Quantitative Analysis for Management, 13/e

2.9 The Exponential Distribution

The exponential distribution, also called the negative exponential distribution, is used in dealing with queuing problems. The exponential distribution often describes the time required to service a customer. The exponential distribution is a continuous distribution. Its probability function is given by

$$f\left(X\right)=\mu e^{\mathrm{-}\mu x}$$ (2-14)

where

• $X=\text{random variable }\left(\text{service times}\right)$

• $\mu =\text{average number of units the service facility can handle in a specific period of time}$

• $\text{e}=2.718\left(\text{the base of the natural logarithm}\right)$

The general shape of the exponential distribution is shown in Figure 2.16. Its expected value and variance can be shown to be

$$\text{Expected value}=\frac{1}{\mu }=\text{Average service time}$$ (2-15)

$$\text{Variance}=\frac{1}{{\mu }^2}$$ (2-16)

As with any other continuous ...