Single Server Queueing Model with Load Dependent Service Rate Having Compound Poisson Truncated Geometric Bulk Arrivals

Abstract

This This paper addresses modeling of a single server queue administration in which the arrivals follows a compound Poisson geometric process with load dependent service. Here it is assumed that the arrivals are in bulk and can be characterized by truncated geometric distribution for the number of consumers  in each arriving module. It is further presumed aforementioned  assistance  process  accompany poisson distribution and the service rate is dependent on the content of the buffer connected to it. Using the difference differential equations, the probability generating function of the queue size distribution is derived. The system characteristics such as mean number of consumers in the queue, the utilization of the server, productive capacity service, middle stand by measure of consumer in queue, variance of consumers are derived explicitly. With  sensitive analysis it is observed that bulk size distribution parameters have significant influence on system parameters. It is also observed that load dependent service rate has influence on system performance measures and this strategy can reduce congestion in queues. This model also includes a number of sooner models as particular cases.