Compound intervened poisson distribution through one server queuing model with non-homogeneous compound poisson arrivals in bulk and its service rates

Abstract

Queuing models are used to determine the pragmatic approach in different fields of engineering, sciences, and allied areas. Most of these, the arrivals are dependent on time and would be described by a Poisson process which is non-homogeneous. In this research paper, a one-server queuing model with model with non-homogeneity compound Poisson bulk arrivals has been studied with Compound Intervention Poisson distribution (CIPD). It is observed that the system performance measures are highly influenced by non-homogeneous bulk arrivals rate and batch size distribution parameters. Simulated studies presented that the intervened and compound intervened parameter increases the service rate in terms of utilization, the mean number of customer who undertakes service and emptiness pattern in the queue. Sensitivity analysis has been carried out for the developed model. Non-Homogeneous Poisson process, bulk arrivals, state dependent service rates, Compound Intervened Poisson distribution

Subject Classification:

• 60K25
• 60E05
• 60K15
• 68M20

Keywords:

• Non-homogeneous Poisson process
• state dependent service rates
• Compound Intervened Poisson distribution
• Bulk arrivals