Queueing Mathematics 2
(updated 17th March 2008)
Keywords: simulating people, simulating crowds, simulating crowd dynamics
Multi-Channel Systems
The formula on the mathematics page is for a single channel systems. Multi-channel systems are complex. To simplify the formula we use the following short-hand notation.
c = number of servers,
n = number of people in the system.
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The service rate for c servers (n people)
The utilisation factor
Multi-channel utilisationUsing the same nomenclature as the single channel system the dynamics of a multi-channel system are as follows:
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Probability that there is no-one in the queue
Probability of n people in the system
The average number of people in the queue
The average number of people in the system
The average time a person spends waiting in the queue
The average time a person spends in the system
The probability that a person has to wait in a queueThe mathematics of queues are complex. The application of queueing theory requires some careful considerations If you would like to ask specific questions about queueing theory or its applications email us with your questions - we have already helped several major international organisations to save millions of dollars of potentially wasted investment by the application of queueing theory.
Recommended reading "Fundamentals of Queueing Theory" by Gross and Harris