Numerical optimization of a queueing system by dynamic programming
type: Item
instance of: scholarly article
title: Numerical optimization of a queueing system by dynamic programming
zbMATH Open document ID: 0677.65147
DOI: 10.1016/0022-247X(89)90207-2
author: S. H. Smith
published in: Journal of Mathematical Analysis and Applications
publication date: 1989-01-01T00:00:00Z
review text: A numerical method for determining the optimal number of servers of a time-dependent multiserver queueing system is presented. First, a queueing system with time-dependent arrival rate is solved numerically to obtain the state probabilities and the expected number of customers in queue. The corresponding finite set of linear differential-difference equations is solved by the fourth-order Runge-Kutta method. Then, using the just obtained probabilities and queue sizes, dynamic programming is implemented to determine the optimal number of servers during each 8-h shift of a 24-h day. A numerical example, considering the arrival and service of aircrafts in an airport, is solved.
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 65K05
zbMATH DE Number: 4110062
zbMATH Keywords: optimal number of servers
zbMATH Keywords: multiserver queueing system
zbMATH Keywords: time-dependent arrival rate
zbMATH Keywords: linear differential-difference equations
zbMATH Keywords: fourth-order Runge-Kutta method
zbMATH Keywords: dynamic programming
zbMATH Keywords: numerical example
zbMATH Keywords: service of aircrafts in an airport
reviewed by: Petko Hr. Petkov
MaRDI profile type: Publication
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full work available at URL: 0022-247x(89)90207-2
OpenAlex ID: W2000402247
description: scientific article; zbMATH DE number 4110062