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## Queuing Theory 2 Notes

This is an extract of our Queuing Theory 2 document, which we sell as part of our Operational Research Techniques Notes collection written by the top tier of LSE students.

The following is a more accessble plain text extract of the PDF sample above, taken from our Operational Research Techniques Notes. Due to the challenges of extracting text from PDFs, it will have odd formatting:

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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