Transient Analysis of Hysteresis Queueing Model Using Matrix Geometric Method

WAIJAH SHAH ； SYED ASIFALI SHAH ； FAISAL KARIM SHAIKH

《Mehran University Research Journal of Engineering and Technology》 30卷4期 (2011/10) Pp. 657-662

摘要

Various analytical methods have been proposed for the transient analysis of a queueing system in the scalar domain. In this paper, a vector domain based transient analysis is proposed for the hysteresis queueing system with internal thresholds for the efficient and numerically stable analysis. In this system arrival rate of customer is controlled through the internal thresholds and the system is analyzed as a quasi-birth and death process through matrix geometric method with the combination of vector form Runge-Kutta numerical procedure which utilizes the special matrices. An arrival and service process of the system follows a Markovian distribution. We analyze the mean number of customers in the system when the system is in transient state against varying time for a Markovian distribution. The results show that the effect of oscillation/hysteresis depends on the difference between the two internal threshold values.

關鍵字

Hysteresis ； Runge-Kutta ； Threshold ； Transient ； Markov Distribution