Paper Info
Title
Ordinary CLT and WLLN versions of L=λW
Abstract
The familiar queueing principle expressed by the formula L = λW Little's law can be interpreted as a relation among strong laws of large numbers SLLNs. Here we prove central-limit-theorem CLT and weak-law-of-large-numbers WLLN versions of L = λW. For example, if the sequence of ordered pairs of interarrival times and waiting times is strictly stationary and satisfies a joint CLT, then the queue-length process also obeys a CLT with a related limiting distribution. In a previous paper we proved a functional-central-limit-theorem version of L = λW, without stationarity, by very different arguments. The two papers highlight the differences between establishing ordinary limit theorems and their functional-limit-theorem counterparts.
Year
DOI
Venue
1988
10.1287/moor.13.4.674
Mathematics of Operations Research
Keywords
DocType
Volume
queueing theory,central limit ae»ems,Ordinary CLT,random sums,conservation laws. little's law,inverse processes.,law of large numbers,WLLN version
Journal
13
Issue
ISSN
Citations 
4
0364-765X
19
PageRank 
References 
Authors
13.40
1
2
Name
Order
Citations
PageRank
Peter W. Glynn11527293.76
Ward Whitt21509658.94