Abstract
The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results.
Highlights
Queueing systems with repeated attempts have been widely used to model many problems in telecommunication and computer systems [1,2,3]
Kumar et al [19] consider an M/G/1 retrial queue with feedback and starting failure, which occurs in the startup period and its repair can be interpreted as a warm up period
Atencia et al [23] analysed a retrial queue with active breakdowns where the interrupted customers have the option of joining the orbit or remaining in the server for the repair in order to conclude their remaining service
Summary
Queueing systems with repeated attempts have been widely used to model many problems in telecommunication and computer systems [1,2,3]. Mokdad and Castel-Taleb [36] propose to use a mathematical method based on stochastic comparisons of Markov chains in order to derive performance indices bounds of fixed and mobile networks Their main objective consists in finding Markovian bounding models with reduced state spaces, which are easier to solve. We use the general theory of stochastic ordering to study monotonicity properties similar to that of Boualem et al [35], for a single server retrial queue with server subject to active breakdowns, that is, the service station can fail only during the service period, relative to the strong stochastic ordering, convex ordering, and Laplace ordering.
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