### Queuing Theory 2 Notes

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Lecture 12: Queuing Theory 2

• Single server, arrival and/or service rates dependant on the • Taha (Chapter 15) • General method for single server, arrival and/or service rates
number in the system, finite waiting room dependent on number in system with finite waiting room
• Queues with several servers • Finite waiting rooms with several servers
• Key performance statistics for several-servers queues • Performance statistics for several-server queues

Single server, arrival and/or service rates dependant on the number in the system, finite waiting room Formulae
• Method: • A given individual server will be idle with probability
○ Identify all relevant values of
○ Identify all relevant values of
○ Use these to calculate the value of • Expected number in the queue is
○ Calculate the corresponding values of
• Expected number in the system = expected number in the
queue + expected number being served
Example of an infinite waiting room
• 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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