A model for compound poisson process queuing system with batch arrivals and services

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. © 2020 Lavoisier. All rights reserved.