Abstract
Queueing theory is being developed with new models to predict the behavior of systems that attempt to provide service for randomly arising demands. A queueing system can be described as customers arriving for service, waiting for service if the server is busy, and leaving the system after receiving the service. In this paper the actual number of customers in an arrival epoch is considered as a random variable X and the Queueing system is developed for atleast k arrivals in a batch. It is assumed that the arrival rate of bulk batches follow Poisson Process with a constant rate. The new Probability generating function and its associated batch size probability distributions are derived. Measures of effectiveness of the Queueing system are evaluated and provided with appropriate illustrations.
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