Introduction to Management Science (10th Edition)

The formula for the exponential distribution is

f ( t ) = µ e ^{µ t} , t

where

µ = average number of customers served during a specified period of time

t = service time

e = 2.71828

The probability that a customer will be served within a specified time period can be determined by using the exponential distribution, in the following form:

P ( T t ) = 1 e ^{µ t}

If, for example, the service rate is six customers per hour, then the probability that a customer will be served within 10 minutes (.17 hour ) is determined as follows :

Thus, the probability of a customer's being served within 10 minutes is .632. Figure C.2 is the exponential probability distribution for this service rate ( µ = 6).