Incremental Routing and Scheduling in Wireless Grids

This paper deals with two fundamental joint routing and scheduling problems in multi-hop wireless mesh networks (WMNs) employing time division multiple access (TDMA). The problems pertain to incremental update of schedules as some of the existing flows terminate and new flow demands are received. In the first problem, referred to as single flow scheduling (SFS) problem, we are given a set of ongoing flows in a WMN, a new incoming flow demand, and a specific potential path for routing the demand. All flows contend for using one of the available wireless channels. We ask whether the new flow demand can be served without perturbing existing slot assignments in the schedule serving the current flows. In the second problem, referred to as single flow routing and scheduling (SFRS) problem, no specific route is given. We first prove that conflict graphs of trees composed of certain class of interference limited paths in wireless networks have bounded treewidth. This characterization yields efficient solution to the SFS problem, among a number of other resource allocation problems in wireless networking. Next we consider the SFRS problem in grid networks. For such networks, we present an efficient solution to a generalized version of the SFRS problem where each link is associated with a cost, and a minimum cost schedulable route is desired. Using both concrete examples and simulation, we show that the devised SFRS algorithm yields improved throughput results over a competing approach that uses tree based routing.