IEEE 802.11s and the Philosophers’ problem

Abstract

IEEE 802.11s is the task group in the IEEE that is in the process of standardizing wireless mesh networks. A hot topic in this standardization effort concerns the need for additional medium access functionality beyond the basic IEEE 802.11 carrier sense multiple access with collision avoidance (CSMA/CA). In this paper, we discuss the connection between CSMA/CA and Dijkstra's classical Philosophers' problem, and its implications for the debate inside IEEE 802.11s. In an alternative view of this paper, we state some new mathematical models, theorems and conjectures related to the Philosophers' problem.

Spatial fairness in linear random-access networks

“…As observed by Durvy et al [6] and Denteneer et al [4], the throughput distribution in this case is highly unfair, in the sense that some nodes have a larger throughput than others. This unfairness can be explained by the node-in-the-middle phenomenon discussed for example in Wang and Kar [22] and Garetto, Salonidis and Knightly [8] for the case n = 3, β = 1: the middle node is in an unfavorable position as it has to wait for both outer nodes to deactivate, whereas these outer nodes only compete for transmission with the middle node.…”

“…Wang and Kar [22] considered three nodes on a line that only block their direct neighbors, and showed that the middle node is starved when the activation rates of all three nodes increase. Such unfairness has been studied for more general networks by Durvy, Dousse and Thiran [6,7] and Denteneer, Borst, Van de Ven and Hiertz [4]. We study a similar model as in [6,7,4], i.e., a network with n nodes on a line, in which active nodes block a certain subset of other nodes.…”

“…Such unfairness has been studied for more general networks by Durvy, Dousse and Thiran [6,7] and Denteneer, Borst, Van de Ven and Hiertz [4]. We study a similar model as in [6,7,4], i.e., a network with n nodes on a line, in which active nodes block a certain subset of other nodes. In particular, unblocked nodes become active, and active nodes deactivate, after exponential times, and an active node blocks the first β nodes on both sides.…”

“…To deal with the unfairness, we shall modify the model in [6,7,4] in one important way: instead of letting nodes activate at the same rate, we allow for node-specific activation rates. By choosing the activation rate ν i of node i as a particular function of the number of its neighbors, we can guarantee that all nodes in the network have the same throughput, completely removing the unfairness.…”

Tandem queueing networks with neighbor blocking and back-offs

“…In view of the complexity, we focus on a regime where the ordinary back-off periods are asymptotically small. We refer to [4,11,13,21,25,27] which consider CSMA/CA networks with standard back-offs only where all nodes are assumed to be saturated. Stability issues in non-saturated networks with standard back-offs and single-hop traffic are pursued in [26].…”