An information-theoretic bound for the capacity of multihop lightwave networks with non-uniform traffic patterns

Abstract

Multihop lightwave networks have recently emerged as prominent candidates for high-speed local, metropolitan, and wide-area networks. Of interest is the end-user capacity which may be afforded by a multihop lightwave network. For uniform traffic patterns, and for certain regular connection graphs, it is possible to compute the expected number of hops taken by a representative packet, the total network capacity, and the capacity available to each end-user. When the traffic patterns are non-uniform, simple expressions for network capacity cannot be produced.

In this paper, we apply information theoretic concepts to find an upper bound on the capacity which may be produced, by any multihop network, for an arbitrary non-uniform user-to-user traffic pattern. Also produced is a lower bound for the expected number of hops. Such bounds are useful as yardsticks against which the performance of specific architectures and connection graphs may be compared, since the methodology does not produce an multihop connection graph capable of achieving the bound. Although the work was stimulated by an interest in multihop lightwave networks, the bounds are equally applicable when non-uniform traffic is presented to any type of network involving packet switching nodes and directed connectivity graphs. Somewhat surprisingly, results obtained suggest that, for certain types of traffic non-uniformity, the capacity achievable per end user does not diminish as the number of network access stations increases.