Measuring the Cost for Some Single Channel Waiting Line Models

Abstract

Queuing models applications are centered on the question of finding the ideal level of services, waiting times and queue lengths. The aim of this study is to measure the cost for three models and compare the cost for the three single channel waiting line models instead of finding the ideal level of services, waiting times and queue lengths which calculated in many studies.  Each model depends on two important parameters arrival rate (λ) and service rate (μ) which followed different distributions.  The cost for the three single channel waiting line models is calculated when arrival rate (λ) is followed Poisson distribution and service rate (μ) is followed different distributions. The objective for the waiting line models is to minimize total expected costs by minimize the sum of service costs and waiting costs. Therefore, the study concerned with changing the distribution of the service rate (μ) and examining its impact on cost. This choice was made to emphasize the basic idea of the study (there is a relationship between the service rate distribution and the cost). The study results showed that there is a relationship between the service rate   distribution and the cost.