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.
[2] 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.
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 this and the fourth equation yields
Simplifying, the formula for the Queuing Rule of Thumb is
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.
Each serving table has 2 sides where people can pick up their food.
Each student needs about 36 seconds to be registered.
How many days are needed to register all students?
[2] Solution: Given s = 1, N = 10,000, r = 36, the rule of thumb yields T:
[2] During the peak hour of the morning about 4500 cars drop off their children at an elementary school.
Each car requires about 6 meters to stop and maneuver.
How much space is needed for the minimum drop off line?
[2] Solution: Given N = 4500, T = 60, r = 1, the rule of thumb yields s:
Given the space for each car is 6 meters, the line should be at least
