Capacity and delay analysis of multi-hop wireless networks

Abstract

The capacity and delay of wireless multi-hop networks are key performance indicators. They are needed in the design of such networks, and are also useful to assess how well applications can run over such networks. However, finding analytical expressions for capacity and delay for a wireless multi-hop network with an arbitrary topology is hard. In this work, a two-step approach is followed to derive expressions for the maximum achievable capacity and the minimum achievable delay in wireless multi-hop networks. These expressions are valid for fixed, conflict-free time-slot scheduling among the nodes, and when each nodes of the network has always packets to send to each of its neighbours. In the first step, expressions for the capacity and delay of the elementary topologies ’string’ and ’star’ are derived, and in the second step, these results are combined to derive the capacity and delay values for a network with an arbitrary topology. This two-step approach is applied to two types of wireless multi-hop networks: those whose nodes have an omni-directional antenna, and those whose nodes have an electronically steerable directional (beam-steering) antenna. Using this approach, we find that the capacity of a path on the network is not a decreasing function of the total number of nodes in the network, as mostly found in literature, but rather a decreasing function of the number of neighbours of the nodes on the path. The results show that the derived maximum value for the capacity (and minimum value for the delay) in networks with beam-steering antennas is larger (lower) than that for networks with omni-directional antennas as more efficient scheduling is possible for the former. The derived analytic expressions for capacity and delay are valuable for the relative comparison of the performance of wireless multi-hop networks.