Estimation of waiting time distribution in an M/M/1 Queue

Estimation of waiting time distribution in the form of its right tail area, known as exceedance probability is carried out in an M/M/1/FCFS/ ∞ / ∞ queue with the help of data consists of non zero waiting time of randomly chosen customer from n independent queues and number of queues with zero waiting time. In the first section, MLE of rate parameters and exceedance probability are obtained and their large sample behaviour is studied. Next section, Bayes estimators of the same parametric function along with the minimum Bayes risks have been derived under squared error loss using McKay’s Bivariate Gamma as prior and also independent Gamma as prior with the prior for arrival rate being truncated between 0 and μ. Some numerical calculations are shown in the last section.