lec21 - Queuing Queueing system systems server 1 enter the...

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Queuing systems some population of individuals enter the system according to some random mechanism server 1 server 2 server c exit the system Depending upon the specifc application there are many varieties oF queuing systems: homogenous, i.e. only one type oF individuals, or several types? random mechanism by which the population enters nature oF the queue: fnite/ infnite nature oF the queuing discipline: ±I±0 or priority (i.e. di²erent types oF individuals get di²erent treatment) number and behavior oF servers; distribution oF service times? 1
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Queuing systems (cont’d) Variety of properties of queues one might want to investigate: mean number of individuals in the system mean queue length fraction of customers turned away (for a Fnite queue length) mean waiting time, etc. Notation: F Y /F S /c/K F Y distribution of inter arrival times Y F S distribution of service times S c number of servers K maximum number of individuals in the system Usually, we will assume a ±I±O queue. 2
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Queuing systems (cont’d) The distributions F Y and F S are chosen from a small set of distributions, denoted by: M exponential (M emoryless) distribution E k Erlang k stage D deterministic distribution G a general, not further speciFed distribution The main properties of interest for a queuing system: L average length of system = average # of individuals in the system W average waiting time (time in queue and service time W s average service time W q average waiting time in queue L q average length of queue 3
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Model queueing systems as Stochastic processes The main idea of a queuing system is to model the number of individuals
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This note was uploaded on 02/01/2012 for the course STAT 330B taught by Professor Zhou during the Spring '11 term at Iowa State.

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lec21 - Queuing Queueing system systems server 1 enter the...

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