#982 - Queuing Theory 2 - Operational Research Techniques

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