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). Figure C.2. Exponential distribution for µ = 6
