The time in the queue is calculated as follows:
time in queue = activity time * (utilization / 1 – utilization) * ((Cv_a^2 + Cv_p^2) / 2)
- activity time = service time factor (average processing time p)
- (utilization / 1 – utilization) = utilization factor
- ((Cv_a^2 + Cv_p^2) / 2) = variability factor
Since the utilization factor is calculated as (u / 1-u), this means that as the waiting time gets higher, the utilization gets closer and closer to 1. The formula for the time in the queue always delivers an average value. This so-called waiting time formula can only be used if the demand is lower than the capacity. If the demand is higher than the capacity, the waiting time will ultimately not be driven by variability, but rather by insufficient capacity.
The total flow time of a flow object can be calculated as:
total flow time = time in the queue + processing time
These lecture notes were taken during 2013 installment of the MOOC “An Introduction to Operations Management” taught by Prof. Dr. Christian Terwiesch of the Wharton Business School of the University of Pennsylvania at Coursera.org.