12th GI/ITG CONFERENCE ON MEASURING, MODELLING AND EVALUATION OF COMPUTER AND COMMUNICATION SYSTEMS 3rd POLISH-GERMAN TELETRAFFIC SYMPOSIUM SENSITIVITY ANALYSIS FOR MAP/MAP/1 QUEUES

A sensitivity analysis of a single-server, infinite-buffer queue with correlated arrivals and correlated service times is performed. We study and compare the isolated impact of (normalized) marginal moments and (normalized) correlation structures of the arrival and service processes on the performance measures of such a queue. For these correlated processes, we use Markovian arrival processes of order 2 (with a hyperexponential marginal distribution), which may be constructed from any permissible set of the first three moments and a correlation parameter. With this closed-form solution for the inverse problem at hand and an appropriate scaling, we take a first step to a consistent and general, completely analytic framework for sensitivity analysis of queueing systems. The presented numerical results focus on the queue behavior in terms of the first two moments of the queue length distribution (computed by means of matrix-analytic techniques). Besides some well-known qualitative tendencies, we observe systematically and comparably the isolated quantitative impact of the involved parameters.