A Survey on Queueing Systems with Mathematical Models and Applications

The important and challenging phenomena for the proposed queueing models is to express into mathematical formulation. There are different notations used to denote the queueing models. Each of the models has its specific characteristics following specific queueing discipline. For each of the queueing disciplines, there are different formulas to calculate the performance measures. Here, we describe some of the queuing disciplines with some of the formulas for their performance measures. Besides the usual notations of arrival rate $\lambda$ and the service rate $\mu$, there are some standard notations and symbols used in the queuing equations which are as follows:

C = Number of service channels

M = Random arrival/service

D = Deterministic service rate (constant rate)

With these, we describe some of the queueing models with their respective formulae in the following subsections.