A stochastic version analysis of an M/G/1 retrial queue with Bernoulli‎ ‎schedule‎

In this worký, ýwe derive insensitive bounds for various performance measures of a single-serverý ýretrial queue with generally distributed inter-retrial times and Bernoulli scheduleý, ýunder the specialý ýassumption that only the customer at the head of the orbit queue (i.e.ý, ýaý ýFCFS discipline governing the flow from the orbit to the server) is allowedý ýto occupy the serverý. ýThe methodology is strongly based on stochastic comparison techniquesý. ýInstead of studying a performance measure in a quantitative fashioný, ýthis approach attempts to reveal the relationship between the performance measures and the parameters of the systemý. ýWe prove the monotonicity of the transition operator of the embedded Markov chain relative to strong stochastic ordering and increasing convex orderingý. ýWe obtain comparability conditions for the distribution of the number of customers in the systemý. ýBounds are derived for the stationary distribution andý ýsome simple bounds for the mean characteristics of the systemý. ýThe proofs of these results are based on the validation of some inequalities for some cumulative probabilities associated with every state (mý,ýn) of the systemý. ýFinallyý, ýthe effects of various parameters on the performance of the system have been examined numerically.