A Model for Compound Poisson Process Queuing System with Batch Arrivals and Services

Abstract

Computing and logistics management systems have a wide area of applications with compound Poisson process Markov system with a batch servicing facility where customers arrive either independently or batches for service into the multi-server queues. The service of the customers is processed either independently or batch-wise based on the requirement of various sizes. The order of service has been found to follow First Come First Service while customers arrive according to the exponential distribution. A mathematical model is proposed to process customers by using generalized spectral expansion method. The explicit type required to service the system is measured as buffer size. For accurate assessment of performance, numerical results have been depicted in graphical form. Keywords:mean queue length, batch arrivals and batch services, QBD -M, multi-server system, compound poisson process THE STEADY-STATE ANALYSIS AND QBD -M PROCESS WITH MULTIPLE JUMPSThe multiprocessor system is modeled by generalized finite QBD -M (Quasi Birth and Death) process with multiple boundaries. Here, the parameter M refers to multiple jumps in the level dimension. A novel approach theory has been evaluated for the steady-state analysis of the system. Unlike

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