Queuing Rule of Thumb

The Queuing Rule of Thumb (QROT) is a mathematical formula, known as the queuing constraint equation when it is used to find an approximation of servers required to service a queue. The formula is written as an inequality relating the number of servers ("s"), total number of service requestors ("N"), service time ("r"), and the maximum time to empty the queue ("T"):
QROT serves as a rough heuristic to address queue problems. Compared to standard queuing formulas, it is simple enough to compute the necessary number of servers without involving probability or queueing theory. The rule of thumb is therefore more practical to use in many situations.
Formula.
A derivation of the QROT formula follows. The "arrival rate" is the ratio of the total number of customers "N" and the maximum time needed to finish the queue "T".
The "service rate" is the reciprocal of service time "r".
It is convenient to consider the ratio of the arrival rate and the service rate.
Assuming "s" servers, the "utilization" of the queuing system must not be larger than 1.
Combining the first three equations gives formula_6. Combining this and the fourth equation yields formula_7.
Simplifying, the formula for the Queuing Rule of Thumb is formula_1.
Usage.
The Queuing Rule of Thumb assists queue management to resolve queue problems by relating the number of servers, the total number of customers, the service time, and the maximum time needed to finish the queue. To make a queuing system more efficient, these values can be adjusted with regards to the rule of thumb.
The following examples illustrate how the rule may be used: