Transient Analysis of Phase Type Hysteresis system with Dual Arrival Rate Through Matrix Geometric Method

Abstract

Transient analysis is the efficient way to observe the system behavior with respect to time when system not reached in steady state. In this paper, we analyze the behavior of phase type hysteresis system with dual arrival rate in transient state. Service process of system is modeled with hypoexponential and hyperexponential phase type distribution and solved through vector domain technique called matrix geometric method. In this system, arrival rate of customer switched between two rates which depends on the system length. We analyze the effect of dual arrival rate and internal thresholds on the system length in the transient state by using hypoexponential and hyperexponential distributions as a service process