Perturbation analysis of the \(GI/GI/1\) queue
type: Item
instance of: scholarly article
title: Perturbation analysis of the \(GI/GI/1\) queue
zbMATH Open document ID: 0812.60085
DOI: 10.1007/BF01158763
author: Michael A. Zazanis
author: Rajan Suri
published in: Queueing Systems
publication date: 1995-05-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 711801
zbMATH Keywords: sensitivity analysis
zbMATH Keywords: second derivatives estimation
zbMATH Keywords: queueing processes
zbMATH Keywords: perturbation analysis algorithms
zbMATH Keywords: simulation
reviewed by: P. R. Parthasarathy
MaRDI profile type: Publication
cites work: Sensitivity analysis for stationary and ergodic queues
cites work: Sensitivity analysis for stationary and ergodic queues: additional results
cites work: A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
cites work: The limiting value of derivative estimators based on perturbation analysis
cites work: Structural Conditions for Perturbation Analysis Derivative Estimation: Finite-Time Performance Indices
cites work: Strongly Consistent Steady-State Derivative Estimates
cites work: Q4039795
cites work: Convergence Properties of Infinitesimal Perturbation Analysis Estimates
cites work: Perturbation analysis and optimization of queueing networks
cites work: Q4002098
cites work: Some inequalities for the queue GI/G/1
cites work: Q4101255
cites work: A Renewal Theoretic Approach to Bias Reduction in Regenerative Simulations
cites work: Sensitivity Analysis for Simulations via Likelihood Ratios
cites work: Open Queueing Systems in Light Traffic
cites work: Q3929947
cites work: Q4084474
cites work: Perturbation Analysis Gives Strongly Consistent Sensitivity Estimates for the M/G/1 Queue
cites work: Q3998392
cites work: Convergence Rates of Finite-Difference Sensitivity Estimates for Stochastic Systems
description: scientific article; zbMATH DE number 711801