2 September, 2001J. Hagstrom, U. of Illinois1 Queuing Systems Jane Hagstrom.

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2 September, 2001J. Hagstrom, U. of Illinois1 Queuing Systems Jane Hagstrom

2 September, 2001J. Hagstrom, U. of Illinois2 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.

2 September, 2001J. Hagstrom, U. of Illinois3 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

2 September, 2001J. Hagstrom, U. of Illinois4 Examples of Simple Queuing Systems Ticket-taking at the movie theater Checkout system at storefront grocery Teller system at bank

2 September, 2001J. Hagstrom, U. of Illinois5 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

2 September, 2001J. Hagstrom, U. of Illinois6 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.

2 September, 2001J. Hagstrom, U. of Illinois7 Simple Queuing System Arrival at Queue Server Departure

2 September, 2001J. Hagstrom, U. of Illinois8 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.

2 September, 2001J. Hagstrom, U. of Illinois9 Manufacturing System Server is machining center Arrival is unit of Product Queue holds units of product awaiting service at the machining center

2 September, 2001J. Hagstrom, U. of Illinois10