On product form approximations for communication networks with losses: Error bounds

Abstract

This paper studies communication networks with packet or message losses due to collisions, transmission errors or finite buffer constraints. Analytic error bounds are derived for simple product form approximations. The approximations are based on ignoring and bounding loss probabilities. The error bounds can be computed easily. Two extreme situations are considered: (1) Networks with infinite capacities but state-dependent loss probabilities; (2) Networks with finite capacities (buffers) and losses due to saturated buffers. The error bounds are of the order β when: (1) the loss probabilities are uniformly bounded by β, or when (2) the steady-state probability of capacity excess is of order β. The results provide formal justification for practical engineering approximations. Extensions to more complex communication networks seem possible.