Series Jackson networks and noncrossing probabilities
Dieker, A. B. and Warren, Jon. (2010) Series Jackson networks and noncrossing probabilities. Mathematics of Operations Research, Vol.35 (No.2). pp. 257-266. ISSN 0364-765XFull text not available from this repository.
Official URL: http://dx.doi.org/10.1287/moor.1090.0421
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 > Statistics|
|Journal or Publication Title:||Mathematics of Operations Research|
|Number of Pages:||10|
|Page Range:||pp. 257-266|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||IBM T.J. Watson Research Center, Yorktown Heights, New York|
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