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ch12 - Chapter 12 Introduction to Queueing Theory ENCS6161...

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Chapter 12 Introduction to Queueing Theory ENCS6161 - Probability and Stochastic Processes Concordia University
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Elements of a Queueing System A queueing system is defined by a/b/m/k , where a : type of arrival process. a = M Poisson Process b : service time distribution. b = M exponential D deterministic G general m : number of servers k : max number of customers allowed in the system ENCS6161 – p.1/12
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Little’s Formula 1 2 c . . . N q ( t ) W τ T N s ( t ) N ( t ) T = W + τ W : waiting time τ : service time ENCS6161 – p.2/12
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Little’s Formula Little’s Formula: E [ N ] = λE [ T ] , where E [ N ] : average number of customers in the system λ : arrival rate E [ T ] : average time that a customer stays in the system Little’s Formula is very general. The system here could be the whole queueing system, the waiting buffer, or the seervice system, etc. Read the proof on your own. ENCS6161 – p.3/12
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M/M/ 1 or M/M/ 1 / Queue Let N ( t ) be the number of customers.
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