Transient analysis of M/M/1 queuing theory: an overview

Queuing is a common phenomenon in our daily life. Mathematical study on waiting line or queues is called queuing theory. Generally, queuing theory has been used extensively by service industry in order to optimize the service effectiveness and improve the customer satisfaction since it helps an organization to understand how a system operates while reviewing the efficiency of the system. Most of queuing theory deals with system performance in steady-state condition. That is, most queuing models assume that the system has been operating with the same arrival rate, service rate and other characteristics for a sufficiently long time that the probabilistic behavior of performance measures such as queue length is independent of initial condition. However, in many situations, the parameters defining the queuing system may vary over time. Under such circumstances, it is most unlikely that such systems are in equilibrium. This paper reviews the transient behavior (no assumption of statistical equilibrium) of the queuing model. The aim is to provide sufficient information to analysts who are interested in studying queuing theory with this special characteristic.