A study on state dependent single server queue with Markov modulated arrival under hyper exponential service times using block matrix structured approach

Abstract

In this research work we study the correlation impact between the inter arrival time and service time of packets arriving to the system for transmission. By assuming the arrival in modulated form the service utilization provided by server acts with varying rate of service. The queuing quantities are obtained in closed form by using matrix geometric method. The expected waiting length of packets and other performance measures are calculated in the stationary state distribution of the process. We establish the analytic frame work of the Markov model between the inter arrival and service time to get correlation impact to study the behavioural effect in queue length, time and other performance measures.

Keywords

• Markov modulated arrival
• Hyper-exponential distribution
• Quasi-birth-death process
• Matrix geometric method
• Stationary vector distribution