Quantitative Analysis for Management, 13/e

12.5 Constant Service Time Model (M /D / 1)

Some service systems have constant service times instead of exponentially distributed times. When customers or equipment are processed according to a fixed cycle, as in the case of an automatic car wash or an amusement park ride, constant service rates are appropriate. Because constant rates are certain, the values for $L_q, W_q, L,$ and W are always less than they would be in the models we have just discussed, which have variable service times. As a matter of fact, both the average queue length and the average waiting time in the queue are halved with the constant service rate model.

Constant service rates speed the process compared to exponentially distributed service times with the same value of $\mu$