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

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 ex-ogenously 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. Other-wise 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 net-work 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 phenomena.

Original languageEnglish
Pages (from-to)753-765
Number of pages13
JournalJournal of Industrial and Management Optimization
Volume7
Issue number3
DOIs
Publication statusPublished - 2011 Aug 1

Fingerprint

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

Keywords

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

ASJC Scopus subject areas

  • Business and International Management
  • Strategy and Management
  • Applied Mathematics
  • Control and Optimization

Cite this

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