Performance Analysis of Retrial Queueing Model with Working Vacation, Interruption, Waiting Server, Breakdown and Repair

Abstract

In this present paper, an M/M/1 retrial queueing model with a waiting server subject to breakdown and repair under working vacation, vacation interruption is considered. Customers are served at a slow rate during the working vacation period, and the server may undergo breakdowns from a normal busy state. The customer has to wait in orbit for the service until the server gets repaired. Steady-state solutions are obtained using the probability generating function technique. Probabilities of different server states and some other performance measures of the system are developed. The variation in mean orbit size, availability of the server, and server state probabilities are plotted for different values of breakdown parameter and repair rate with the help of MATLAB software. Finally, cost optimization of the system is also discussed, and the optimal value of the slow service rate for the model is obtained.

Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation

“…A retrial queue with general retrial times and single working vacation was studied by Li et al [16] by utilizing the supplementary variable method. Gupta and Kumar [17] studied a retrial queue with a single waiting server subject to breakdown and repair under working vacation and interruption. In the work of Muthusamy et al [18], they considered a working vacation retrial queue with three different classes of customers and optional reservice during working vacations in the Bernoulli schedule.…”

Optimization of M/M/2 Queueing Model with Working Vacations

“…Chakravarthy et al [8] studied MAP/PH/1 queueing model using the matrix geometric method under certain conditions like server breakdown, vacations, repairs, and backup servers and established results for steady-state analysis with illustrative examples. Gupta and Kumar [9] investigated an M/M/1 retrial queueing model with working vacation and vacation interruption due to breakdown and repair. Mean system size and probabilities in various server states are obtained using the probability-generating function technique.…”