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Queuing Systems

Queuing Systems. Jane Hagstrom. What is a Queuing System?. A queuing system consists of one or more servers together with queues where entities can await service. A complex queuing system is described as a queuing network.

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Queuing Systems

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  1. Queuing Systems Jane Hagstrom J. Hagstrom, U. of Illinois

  2. What is a Queuing System? • A queuing system consists of one or more servers together with queues where entities can await service. • A complex queuing system is described as a queuing network. • Usually, travel times between servers are not of interest in a queuing system. J. Hagstrom, U. of Illinois

  3. Simple Queuing System • Has one or more identical servers, any of which can provide the same service • Has a single queue with unlimited capacity • Entities arrive singly into the system • There is an unlimited supply of entities • Entities are taken out of the queue for service on a First-In First-Out basis J. Hagstrom, U. of Illinois

  4. Examples of Simple Queuing Systems • Ticket-taking at the movie theater • Checkout system at storefront grocery • Teller system at bank J. Hagstrom, U. of Illinois

  5. Terminology Concerning Time • Duration – a length of time • Example: They remained in Pearl Harbor for the duration of the war • Epoch – a moment in time • Example: A significant epoch in the history of the U.S. was the day of Victory in Japan J. Hagstrom, U. of Illinois

  6. Basic Queuing System Terminology • Server gives service over a period of time called the service duration. • An arrival arrives requiring service from the server. The time between arrivals is the interarrival duration. • If an arrival arrives at an epoch when the server(s) is busy taking care of previous arrivals, the arrival waits in a queue. J. Hagstrom, U. of Illinois

  7. Simple Queuing System Arrivalat Queue Departure Server J. Hagstrom, U. of Illinois

  8. Notation for Simple Queuing System • (arrival distribution)/(service distribution)/number of servers • Examples: • M/M/1 Interarrival duration is distributed according to an exponential distribution; service duration is distributed according to an exponential distribution; number of servers is 1. • D/T/3 Interarrival duration is deterministic; service duration is distributed according to a triangular distribution; number of servers is 3. J. Hagstrom, U. of Illinois

  9. Manufacturing System • Server is machining center • Arrival is unit of Product • Queue holds units of product awaiting service at the machining center J. Hagstrom, U. of Illinois

  10. J. Hagstrom, U. of Illinois

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