channel errors. In [30] the specific wireless channel models [17] are considered and in [2] channel models are presented. The more general error analysis is developed here

Simulation model and validation

The main objective of the simulation model is to provide an unbiased and systematic performance analysis of the queueing analytical model. This section presents the simulation environment, the system parameters, design of the simulation, discussion of the statistical analysis of the simulation results, and model validation.

Sensitivity analysis

The objective of this study requires the development of a sensitivity analysis which gives a deeper insight into the inherent characteristics of IEEE 802.11 MAC protocol.

The first sensitivity analysis is done by changing the number of nodes in the system. The results for all performance metrics are shown in Fig. 9, Fig. 10. As the number of nodes increases, all performance metrics deteriorate in a very clear way. That is because more nodes lead to more collision in the network. By restricting

Conclusion

This paper represents an important advance in the analysis and design of effective ad hoc networks. It also provides a significant contribution to the performance analysis of IEEE 802.11 wireless LANs. A novel queuing theoretic model based on the M/MMGI/1/K queue and parametric service model for IEEE 802.11 DCF was solved. The results are based on the single-hop case, but they represent an extensible and flexible approach. It is investigated using the sensitivity analysis results what causes

Acknowledgement

This research was partially supported by NSF Career Award 2004 CISE 0347698.

Mustafa Özdemir received his B.S. from Bilkent University, Turkey, in 1998 and his M.S. from Northeastern University, USA, in 2001, both in Electrical Engineering. Currently he is working toward his Ph.D. degree in the Reconfigurable Wireless Networks research group in the department of Electrical and Computer Engineering at Northeastern University. His research interests include theoretical analysis, design, implementation and performance evaluation of wireless communications and ad hoc

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    Mustafa Özdemir received his B.S. from Bilkent University, Turkey, in 1998 and his M.S. from Northeastern University, USA, in 2001, both in Electrical Engineering. Currently he is working toward his Ph.D. degree in the Reconfigurable Wireless Networks research group in the department of Electrical and Computer Engineering at Northeastern University. His research interests include theoretical analysis, design, implementation and performance evaluation of wireless communications and ad hoc systems.

    A. Bruce McDonald is a Professor of Electrical and Computer Engineering (ECE) at Northeastern University in Boston, MA where he heads the Reconfigurable Wireless Networks research group. His main research interests are focused on theoretical analysis and engineering design problems associated with wireless ad hoc and sensor networks. The aim of his research is to build broad theoretic understanding of the performance characteristics and inter-layer interactions inherent to these systems in order to enhance our ability to support the statistically bounded QoS guarantees required for many innovative applications. His research group has worked with numerous corporate partners sharing interest in cross-layer design methods intended to narrow the gap between theory and practice. Prof. McDonald received the B.S. degree in Electrical Engineering from Northwestern University (1986) and the M.S. and Ph.D. degrees from the University of Pittsburgh (1995, 2000). From 1996 to 2000 he served as a Senior Computer Engineer in the Department of Clinical and Computational Neurophysiology at Children’s Hospital in Pittsburgh, PA. In 1996 he was a Visiting Researcher in the Applied Network Research Group at Bellcore in Redbank, NJ. He received an appointment as the Zraket Assistant Professor of ECE at Northeastern University in 2001 and was awarded the NSF Career Grant in 2004.

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