In this work, we study an M∕M∕1∕N queuing system with multiple vacations, Bernoulli feedback, balking, reneging and retention of the impatient customers, and the possibility of a server breakdown and repair. First, by using the Q-matrix (infinitesimal generator matrix) method, we obtain the steady-state probabilities of the system. Then, some useful performance measures are derived. Finally, the influence of the reliability parameters on the performance measures of the system has been examined numerically.

No abstract

In this work, we considered the parametric estimation of the characteristics of the M / M / 1 / N {M/M/1/N} waiting model with Bernoulli feedback. Through a Monte-Carlo simulation study, we have illustrated the effect of the estimation of the starting parameters of the considered waiting system on the statistical properties of its performance measures estimates, when these latter are obtained using the plug-in method. In addition, several types of convergence (bias, variance, MSE, in law) of these performance measure estimators have also been showed by simulation.

No abstract