## What is Queuing Theory?

Queuing theory or queuing model is a body of knowledge dealing with waiting line that attempt to estimate queuing behavior based on certain numbers of assumptions.

In the simplest form, queuing model assumes that there are inputs of distribution of arrival and distribution of service time for a number of servers. The direct output of queuing theory is measurement of effectiveness or operating characteristic that measures the performance of a queuing system.

If your queuing system has similar distribution to the assumptions of theory, you can simply use the formulas of the queuing theory to predict the long term behavior (sometimes called steady state condition) of the queuing system in term of its performance. For example, you can estimate the waiting time or delay, the queue length or probability that the server is idle. From those measurements of effectiveness, you can compute the needs of the number of servers or estimate the service time requirement to meet your demand. You can also estimate the cost of the queuing and experimenting with certain ideas to improve the queuing system.

When you use the results of computation from the queuing model, you need to understand that these results are only correct for the underlying assumptions that form the queuing theory. For example, the queuing theory only predicts the long term behavior the queuing system. It means the queuing system must be opened for infinite number of hours. However, your queuing system only opens for certain limit of working hours. Queuing model also assumes certain types of distributions (such as Exponential or Poisson or Erlang distribution) that may not happen within your system. You need to do goodness of fit to check whether the arrival and service time of your system really fit with the underlying assumption of the distribution in the queuing theory.

Thus, using queuing model alone you may not get the exact results for your system. Nevertheless, you still can use the queuing theory for comparison purposes. For example, you can compare different ideas of improvement of the queuing system such as reduction of service time or better configurations of number of servers, and compute the cost effectiveness of such systems.

Queuing model allow you to test alternatives of ideas of queuing improvement. The output of the model includes the average number of customers waiting in the queue, their average waiting time, queue length and the number of optimum servers as well as their utilization (the probability that the servers will idle or busy).

Thus, subject of queuing theory is very important because you can see how we can optimize queuing. Using queuing theory you can minimize the waiting line and reduce the delay while keeping the optimum cost for both customer and the owner of the system.

Preferable reference for this tutorial is

Teknomo, Kardi. (2014) Queuing Theory Tutorial
http://people.revoledu.com/kardi/tutorial/Queuing/