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.
- M. S. Aguir, F. Karaesmen, O. Z. Akşin and F. Chauvet, The impact of retrials on call center performance, OR Spectrum 26 (2004), 353--376.Google ScholarCross Ref
- M. S. Aguir, O. Z. Akşin, F. Karaesmen and Y. Dallery, On the interaction between retrials and sizing of call centers, European Journal of Operational Research 191 (2008), 398--408.Google ScholarCross Ref
- J. R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990--1999, Top 7 (1999), 187--211.Google ScholarCross Ref
- J. R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model. 30 (1999), 1--6. Google ScholarDigital Library
- J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000--2009, to appear in Math. Comput. Model.Google Scholar
- J. R. Artalejo, A. Economou and A. Gómez-Corral, Applications of maximum queue lengths to call center management, Computers & Operations Research 34 (2007), 983--996.Google Scholar
- J. R. Artalejo and A. Gómez-Corral, Retrial Queueing Systems, Springer, 2008.Google ScholarCross Ref
- J. R. Artalejo and A. Pla, On the impact of customer balking, impatience and retrials in telecommunication systems, Computers and Mathematics with Applications 57 (2009), 217--229. Google ScholarDigital Library
- M. Bramson, "Stability of two families of queueing networks and a discussion of fluid limits", Queueing Systems, 28, 7--31, 1998. Google ScholarDigital Library
- H. Chen, "Fluid approximations and stability of multiclass queueing networks I: work conserving disciplines", Annals of Applied Probability, 5, 637--665, 1995.Google ScholarCross Ref
- B. D. Choi and B. Kim, "Non-ergodicity Criteria for Denumerable Continuous Time Markov Processes", Operations Research Letters, Vol. 5 No. 6, 574--580, Nov., 2004. Google ScholarDigital Library
- J. G. Dai, "On positive Harris recurrence of multiclass queueing network: A unified approach via fluid limit models", Annals of Applied Probability, 5, 49--77, 1995.Google ScholarCross Ref
- J. G. Dai, "A fluid-limit model criterion for instability of multiclass queueing networks", Annals of Applied Probability, 6, 751--757, 1996.Google ScholarCross Ref
- J. G. Dai, J. J. Hasenbein and B. Kim, "Stability of Join-the-Shortest-Queue Networks", Queueing Systems, Vol. 57, No. 4, 129--145, December, 2007. Google ScholarDigital Library
- G. I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127--168. Google ScholarDigital Library
- G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.Google Scholar
- R. Foley and D. McDonald, "Join the shortest queue: Stability and exact asymptotics", Preprint, Georgia Institute of Technology and University of Ottawa, 1999.Google Scholar
- S. Foss and N. Chernova, "On the stability of partially accessible queue with state-dependent routing", Queueing Systems, 29, 55--73, 1998. Google ScholarDigital Library
- B. Kim and I. Lee, "Tests for Nonergodicity of Denumerable Continuous Time Markov Processes", Computers and Mathematics with Applications, Vol. 55, No. 6, 1310--1321, March, 2008. Google ScholarDigital Library
- J. Kim, J. Kim and B. Kim, Tail asymptotics for the queue size distribution in the M/M/m retrial queue, submitted.Google Scholar
- I. A. Kurkova, "A Load-Balanced Network with Two Servers", Queueing Systems, 37, 379--389, 2001. Google ScholarDigital Library
- Yu. M. Suhov and N. D. Vvedenskaya, "Fast Jackson-type networks with dynamic routing", Problems of Information Transmission, 38(2), 136--153, 2002. Google ScholarDigital Library
- T. Yang and J. G. C. Templeton, A survey on retrial queues, Queueing Systems 2 (1982), 201--233. Google ScholarDigital Library
Index Terms
- Stability of a retrial queueing network with different classes of customers and restricted resource pooling
Recommendations
A repairable queueing model with two-phase service, start-up times and retrial customers
A repairable queueing model with a two-phase service in succession, provided by a single server, is investigated. Customers arrive in a single ordinary queue and after the completion of the first phase service, either proceed to the second phase or join ...
Multi-server retrial queue with negative customers and disasters
AbstractWe consider a multi-server retrial queue with waiting places in service area and four types of arrivals, positive customers, disasters and two types of negative customers, one for deleting customers in orbit and the other for deleting customers in ...
Stability analysis of single server retrial queueing system with Erlang service
QTNA '11: Proceedings of the 6th International Conference on Queueing Theory and Network ApplicationsThe objective of this paper is to study the stability analysis of single server retrial queueing system with Erlang-k service under various constraints over the behavior of server and customers, in which customers arrive in a Poisson process with ...
Comments