On Comparison of Multiserver Systems with Multicomponent Mixture Distributions

Abstract

In this paper, we introduce and study the relations between parameters of the m-component mixture distributions which imply the stochastic and failure rate comparisons. Then we apply the failure rate and stochastic ordering techniques to construct the upper and lower bounds for the steady-state performance indexes in a multiserver queueing system with multicomponent exponential-Pareto mixture service time distribution. The uniform distance between multicomponent mixture distribution and its parent distribution is discussed. The obtained theoretical results are then illustrated by a few numerical examples based on the regenerative simulation multiserver queueing systems with mixture service time distributions.

Bounds and Maxima for the Workload in a Multiclass Orbit Queue

“…It is clear from (29) that the definition of R(x, a) in ( 31) is exactly the same as in (28) (it is also noted implicitly in [34]).…”

“…The topic of extreme values of the performance indexes in the queuing setting is studied in [19][20][21][22][23][24][25], to mention a few. We also mention some works in this field of the authors of this research [26][27][28][29][30]. The extreme behaviour of the stationary waiting time in classical GI/G/1 systems has been studied in the works [26,27].…”

“…It has been established in [28] that the limiting distribution of the waiting-time maxima in the systems with exponential-Pareto service times is Frechettype. In the paper [29], the authors use failure-rate ordering and stochastic ordering to construct the upper and lower bounds for the stationary workload in a multiserver queueing system with multicomponent exponential-Pareto service time.…”