Abstract
We consider a network with a fixed number of links whose transmitters are saturated and access a channel using a random back-off algorithm. Some of the links may be hidden in the sense that they do not interfere with all other links but rather with a subset of the links. Using mean field techniques, we analyze a variety of random back-off algorithms by explicit calculating the throughput of the links in such networks. We apply our results to analyze the performance of the exponential back-off algorithm in networks with partial interaction. The results are striking and confirm experimental results. Hidden transmitters that fail to sense collisions with other links unfairly grab too much bandwidth at the expense of transmitters that comply with the back-off rules. We believe the model can be used to develop new algorithms realizing an adequate trade-off between fairness and efficiency.
This work was done during C. Bordenave’s and A. Proutiere’s visit to University of Ottawa. We wish to thank Prof. McDonald for his kind hospitality.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
IEEE Standard for Wireless LAN Medium Access Protocol and Physical Layer Specifications, IEEE std. (August 1999)
Abramson, N.: The ALOHA system - Another alternative for computer communications. In: Proc. of AFIPS press (1970)
Baccelli, F., Brémaud, P.: Elements of Queueing Theory: Palm-Martingale Calculus and Stochastic Recurrences. Springer, Heidelberg (1994)
Bianchi, G.: Performance Analysis of the IEEE 802.11 Distributed Coordination Function. IEEE Journal on Selected Areas in Communications 18(3), 535–547 (2000)
Billingsley, P.: Convergence of Probability Measures. Wiley, New York (1968)
Bordenave, C., McDonald, D., Proutiere, A.: A Random Multi-access Algorithms: A Mean Field analysis. In: Proceedings of the Allerton Conference on Communication, Control, and Computing (2005)
Bordenave, C., McDonald, D., Proutiere, A.: Mean-field limits of a particle system interacting with a rapidly varying environment. Submitted (2006), Available at http://www.cos.ict.kth.se/alepro/mathpap.pdf
Durvy, M., Thiran, P.: A Packing Approach to Compare Slotted and Non-slotted Medium Access Control. In: Proc. of IEEE Infocom, IEEE Computer Society Press, Los Alamitos (2006)
Kelly, F.P.: Loss Networks. The Annals of Applied Probability 1(3), 319–378 (1991)
Li, J., Blake, C., De Couto, D.S.J., Lee, H.I., Morris, R.: Capacity of Ad Hoc wireless networks. In: Proc. of ACM Mobicom, ACM Press, New York (2001)
Nguyen, G.D., Wieselthier, J., Ephremides, A.: Random Access in Overlapping Cells. In: Proc. of European Wireless (2005)
Sharma, G., Ganesh, A., Key, P.: Performance Analysis of Contention Based Medium Access Control Protocols. In: Proc. IEEE Infocom, IEEE Computer Society Press, Los Alamitos (2006)
Sznitman, A.S.: Propagation of chaos. In: Ecole d’été de probabilités de Saint-Flour XIX. Lecture Notes in Mathematics, vol. 1464, Springer, Berlin (1991)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bordenave, C., McDonald, D., Proutiere, A. (2007). Random Multi-access Algorithms in Networks with Partial Interaction: A Mean Field Analysis. In: Mason, L., Drwiega, T., Yan, J. (eds) Managing Traffic Performance in Converged Networks. ITC 2007. Lecture Notes in Computer Science, vol 4516. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72990-7_68
Download citation
DOI: https://doi.org/10.1007/978-3-540-72990-7_68
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72989-1
Online ISBN: 978-3-540-72990-7
eBook Packages: Computer ScienceComputer Science (R0)