Title of article :
A stochastic version analysis of an M/G/1 retrial queue with Bernoulli schedule
Author/Authors :
Boualem ، M. - University of Bejaia , Cherfaoui ، M. - University of Biskra , Djellab ، N. - University of Badji Mokhtar , Aissani ، D. - University of Bejaia
Abstract :
In this work, we derive insensitive bounds for various performance measures of a singleserver retrial queue with generally distributed interretrial times and Bernoulli schedule, under the special assumption that only the customer at the head of the orbit queue (i.e., a FCFS discipline governing the flow from the orbit to the server) is allowed to occupy the server. The methodology is strongly based on stochastic comparison techniques. Instead of studying a performance measure in a quantitative fashion, this approach attempts to reveal the relationship between the performance measures and the parameters of the system. We prove the monotonicity of the transition operator of the embedded Markov chain relative to strong stochastic ordering and increasing convex ordering. We obtain comparability conditions for the distribution of the number of customers in the system. Bounds are derived for the stationary distribution and some simple bounds for the mean characteristics of the system. The proofs of these results are based on the validation of some inequalities for some cumulative probabilities associated with every state (m, n) of the system. Finally, the effects of various parameters on the performance of the system have been examined numerically.
Keywords :
Retrial queues , performance measures , stochastic orders , monotonicity , simulation.
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
