###### Operational Research Notes > Lse Operational Research Notes > Operational Research Techniques Notes

# 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

* The following is a plain text extract of the PDF sample above, taken from our Operational Research Techniques Notes. This text version has had its formatting removed so pay attention to its contents alone rather than its presentation. The version you download will have its original formatting intact and so will be much prettier to look at.*

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

Reading

• 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

** ****************************End Of Sample*******************************

*Buy the full version of these notes or essay plans and more in our Operational Research Techniques Notes.*