Towards time domain invariant QoS measures for queues with correlated traffic

• Queues with correlated traffic are investigated.
• Closed form expressions of QoS measures for BRAP queues are derived.
• The QoS measures are shown time invariant.
• The adverse impact of traffic correlation upon QoS measures is assessed.
• The QLD of BRAP queue is verified and interpreted in entropy maximisation.

An investigation is carried out on the nature of QoS measures for queues with correlated traffic in both discrete and continuous time domains. The study focuses on the single server GIG/M[X]/1/N and GIG/Geo[X]/1/N queues with finite capacity, N, a general batch renewal arrival process (BRAP), GIG and either batch Poisson, M[X] or batch geometric, Geo[X] service times with general batch sizes, X. Closed form expressions for QoS measures, such as queue length and waiting time distributions and blocking probabilities are stochastically derived and showed to be, essentially, time domain invariant. Moreover, the sGGeosGGeo/Geo/1/N queue with a shifted generalised geometric (sGGeo) distribution is employed to assess the adverse impact of varying degrees of traffic correlations upon basic QoS measures and consequently, illustrative numerical results are presented. Finally, the global balance queue length distribution of the MGeo/MGeo/1/N queue is devised and reinterpreted in terms of information theoretic principle of entropy maximisation.