Retrial queueing systems modelling with interrupted service and orbital search
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Date
2024
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Université Badji Mokhtar Annaba
Abstract
In this work, we first propose an M/M/1 retrial queue system with interrupted service by the customer being served, where the access to the orbit is done after a first pass through the server, and we also consider a single server, whose orbit and queue have infinite capacity. Our interest is in the customers who can decide between leaving the system forever or joining the orbit for coming back again to the server after a random time in order to get another service, so we present the generation functions of different stationary distributions and the calculation of some performance measures. Using the infinitesimal generator, we obtain the stationary distributions of this model, and we also use the matrix analytical method to provide some numerical results to illustrate the impact of different parameters on the model's characteristics.
In addition to the above assumptions, we assume that the retrial policy is linear. Then, we generalize the first model, taking into account the fact that the access to the server can be made in the following three cases: from the queue by a primary customer, or from the orbit by a secondary customer (who have already made at least one pass through the server), or the server itself searches for customers in orbit immediately after the end of a service (assuming the queue is free).
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Keywords
retrial queue; interrupted service; orbital search; linear retrial policy; matrix-analytic method; performance measure