Single Server Poisson Queueing Model with Additive Exponential Service Time Distribution

A stochastic process associated with queuing system is specified by the knowledge of (i) Arrival process (ii) Queue discipline (iii) Service process. Among these three, the service process is more important since it can be controlled by the operators of the system. A long with many other assumptions, it is customary to consider that the inter service time are Exponential. A generalization of it is Erlangian service time in which it is assumed that there are k-phase of service and each have identically distributed as Negative Exponential Distribution. But in many practical situations the service times are not identical. Hence in this paper we consider a queueing system with Poisson arrival having component of additive exponential service times. Using the probability generating function the system size distribution is derived. The system behaviour analyzed by deriving the system characteristics like, average number of customer in the system, the variability of system size, etc,. The waiting time distribution of the system is also derived. The sensitivity of the model with respect to the parameter is analyzed. It is observed that the system performance is influenced by the service time distribution parameters. This model includes M/M/1, M/E/1 models as particular cases for specific or timely value of parameters.