Waiting-time tail probabilities in queues with long-tail service-time distributions
The authors have recently developed algorithms for the waiting-time tail probabilities \(P (W>x)\) in a large class of single-server queues [Oper. Res (1994), and Commun. Stat., Stochastic Models 10, No. 1, 99-143 (1994; Zbl 0801.60082)]. In this paper, the authors consider a \(GI/G/1\) queueing model assuming that the service time distribution is a Pareto mixture of exponential distribution with mean 1. They develop algorithms for computing the waiting-time distribution. They investigate the quality of approximations based on asymptotics for \(P (W>x)\), as \(x\to\infty\). They also derive multi-term asymptotic expansions for the \(M/G/1\) queue.
Pareto mixture of exponential distribution
scientific article; zbMATH DE number 622033
scientific article