Bottleneck Analysis for Routing and Call Scheduling in Multi-Hop Wireless Networks

In this paper, we address the routing and call scheduling problem in which one has to find a minimum-length schedule of selected links in a TDMA (time division multiple access) based wireless network. As we deal with multi-hop networks, these selected links represent a routing solution (paths) providing enough capacity to achieve the routers requirements of bandwidth. We present a cross-layer formulation of the problem that computes joint routing and scheduling. We use a branch-and-price algorithm to solve optimally the problem. A column generation algorithm is used to cope with the exponential set of rounds. The branch-and-bound algorithm provides mono-routing. We run experiments on networks from the literature, with different number of gateways. Experimental results as well as theoretical insights let us conjecture that the bottleneck region analysis is enough to find the optimal solution. The Integer Round-Up Property (IRUP) seems to hold for our problem.