• ANALYSIS OF MARKOVIAN QUEUEING SYSTEM AND PERFORMANCE MEASURES OF BULK ARRIVAL SYSTEM BY USING FIRST COME FIRST SERVE AND BULK SERVICE

Abstract

This paper analyzes a single server queueing model with Markov process where customers arrive according to the Poisson process and served with the two types of distributions Exponential distribution and Erlang distribution. According to the service discipline rule FCFS for the first ‘w’ number of customers are served by the Exponential distribution after that server starts providing service to other customers in batches to reach the system capacity M. We determine the Joint Distribution of the number of customers in the queue and the number with the departing batch at departure epoch by tracking down the number left behind in the queue by departing batch. Our aim is to determine the probability that server is busy and measures the performance of the system, number of customer in the queue, number of customers in the system, waiting time of the customers in the system with the help of theorem.