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On a Retrial Single-Server Queueing System with Finite Buffer and Poisson Flow

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Abstract

A retrial single-server queueing system with finite buffer is considered. The primary incoming flow is Poissonian. If the buffer is overflown, a call entering the system becomes a repeat call and joins the group of repeat calls referred to as an orbit. The maximum number of calls that can simultaneously be contained in the orbit is limited. A call from the orbit makes new attempts to enter the system until a vacancy occurs. Time between repeat attempts for each call is an exponentially distributed random variable. At the initial moment of service, a type of a call is defined: with probability a i it becomes a call of type i and its service time in this case has distribution function B i (x), i = \(\overline {1,K}\). For this system, the stationary joint distribution of queues in the buffer and orbit is found. Numerical examples are given.

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Authors
  1. P. P. Bocharov
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  2. C. D'Apice
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  3. N. H. Phong
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Bocharov, P.P., D'Apice, C. & Phong, N.H. On a Retrial Single-Server Queueing System with Finite Buffer and Poisson Flow. Problems of Information Transmission 37, 248–261 (2001). https://doi.org/10.1023/A:1013882108415

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  • DOI: https://doi.org/10.1023/A:1013882108415

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