Abstract
The motivation of mixing distributions in communication/queueing systems modeling is that some input data (e.g., service time in queueing models) may follow several distinct distributions in a single input flow. In this paper, we study the sensitivity of performance measures on proximity of the service time distributions of a multiserver system model with two-component Pareto mixture distribution of service times. The theoretical results are illustrated by numerical simulation of the M/G/c systems while using the perfect sampling approach.
Highlights
Mixtures of distributions arise in complex stochastic systems and they are extensively used for statistical analysis in many real fields, such as lifetime modeling, ageing or failure processes, engineering reliability [1], and survival theory [2], where data are assumed to be heterogeneous
This paper is dedicated to sensitivity analysis of a steady-state performance index of a multiserver system with respect to service time distribution having the form of the so-called finite mixture [14]
We demonstrate how stochastic and failure rate ordering can be applied to multiserver systems with mixed service time distribution
Summary
Mixtures of distributions arise in complex stochastic systems and they are extensively used for statistical analysis in many real fields, such as lifetime modeling, ageing or failure processes, engineering reliability [1], and survival theory [2], where data are assumed to be heterogeneous. This paper is dedicated to sensitivity analysis of a steady-state performance index of a multiserver system with respect to service time distribution having the form of the so-called finite mixture [14]. We compare the basic system to a disturbed one, using a sensitivity measure (Kolmogorov–Smirnov distance) both for the service time distributions, and for the steady-state performance estimate (queue size). The key idea of the present paper is to study qualitatively the sensitivity of the steady-state distribution of the system performance index (steady-state queue size) to the variability of service time distribution by means of simulation. We study the sensitivity of the steady-state queue size distribution with respect to (w.r.t.) the shape parameters of mixture and the mixing coefficient and illustrate stochastic monotonocity of the system performance. The discussion of the simulation results finalizes the paper in the concluding Section 6
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