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Stability Analysis and Simulation of N-class Retrial System with Constant Retrial Rates and Poisson Inputs
- Source :
- Asia-Pacific Journal of Operational Research, Asia-Pacific Journal of Operational Research, World Scientific Publishing, 2014, 31 (02), pp.18. ⟨10.1142/S0217595914400028⟩, ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, Asia-Pacific Journal of Operational Research, 2014, 31 (02), pp.18. ⟨10.1142/S0217595914400028⟩
- Publication Year :
- 2014
- Publisher :
- HAL CCSD, 2014.
-
Abstract
- In this paper, we study a new retrial queueing system with N classes of customers, where a class-i blocked customer joins orbit i. Orbit i works like a single-server queueing system with (exponential) constant retrial time (with rate [Formula: see text]) regardless of the orbit size. Such a system is motivated by multiple telecommunication applications, for instance wireless multi-access systems, and transmission control protocols. First, we present a review of some corresponding recent results related to a single-orbit retrial system. Then, using a regenerative approach, we deduce a set of necessary stability conditions for such a system. We will show that these conditions have a very clear probabilistic interpretation. We also performed a number of simulations to show that the obtained conditions delimit the stability domain with a remarkable accuracy, being in fact the (necessary and sufficient) stability criteria, at the very least for the 2-orbit M/M/1/1-type and M/Pareto/1/1-type retrial systems that we focus on.
- Subjects :
- Retrial system
Technology and Engineering
Real-time computing
Ocean Engineering
Management Science and Operations Research
Poisson distribution
Stability (probability)
Retrial system, constant retrial rate, stability condition, regenerative approach, busy probability, multi-class system
stability condition
multi-class system
symbols.namesake
[INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI]
Applied mathematics
Queues
busy probability
Queue
Mathematics
Probabilistic logic
Exponential function
Computer Science::Performance
Stability conditions
symbols
regenerative approach
Orbit (control theory)
Constant (mathematics)
constant retrial rate
Subjects
Details
- Language :
- English
- ISSN :
- 02175959
- Database :
- OpenAIRE
- Journal :
- Asia-Pacific Journal of Operational Research, Asia-Pacific Journal of Operational Research, World Scientific Publishing, 2014, 31 (02), pp.18. ⟨10.1142/S0217595914400028⟩, ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH, Asia-Pacific Journal of Operational Research, 2014, 31 (02), pp.18. ⟨10.1142/S0217595914400028⟩
- Accession number :
- edsair.doi.dedup.....f95f8df52cbec6f1c71ccda5384612e9