Comparison of performance measures in non-Markovian queues

Abstract

Systems that involve waiting before attention are framed within the Theory of queues. This work seeks to compare performance measures in non-Markovian queues. For this, single-tail systems were simulated, which were formed from the combinations of time distributions between arrivals (normal, lognormal, Weibull or triangular), their parameters (Test 1, Test 2 or Test 3), and the distributions of service times (constant or triangular). Some results show that when comparing each performance measure individually, for systems that maintain constant arrival parameters, service distributions, and vary the distribution of time between arrival, their joint behavior is statistically different. On the other hand, the systems that included normal or uniform input distributions, setting the distribution parameters with one or two standard deviations (1σ; 2 σ), and the service distribution, showed that in the evaluation of each measure of particular performance, had statistically equal values. In the case of the systems that included the parameters with the highest standard deviation and the lognormal and Weibull, or lognormal and uniform distributions, they presented statistically similar behavior in three of four performance measures.