This Article 
 Bibliographic References 
 Add to: 
A Statistical Mechanics-Based Framework to Analyze Ad Hoc Networks with Random Access
April 2012 (vol. 11 no. 4)
pp. 618-630
Sunil Srinivasa, University of Notre Dame, Notre Dame
Martin Haenggi, University of Notre Dame, Notre Dame
Characterizing the performance of ad hoc networks is one of the most intricate open challenges; conventional ideas based on information-theoretic techniques and inequalities have not yet been able to successfully tackle this problem in its generality. Motivated thus, we promote the totally asymmetric simple exclusion process (TASEP), a particle flow model in statistical mechanics, as a useful analytical tool to study ad hoc networks with random access. Employing the TASEP framework, we first investigate the average end-to-end delay and throughput performance of a linear multihop flow of packets. Additionally, we analytically derive the distribution of delays incurred by packets at each node, as well as the joint distributions of the delays across adjacent hops along the flow. We then consider more complex wireless network models comprising intersecting flows, and propose the partial mean-field approximation (PMFA), a method that helps tightly approximate the throughput performance of the system. We finally demonstrate via a simple example that the PMFA procedure is quite general in that it may be used to accurately evaluate the performance of ad hoc networks with arbitrary topologies.

[1] J. Andrews, N. Jindal, M. Haenggi, R. Berry, D. Guo, M. Neely, S. Weber, S. Jafar, and A. Yener, “Rethinking Information Theory for Mobile Ad Hoc Networks,” IEEE Comm. Magazine, vol. 46, no. 2, pp. 94-101, Dec. 2008.
[2] R.C. Alamino and D. Saad, “Statistical Mechanics Analysis of LDPC Coding in MIMO Gaussian Channels,” J. Physics A: Math. and Theoretical, vol. 40, no. 41, pp. 12259-12279, Oct. 2007.
[3] K. Takeuchi and T. Tanaka, “Statistical-Mechanics-Based Analysis of Multiuser MIMO Channels with Linear Dispersion Codes,” J. Physics: Conf. Series, vol. 95, no. 1, pp. 012008-1-012008-11, Jan. 2008.
[4] D. Guo and S. Verdu, “Randomly Spread CDMA: Asymptotics via Statistical Physics,” IEEE Trans. Information Theory, vol. 51, no. 4, pp. 1261-1282, Apr. 2005.
[5] N. Rajewsky, L. Santen, A. Schadschneider, and M. Schreckenberg, “The Asymmetric Exclusion Process: Comparison of Update Procedures,” J. Statistical Physics, vol. 92, nos. 1/2, pp. 151-194, July 1998.
[6] L. Kleinrock, Queueing Systems, Vol. II: Computer Applications. Wiley Interscience, 1976.
[7] L. Galluccio and S. Palazzo, “End-to-End Delay and Network Lifetime Analysis in a Wireless Sensor Network Performing Data Aggregation,” Proc. IEEE Global Telecomm. Conf. (GlobeCom), 2009.
[8] T. Jun and C. Julien, “Delay Analysis for Symmetric Nodes in Mobile Ad Hoc Networks,” Proc. Fourth ACM Workshop Performance Monitoring and Measurement of Heterogeneous Wireless and Wired Networks, Oct. 2009.
[9] N. Ryoki, K. Kawahara, T. Ikenaga, and Y. Oie, “Performance Analysis of Queue Length Distribution of Tandem Routers for QoS Measurement,” Proc. IEEE Symp. Applications and the Internet, pp. 82-87, Jan./Feb. 2002.
[10] H. Daduna and R. Szekli, “On the Correlation of Sojourn Times in Open Networks of Exponential Multiserver Queues,” Queueing Systems, vol. 34, nos. 1-4, pp. 169-181, Mar. 2000.
[11] M. Xie and M. Haenggi, “Towards an End-to-End Delay Analysis of Wireless Multihop Networks,” Elsevier Ad Hoc Networks, vol. 7, pp. 849-861, July 2009.
[12] M. Xie and M. Haenggi, “A Study of the Correlations between Channel and Traffic Statistics in Multihop Networks,” IEEE Trans. Vehicular Technology, vol. 56, no. 6, pp. 3550-3562, Nov. 2007.
[13] S. Srinivasa and M. Haenggi, “The TASEP: A Statistical Mechanics Tool to Study the Performance of Wireless Line Networks,” Proc. Int'l Conf. Computer Comm. and Networks, Aug. 2010.
[14] B. Derrida, E. Domany, and D. Mukamel, “An Exact Solution of a One-Dimensional Asymmetric Exclusion Model with Open Boundaries,” J. Statistical Physics, vol. 69, nos. 3/4, pp. 667-687, Nov. 1992.
[15] G. Schütz and E. Domany, “Phase Transitions in an Exactly Soluble One-Dimensional Exclusion Process,” J. Statistical Physics, vol. 72, nos. 1/2, pp. 4265-4277, July 1993.
[16] B. Derrida, M.R. Evans, V. Hakim, and V. Pasquier, “Exact Solution of a 1D Asymmetric Exclusion Model Using a Matrix Formulation,” J. Physics A: Math. and General, vol. 26, no. 7, pp. 1493-1517, Apr. 1993.

Index Terms:
Ad hoc networks, throughput, end-to-end delay, statistical mechanics, network topology.
Sunil Srinivasa, Martin Haenggi, "A Statistical Mechanics-Based Framework to Analyze Ad Hoc Networks with Random Access," IEEE Transactions on Mobile Computing, vol. 11, no. 4, pp. 618-630, April 2012, doi:10.1109/TMC.2011.96
Usage of this product signifies your acceptance of the Terms of Use.