Waiting time, busy periods and output models of a server analyzed via Wiener–Hopf factorization

Non-renewal processes are relevant in queueing analysis to include various types of traffic arising in integrated services communication networks. We consider a workload based approach to the single server queue in discrete time domain with semi-Markov arrivals (SMP/GI/1). By dividing the busy periods into phases, we generalize a computationally attractive algorithm for the discrete time GI/GI/1 queue. The stationary distributions of the waiting and idle time as well as the moments of the busy period are computed. Performance results are given for deterministic servers with autoregressive input. The output process of a server is modeled by adapting a SMP with a few states to information obtained from busy and idle period analysis.