
The Library
Series Jackson networks and noncrossing probabilities
Tools
Dieker, A. B. and Warren, Jon (2010) Series Jackson networks and noncrossing probabilities. Mathematics of Operations Research, Vol.35 (No.2). pp. 257-266. doi:10.1287/moor.1090.0421 ISSN 0364-765X.
Research output not available from this repository.
Request-a-Copy directly from author or use local Library Get it For Me service.
Official URL: http://dx.doi.org/10.1287/moor.1090.0421
Abstract
This paper studies the queue-length process in series Jackson networks with external input to the first station only. We show that its Markov transition probabilities can be written as a finite sum of noncrossing probabilities, so that questions on time-dependent queueing behavior are translated to questions on noncrossing probabilities. This makes previous work on noncrossing probabilities relevant to queueing systems and allows new queueing results to be established. To illustrate the latter, we prove that the relaxation time (i.e., the reciprocal of the "spectral gap") of a positive recurrent system equals the relaxation time of an M/M/1 queue with the same arrival and service rates as the network's bottleneck station. This resolves a conjecture of Blanc that he proved for two queues in series.
Item Type: | Journal Article | ||||
---|---|---|---|---|---|
Subjects: | H Social Sciences > HD Industries. Land use. Labor > HD28 Management. Industrial Management Q Science > QA Mathematics |
||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Journal or Publication Title: | Mathematics of Operations Research | ||||
Publisher: | Informs | ||||
ISSN: | 0364-765X | ||||
Official Date: | May 2010 | ||||
Dates: |
|
||||
Volume: | Vol.35 | ||||
Number: | No.2 | ||||
Number of Pages: | 10 | ||||
Page Range: | pp. 257-266 | ||||
DOI: | 10.1287/moor.1090.0421 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access | ||||
Funder: | IBM T.J. Watson Research Center, Yorktown Heights, New York |
Data sourced from Thomson Reuters' Web of Knowledge
Request changes or add full text files to a record
Repository staff actions (login required)
![]() |
View Item |