• TRANSIENT ANALYSIS OF SINGLE SERVER QUEUEING SYSTEM WITH BATCH SERVICE UNDER CATASTROPHE

Abstract

Consider a single server queueing system with batch service and Catastrophe in which the arrival rate λ follows a Poisson process and the service time follows an exponential distribution with parameter μ. Further we assume that the catastrophe occur at the rate of ν and follows a Poisson process. As and when the customers come, they enter into the system and the service will be initiated by the server only if there is a batch of k customers in the system and this batch of customers will  leave from the system after the completion of service. In this batch service model, we are analyzing the possibility of catastrophe that is whenever a catastrophe occurs at the system, all the customers who are in the system will be completely destroyed and system becomes an empty and server becomes an idle. This model is completely solved by constructing the generating function and Rouche’s theorem is applied and we have derived the closed form solutions for probability of number of customers in the queue during the server idle and busy. Further we are providing the analytical solution for mean number of customers and variance of the system. Numerical studies have been done for analysis of mean and variance for various values of λ, µ, ν and k and also various particular cases of this model have been discussed.