Wireless random-access networks with bipartite interference graphs

Abstract

We consider random-access networks where each node represents a server with a queue. Each node can be either active or inactive. A node deactivates at unit rate, while activates a rate that depends on its queue, provided none of its neighbors is active.We consider arbitrary bipartite graphs in the limit as the queues become large. We identify the transition time between the two states where one half of the network is active and the other half is inactive. We decompose the transition into a succession of transitions on complete bipartite subgraphs. We formulate a greedy algorithm that takes the graph as input and gives as output the set of transition paths the system is most likely to follow. Along each path we determine the mean transition time and its law on the scale of its mean. Depending on the activation rate functions, we identify three regimes of behavior.

Adding edge dynamics to bipartite random-access networks

“…In [4] we analyzed the mean transition time and its law on the scale of its mean for arbitrary bipartite interference graphs. They key factor is the introduction of randomized algorithm that takes as input the graph and gives as output the possible orders of activation of the nodes in V (admissible paths), together with their probabilities.…”

“…We focus on queue-based activation rates, in line with the models and the results in [3] and [4]. This leads to two level of complexity, driven by the queue dependences of the activation rates and by the edge dynamics.…”

“…We consider the bipartite graph G = ((U, V ), E), where U ∪ V is the set of nodes and E is the set of bonds that connect a node in U to a node in V , and vice versa (bonds are undirected). We recall some definitions and basic facts from [3] and [4].…”

“…The present paper is a continuation of [3] and [4]. We introduce an edge dynamics on the bipartite interference graph by allowing edges to appear and disappear over time.…”

“…In Section 1.2 we describe the setting and the mathematical model of interest in this paper by specifying edge dynamics. In Section 1.3, after a discusson of the results from [4] for arbitrary bipartite graphs, we state the main results on the mean transition time of the network under the effects of the dynamics. In Section 1.4 we anticipate the main idea behind our analysis and give an outline of the remainder of the paper.…”