Optimality of the shortest line discipline with state-dependent service rates
type: Item
instance of: scholarly article
title: Optimality of the shortest line discipline with state-dependent service rates
zbMATH Open document ID: 0675.60084
DOI: 10.1016/0377-2217(89)90378-0
author: Pravin K. Johri
published in: European Journal of Operational Research
publication date: 1989-01-01T00:00:00Z
review text: The paper deals with the shortest line discipline, also known as the join the shortest queue (JSQ) rule extended to queues with state-dependent, exponential service rates, which include queues with multiple exponential servers. It is assumed that arrivals occur according to an independent Poisson process. Service times are exponentially distributed. There is a single server in each queue whose service rate depends on the number of customers in its queue. In particular if there are k customers in the queue, then the service rate is \(\mu_ k\). The sequence \(\{\mu_ k\}\) of service rates is assumed to be non-decreasing and bounded with the concavity property that the increment \(\mu_{k+1}-\mu_ k\) is non- increasing in k. It is shown that JSQ stochastically minimizes the number of customers in the system at any time \(t>0\) and also minimizes the long run average response (waiting) time.
reviewed by: János Sztrik
Mathematics Subject Classification ID: 60K25
Mathematics Subject Classification ID: 90B22
zbMATH DE Number: 4106015
zbMATH Keywords: shortest line discipline
zbMATH Keywords: multiple exponential servers
zbMATH Keywords: concavity property
MaRDI profile type: Publication
full work available at URL: 0377-2217(89)90378-0
OpenAlex ID: W1973362606
cites work: A simple dynamic routing problem
cites work: Stochastically minimizing the number of customers in exponential queueing systems
cites work: Applying a New Device in the Optimization of Exponential Queuing Systems
cites work: On the optimal assignment of customers to parallel servers
cites work: Deciding Which Queue to Join: Some Counterexamples
cites work: Optimality of the shortest line discipline
description: scientific article; zbMATH DE number 4106015