Bayesian Predictions in M/G/ 1 Queueing System

In this paper we consider M/G/1 queueing system. We assume that there is a single server and the customers arrive according to Poisson process with mean and service time distribution is general. Let the state of the system be defined by a pair of variables the number X(t) in the system at epoch t and the elapsed serviced time Y(t) of the customer who is under going service. Then we have studied the bivariate Markovian process {X(t), Y(t)} in order to obtain the results of Non-Markovian process {X(t)}. In M/G/1 queueing system customer’s arrival follow a Poisson process with mean rate and are served one at a time on FCFS basis. The general aim here is to analyze from Bayesian point of view the available information about the unknown parameter vector = ( , μ). To obtain sample information about the queue system, we observe n interarrival times say xi (i=1, 2, ....n) and simultaneously or not, m complete service times yj (j=1, 2, ....m). This design is not the one most widely used by the classical approach providing complete sample information about the system which consists in observing the arrival and service processes simultaneously and continuously over a fixed period of time.