Tandem Behaviour of a Telecommunication System with Repeated Calls: A Markovian Case with Buffers

Abstract

The performance of a telecommunication system consisting of a set of transmitters with finite capacity buffers is modelled with a Markovian queueing network, and its tandem behaviour is approximated, in steady state. In this system, a fraction of the units which, at the instants of their arrival at each transmitter, find it busy may retry to be processed by merging with the incoming arrival units at the same transmitter after a fixed delay time. The performance of this system is approximated by a recursive algorithm, in steady state. Furthermore, the approximation outcomes are compared against those from a simulation study. In summary, our numerical results indicate that approximating the non-renewal superposition arrival, the non-renewal overflow and the non-renewal departure processes at each node of the network can be approximated with compatible Poisson processes.