Upper and lower bounds for the waiting time in the symmetric shortest queue system
type: Item
instance of: scholarly article
title: Upper and lower bounds for the waiting time in the symmetric shortest queue system
zbMATH Open document ID: 0795.60090
DOI: 10.1007/BF02024665
author: G. J. Van Houtum
author: Jan van der Wal
author: Ivo Adan
published in: Annals of Operations Research
publication date: 1994-04-07T00:00:00Z
review text: The classical shortest queue model with two servers is considered. To evaluate performance of the system numerically with error bounds the authors introduce two auxiliary models: the shortest queue system with threshold jockeying and the shortest queue system with threshold blocking. In the system with threshold jockeying one customer moves from the longest queue to the shortest queue as soon as the difference between these queues exceeds a certain threshold. In the system with threshold blocking the server in the shortest queue is switched of as soon as the difference between these queues reaches a certain threshold. The main result of the paper states that the total number of customers in the original system is stochastically less (greater) than the total number of customers in the system with threshold blocking (jockeying). Since the auxiliary systems can be effectively analyzed numerically with the help of matrix-geometric technique due to M. Neuts, this allows calculation of performance characteristics of the original system.
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 513135
zbMATH Keywords: numerical analysis
zbMATH Keywords: threshold jockeying
zbMATH Keywords: threshold blocking
zbMATH Keywords: matrix- geometric technique
zbMATH Keywords: performance characteristics
reviewed by: G. I. Falin
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02024665
OpenAlex ID: W2121943414
description: scientific article; zbMATH DE number 513135