A Survey and Experimental Comparison of Service-Level-Approximation Methods for Nonstationary M(t)/M/s(t) Queueing Systems with Exhaustive Discipline

We compare the performance of seven methods in computing or approximating service levels for nonstationary M(t)/M/s(t) queueing systems: an exact method (a Runge-Kutta ordinary-differential-equation solver), the randomization method, a closure (or surrogate-distribution) approximation, a direct infi...

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Bibliographic Details
Published inINFORMS journal on computing Vol. 19; no. 2; pp. 201 - 214
Main Authors Ingolfsson, Armann, Akhmetshina, Elvira, Budge, Susan, Li, Yongyue, Wu, Xudong
Format Journal Article
LanguageEnglish
Published Linthicum INFORMS 01.05.2007
Institute for Operations Research and the Management Sciences
Subjects
Accuracy
Algorithms
Analysis
Approximation
Approximation theory
approximations
Call centers
Comparative studies
Customer services
Labor costs
Methods
nonstationary
Ordinary differential equations
Performance evaluation
Probability
queues
Queuing theory
Randomized algorithms
Schedules
Servers
Service industries
Software
Workforce planning
Canada
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Summary:We compare the performance of seven methods in computing or approximating service levels for nonstationary M(t)/M/s(t) queueing systems: an exact method (a Runge-Kutta ordinary-differential-equation solver), the randomization method, a closure (or surrogate-distribution) approximation, a direct infinite-server approximation, a modified-offered-load infinite-server approximation, an effective-arrival-rate approximation, and a lagged stationary approximation. We assume an exhaustive service discipline, where service in progress when a server is scheduled to leave is completed before the server leaves. We used all of the methods to solve the same set of 640 test problems. The randomization method was almost as accurate as the exact method and used about half the computational time. The closure approximation was less accurate, and usually slower, than the randomization method. The two infinite-server-based approximations, the effective-arrival-rate approximation, and the lagged stationary approximation were less accurate but had computation times that were far shorter and less problem-dependent than the other three methods.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1050.0157