Perturbation analysis of the \(GI/GI/1\) queue
The authors consider a family of \(GI/GI/1\) queueing processes with service time distribution belonging to a parametric family \(F(x,\theta)\), where the system is assumed to be stable for all \(\theta \in [a,b]\). Let \(T(\theta)\) be a random variable distributed according to the steady state distribution of the system time of a customer. They establish the existence of \((d/d \theta) E(T)\) and obtain an expression suitable for the estimation from a single simulation experiment. Under natural moment conditions, they show that the corresponding perturbation analysis estimates are strongly consistent. They prove that the second derivatives of \(E(T)\) exist by using direct sample path arguments. They also present perturbation analysis algorithms and demonstrate their performance by using simulation.
scientific article; zbMATH DE number 711801
scientific article