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Added by
Guoqiang Mao Dr
Publication date
2014
fields
Informatics Engineering
and research's language is
English
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In this paper, we study the transport capacity of large multi-hop wireless CSMA networks. Different from previous studies which rely on the use of centralized scheduling algorithm and/or centralized routing algorithm to achieve the optimal capacity scaling law, we show that the optimal capacity scaling law can be achieved using entirely distributed routing and scheduling algorithms. Specifically, we consider a network with nodes Poissonly distributed with unit intensity on a $sqrt{n}timessqrt{n}$ square $B_{n}subsetRe^{2}$. Furthermore, each node chooses its destination randomly and independently and transmits following a CSMA protocol. By resorting to the percolation theory and by carefully tuning the three controllable parameters in CSMA protocols, i.e. transmission power, carrier-sensing threshold and count-down timer, we show that a throughput of $Thetaleft(frac{1}{sqrt{n}}right)$ is achievable in distributed CSMA networks. Furthermore, we derive the pre-constant preceding the order of the transport capacity by giving an upper and a lower bound of the transport capacity. The tightness of the bounds is validated using simulations.
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This work started out with our accidental discovery of a pattern of throughput distributions among links in IEEE 802.11 networks from experimental results. This pattern gives rise to an easy computation method, which we term back-of-the-envelop (BoE) computation, because for many network configurations, very accurate results can be obtained within minutes, if not seconds, by simple hand computation. BoE beats prior methods in terms of both speed and accuracy. While the computation procedure of BoE is simple, explaining why it works is by no means trivial. Indeed the majority of our investigative efforts have been devoted to the construction of a theory to explain BoE. This paper models an ideal CSMA network as a set of interacting on-off telegraph processes. In developing the theory, we discovered a number of analytical techniques and observations that have eluded prior research, such as that the carrier-sensing interactions among links in an ideal CSMA network result in a system state evolution that is time-reversible; and that the probability distribution of the system state is insensitive to the distributions of the on and off durations given their means, and is a Markov random field. We believe these theoretical frameworks are useful not just for explaining BoE, but could also be a foundation for a fundamental understanding of how links in CSMA networks interact. Last but not least, because of their basic nature, we surmise that some of the techniques and results developed in this paper may be applicable to not just CSMA networks, but also to other physical and engineering systems consisting of entities interacting with each other in time and space.
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