Generation The Transition Rate Matrix (TRM) for Exponential Distribution

Abstract

In some times queuing process does not found solution and so not reach to steady state. If not use transient solution. This case happen when the queuing system is work for short time, arrival and service rates are fluctuation with time and service station is work intermittently. In this research we study the transient behavior for one of phase distributions which is exponential distribution; the square coefficient of variation to this distribution is equal to one. That is the customer will complete one phase in arrival station and one phase in service station. The case that we assume it is inter arrival and service times are exponentially distributed, single service station, finite system capacity, and infinite population capacity. After that we generate differential equation for this system and we solved this equation by using Rung- Kutta order 4 method, and so obtain on the transient solution and steady state solution.