Queue-length balance equations in multiclass multiserver queues and their generalizations

M.A.A. Boon, O.J. Boxma, O. Kella, M. Miyazawa

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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Uittreksel

A classical result for the steady-state queue-length distribution of single-class queueing systems is the following: The distribution of the queue length just before an arrival epoch equals the distribution of the queue length just after a departure epoch. The constraint for this result to be valid is that arrivals, and also service completions, with probability one occur individually, i.e., not in batches. We show that it is easy to write down somewhat similar balance equations for multidimensional queue-length processes for a quite general network of multiclass multiserver queues. We formally derive those balance equations under a general framework. They are called distributional relationships and are obtained for any external arrival process and state-dependent routing as long as certain stationarity conditions are satisfied and external arrivals and service completions do not simultaneously occur. We demonstrate the use of these balance equations, in combination with PASTA, by (1) providing very simple derivations of some known results for polling systems and (2) obtaining new results for some queueing systems with priorities. We also extend the distributional relationships for a nonstationary framework.

Originele taal-2Engels
Pagina's (van-tot)277-299
Aantal pagina's23
TijdschriftQueueing Systems
Volume86
Nummer van het tijdschrift3-4
DOI's
StatusGepubliceerd - 22 mei 2017

Vingerafdruk

Multi-server
Balance Equations
Queue Length
Multi-class
Queue
Queueing System
Completion
Polling Systems
Queue Length Distribution
Steady-state Distribution
Stationarity
Batch
Routing
Valid
Generalization
Dependent
Demonstrate
Relationships
Framework

Citeer dit

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Queue-length balance equations in multiclass multiserver queues and their generalizations. / Boon, M.A.A.; Boxma, O.J.; Kella, O.; Miyazawa, M.

In: Queueing Systems, Vol. 86, Nr. 3-4, 22.05.2017, blz. 277-299.

Onderzoeksoutput: Bijdrage aan tijdschriftTijdschriftartikelAcademicpeer review

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