Abstract
We analyse a single-server retrial queueing system with infinite buffer, Poisson arrivals, general distribution of service time and linear retrial policy. If an arriving customer finds the server occupied, he joins with probabilityp a retrial group (called orbit) and with complementary probabilityq a priority queue in order to be served. After the customer is served completely, he will decide either to return to the priority queue for another service with probability ϑ or to leave the system forever with probability\(\bar \theta \)=1−ϑ, where 0≤ϑ<1. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime. Moreover, we obtain the generating function of system size distribution, which generalizes the well-knownPollaczek-Khinchin formula. Also we obtain a stochastic decomposition law for our queueing system and as an application we study the asymptotic behaviour under high rate of retrials. The results agree with known special cases. Finally, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.
Similar content being viewed by others
References
Artalejo J.R. and Falin G.I. (1994). Stochastic decomposition for retrial queues.Top 2, 329–342.
Artalejo J.R. and Gómez-Corral A. (1997). Steady state solution of a single-server queue with linear repeated requests.Journal of Applied Probability 34, 223–233.
Artalejo J.R. (1998). Some results on theM/G/1 queue withN-policy.Asia-Pacific Journal of Operational Research 15, 147–157.
Atencia I., Bouza G. and Rico R. (2002). A queueing system with constant repeated attempts and Bernoulli schedule. Fifth International Conference on Operations Research, La Habana, Cuba.
Choi B.D. and Kulkarni V.G. (1992). Feedback retrial queueing systems. In: Bhat U.N. and Basawa I.V. (eds.),Queueing and related models. Oxford University Press, 93–105.
Choi B.D. and Park K.K. (1990). TheM/G/1 retrial queue with Bernoulli schedule.Queueing Systems 7, 219–227.
Falin G.I., Artalejo J.R. and Martin M. (1993). On the single server retrial queue with priority customers.Queueing Systems 14, 439–455.
Fayolle G. (1986). A simple telephone exchange with delayed feedbacks.Teletraffic Analysis and Computer Performance Evaluation 22, 245–253.
Langaris C. and Moutzoukis E. (1995). A retrial queue with structured batch arrivals, priorities and server vacations.Queueing Systems 20, 341–368.
Moutzoukis E. and Langaris C. (1996). Non-preemptive priorities and vacations in a multiclass retrial queueing system.Stochastic Models 12, 455–472.
Pakes A.G. (1969). Some conditions for ergodicity and recurrence of Markov chains.Operations Research 17, 1058–1061.
Takacs L. (1963). A single-server queue with feedback.Bell System Technical Journal 42, 505–519.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Atencia, I., Moreno, P. A queueing system with linear repeated attempts, bernoulli schedule and feedback. Top 11, 285–310 (2003). https://doi.org/10.1007/BF02579046
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02579046