Paper Info
Title
Deciding Which Queue to Join: Some Counterexamples
Abstract
Consider a queueing system with two or more servers, each with its own queue with infinite capacity. Customers arrive according to some stochastic process e.g., a Poisson process and immediately upon arrival must join one of the queues, thereafter to be served on a first-come first-served basis, with no jockeying or defections allowed. The service times are independent and identically distributed with a known distribution. Moreover, the service times are independent of the arrival process and the customer decisions. The only information about the history of the system available for deciding which queue to join is the number of customers currently waiting and being served at each server. Joining the shortest queue is known to minimize each customer's individual expected delay and the long-run average delay per customer when the service-time distribution is exponential or has nondecreasing failure rate. We show that there are service-time distributions for which it is not optimal to always join the shortest queue. We also show that if, in addition, the elapsed service times of customers in service are known, the long-run average delay is not always minimized by customers joining the queue that minimizes their individual expected delays.
Year
DOI
Venue
1986
10.1287/opre.34.1.55
Operations Research
Field
DocType
Volume
Mathematical optimization,Bulk queue,Multilevel queue,Computer science,Queue,Priority queue,Independent and identically distributed random variables,M/M/∞ queue,Fork–join queue,Queue management system
Journal
34
Issue
ISSN
Citations 
1
0030-364X
107
PageRank 
References 
Authors
17.28
6
1
Search Limit
100107
Name
Order
Citations
PageRank
Ward Whitt11509658.94