Queuing theory or waiting line models are basically a mathematical approach applied to the
analysis of waiting lines. Most queuing models applications are centered on the question of finding
the ideal level of services, waiting times and queue lengths. When an organization retain an excellent
customer service. The customers are kept happy or satisfaction but for the an organization become
expensive. Most managers recognize the trade – off that must take place between the cost of
providing good service and the cost of customer waiting time. The objective of this study is to
measure the cost for three single channel waiting line models. The aim of this study is to compare
between three single channel waiting line models. The cost for the three single channel waiting line
models is calculated with different distributions. The study results showed that the cost which
calculated for the (M/D/1) model is less than the other two models when the same data are used.
Second the results showed that the cost which calculated for the (M/G/1) model when the service
rate (μ) is followed weibull distribution is less than the same model when the service rate (μ) is
followed exponential and gamma distributions.