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Bounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls
- Source :
- Yugoslav Journal of Operations Research, Vol 29, Iss 3, Pp 375-391 (2019)
- Publication Year :
- 2019
- Publisher :
- National Library of Serbia, 2019.
-
Abstract
- In this article we analyze the M=G=1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that cannot be analyzed numerically, we propose to bound it by a new Markov chain, which is easier to solve by using a stochastic comparison approach. Particularly, we study the monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M=M=1 retrial queue with two-way communication and n types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.
- Subjects :
- Discrete mathematics
Stationary distribution
outgoing calls
Markov chain
Service time
Regular polygon
Monotonic function
Retrial queue
Management Science and Operations Research
retrial queues
stochastic comparison
Distribution (mathematics)
markov chain
lcsh:T58.6-58.62
lcsh:Management information systems
Two-way communication
Mathematics
Subjects
Details
- ISSN :
- 1820743X and 03540243
- Volume :
- 29
- Database :
- OpenAIRE
- Journal :
- Yugoslav Journal of Operations Research
- Accession number :
- edsair.doi.dedup.....3eaa13f01a5440deaad6ed65877f70ff