Queueing theory is the study of queues as based on probability theory, statistics and other sub-fields of mathematics. The idea behind queueing theory is to propose models to apply to describe queues and the processes behind them. In queueing theory, queues tend to be modeled by stochastic processes, which are random functions based on probability distributions. Queueing theory has many applications, including the design of computer systems, customer service and Internet database management.

## Coefficient of Variation

Because queueing theory models are based on the exponential distribution, these models work through applying the traits of the exponential distribution. The main problem lies in that the exponential distribution has a coefficient of variation of one. This fact precludes the modeling of any process that has a coefficient of variation significantly different from one. Because of the low likelihood of a random process having a coefficient of variation of one, queueing theory has the disadvantage of low applicability.

## Simplicity

Queuing theory offers us a method to easily and definitely describe queues in mathematical terms. This advantage of queueing theory is an advantage that plain language, economic models and pure observation lack. Through applying basic probabilistic distributions, such as the Poisson and exponential distributions, mathematicians can model the complex phenomenon of waiting in a queue as an elegantly simplistic mathematical equation. Mathematicians can later analyze these equations to understand and predict behavior.

## Assumptions

While the assumptions for most applications of queueing models are few, the assumptions that are needed tend to be somewhat irrational. Especially in regard to human queues, queueing theory requires assumptions that cannot possibly hold true in the real world. In general, queueing theory presumes that human behavior is deterministic. These assumptions usually are a set of rules for what a person will do. For example, one assumption may be that a person will not enter a queue if there are too many people already queued up. In reality, this is not true; otherwise, there would be no lines outside stores or for store openings, and holiday shoppers who waited too late to buy gifts would just give up.

## Simulation

Queueing theory has flourished due to the advent of the computer age. The past difficulty of arriving at numerical solutions for queueing models is no longer a disadvantage, as mathematicians can run simulations to arrive at approximate answers. The simulation of queueing theory models also allows researchers to change the value of variables involved and analyze the results of the change, which can help in the optimization of queue design.

#### References

- “An Introduction to Queueing Theory and Matrix-Analytic Methods”; Breuer Baum; 2005
- “Fundamentals of Queueing Theory”; Donald Gross and Carl Harris; 1998

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