Stability of a retrial queueing network with different classes of customers and restricted resource pooling

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider a retrial queueing network with different classes of customers and several servers. Each customer class is associated with a set of servers who can serve the class of customers. Customers of each class exogenously arrive according to a Poisson process. If an exogenously arriving customer finds upon his arrival any idle server who can serve the customer class, then he begins to receive a service by one of the available servers. Otherwise he joins the retrial group, and then tries his luck again after exponential time, the mean of which is determined by his customer class. Service times of each server are assumed to have general distribution. The retrial queueing network can be represented by a Markov process, with the number of customers of each class, and the customer class and the remaining service time of each busy server. Using the fluid limit technique, we find a necessary and sufficient condition for the positive Harris recurrence of the representing Markov process. This work is the first that applies the fluid limit technique to a model with retrial phenomenon.

Original languageEnglish
Title of host publication5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings
Pages87-93
Number of pages7
DOIs
Publication statusPublished - 2010 Sep 8
Event5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Beijing, China
Duration: 2010 Jul 242010 Jul 26

Other

Other5th International Conference on Queueing Theory and Network Applications, QTNA 2010
CountryChina
CityBeijing
Period10/7/2410/7/26

Fingerprint

Retrials
Queueing networks
Queueing Networks
Pooling
Servers
Customers
Resources
Server
Fluid Limits
Markov processes
Markov Process
Fluids
Harris Recurrence
Positive Recurrence
Luck
Class
Exponential time
Poisson process
Join
Necessary Conditions

Keywords

  • Fluid limit
  • Positive Harris recurrence
  • Resource pooling
  • Retrial queue
  • Stability

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Theoretical Computer Science

Cite this

Kim, B. (2010). Stability of a retrial queueing network with different classes of customers and restricted resource pooling. In 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings (pp. 87-93) https://doi.org/10.1145/1837856.1837870

Stability of a retrial queueing network with different classes of customers and restricted resource pooling. / Kim, Bara.

5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings. 2010. p. 87-93.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kim, B 2010, Stability of a retrial queueing network with different classes of customers and restricted resource pooling. in 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings. pp. 87-93, 5th International Conference on Queueing Theory and Network Applications, QTNA 2010, Beijing, China, 10/7/24. https://doi.org/10.1145/1837856.1837870
Kim B. Stability of a retrial queueing network with different classes of customers and restricted resource pooling. In 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings. 2010. p. 87-93 https://doi.org/10.1145/1837856.1837870
Kim, Bara. / Stability of a retrial queueing network with different classes of customers and restricted resource pooling. 5th International Conference on Queueing Theory and Network Applications, QTNA 2010 - Proceedings. 2010. pp. 87-93
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