M/M/1 RETRIAL QUEUES WITH CONSTANT RETRIAL POLICY
DOI:
https://doi.org/10.67772/5j4cyv62Keywords:
Retrial queue, orbit, infinitesimal generator matrix, constant retrial rate, matrix-geometric method, quasi-birth-and-death processAbstract
An M/M/1 retrial queue with constant retrial policy is discussed. The system is modelled as a level-independent quasi-birth-and-death (QBD) process and its infinitesimal generator matrix is obtained. The stability condition λλ+μ<μν is derived from the mean drift condition. The rate matrix R of the matrix-geometric method is obtained in closed form, and from it the limiting probabilities of the system are calculated explicitly. Several performance measures, such as the mean orbit size, the mean system size, the mean waiting times and the expected number of retrials, are derived. The analytical results are verified numerically and by simulation, and the effect of the system parameters is illustrated through tables and graphs.
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