A queueing system with linear repeated attempts,bernoulli schedule and feedback |
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Authors: | I Atencia P Moreno |
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Institution: | (1) Departamento de Matemática Aplicada, E.T.S.I. Telecomunicación, Universidad de Málaga, Campus de Teatinos, 29071 Málaga, Spain |
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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
=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. |
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Keywords: | Embedded Markov chain ergodicity steady-state distribution stochastic decomposition Bernoulli feedback |
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