# Simulating a Multiple Server Queue

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In queuing theory, the simplest model is called the M/M/1 or M/M/c model (Markovian arrivals, Markovian service, and 1 or servers). Customers arrive at a facility and either get served immediately by a free server or join a queue that waits for a server to become available. Standard notation is:

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Contributed by: Karl W. Heiner (SUNY New Paltz) and Stan Wagon (Macalester College) (August 2011)

Open content licensed under CC BY-NC-SA

## Snapshots

## Details

The first snapshot shows the situation starting from an empty queue (initial deletion ratio is 0) and with . In that case the queue builds up and then increases without bound. The last two snapshots use two servers, with and . The first 70% of the time interval is deleted, thus giving a more typical window on the queue formation process. Still there is a lot of variation in the size of the queue: in the first case the average number of people waiting is 0.57 while in the second it is 13. For more information, see [1] and [2].

References

[1] F. S. Hillier and G. J. Lieberman, *Introduction to Operations Research,* 8th ed., New York: McGraw-Hill, 2004, pp. 765–774.
[2] R. B. Chase, F. R. Jacobs, and N. J. Aquilano, *Operations Management for Competitive Advantage*, 10th ed., New York: McGraw-Hill, 2004.

## Permanent Citation