# Queuing Theory 2 Notes

This is a sample of our (approximately) 4 page long Queuing Theory 2 notes, which we sell as part of the Operational Research Techniques Notes collection, a 1st Class package written at LSE in 2011 that contains (approximately) 104 pages of notes across 17 different documents.

### Queuing Theory 2 Revision

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Lecture 12: Queuing Theory 2 Topics

• Single server, arrival and/or service rates dependant on the number in the system, finite waiting room

• Queues with several servers

• Key performance statistics for several-servers queues

• Taha (Chapter 15)

Single server, arrival and/or service rates dependant on the number in the system, finite waiting room

• Method:
○ Identify all relevant values of
○ Identify all relevant values of
○ Use these to calculate the value of
○ Calculate the corresponding values of Example of an infinite waiting room

Key Points

• General method for single server, arrival and/or service rates dependent on number in system with finite waiting room

• Finite waiting rooms with several servers

• Performance statistics for several-server queues Formulae

• A given individual server will be idle with probability

• Expected number in the queue is

• Expected number in the system = expected number in the queue + expected number being served

• Expected number in the system is

• Expected proportion of time a server is idle is

• Expected waiting time in the queue is

• Expected waiting time in the system = expected queuing time + expected service time

• Expected waiting time in the system is

• The expected number being served =

• The limitation with this is that it is not realistic to assume than an infinite number of children can fit into the shop Example of a finite waiting room

Course Notes Page 25

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