Using the Transition Rate Matrix for Performance Evaluation: An Empirical Analysis

Abstract

This paper aims to use Transition Rate Matrix for queueing theory in evaluating the work of some maintenance centers for the General Company for the Distribution of Najaf Electricity. They are three independent maintenance centers in their work one from the other, and each maintenance center is responsible for repairing of specific regions. The arrival and service data for the work of these centers has been collected and these data entered into the (Fitting Distribution) program. Through this program, we can identify the potential distribution of interfaces of arrival and service times and know the number of phases that the customer will enter (malfunction), whether at the arrival station or service. After obtaining these indicators, we can build a queueing system for the three maintenance centers that were, in this system the probability distribution of interconnection times is according to the exponential distribution, whereas the distribution of service times is according to the Coxian distribution in three phases and with a regular transmission rate between phases. The results also show the solution of these differential equations in the numerical way known as the (fourth level cottage-fourth method) through a program prepared in the language of (Visual Basic). This program works for a certain number of steps (Step) until the system reaches a steady state, and get the numerical solution, if the time period of the system will be changed by one. The benefit of the Coxian distribution is that it is a flexible distribution that can be approximated to many other types of phase distributions.