We analyze the delay performance of a multi-hop wireless network in which the routes between source-destination pairs are fixed. We develop a new queue grouping technique to handle the complex correlations of the service process resulting from the multi-hop nature of the flows and their mutual sharing of the wireless medium. A general setbased interference model is assumed that imposes constraints on links that can be served simultaneously at any given time. These interference constraints are used to obtain a fundamental lower bound on the delay performance of any scheduling policy for the system. Delay Analysis and Optimality of Scheduling Policies for Multi-Hop Wireless Networks
We consider a simple distributed scheduling strategy, maximal scheduling, and prove that it attains a guaranteed fraction of the maximum throughput region in arbitrary wireless networks. The guaranteed fraction depends on “interference degree” of the network which is the maximum number of sessions that interfere with any given session in the network and do not interfere with each other. Depending on the nature of communication, the transmission powers and the propagation models, the guaranteed fraction can be lower bounded by the maximum link degrees in the underlying topology, or even by constants that are independent of the topology. The guarantees also hold in networks with multicast communication and an arbitrary number of frequencies. We prove that the guarantees are tight in that they cannot be improved any further with maximal scheduling.
We consider the lower bound analysis as an important first step towards a complete delay analysis of multi-hop wireless systems. For a network with node exclusive interference, our lower bound is tight in the sense that it goes to infinity whenever the delay of any throughput optimal policy is unbounded. For a tandem queueing network, the average delay of a delay optimal policy proposed numerically coincides with the lower bound provided in this paper.
We are able to apply known techniques to obtain a sample path delay-optimal scheduling policy. We also obtain policies that minimize a function of queue lengths at all times on a sample path basis. Further, for a tandem queueing system, we show numerically that the expected delay of a previously known delay-optimal policy coincides with the lower bound.