class12mg1q

class12mg1q - Urban Operations Research Supplementary Notes...

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Urban Operations Research Supplementary Notes Pinker, 1994 Updated by Kang, 2001 The M/G/1 Queueing System For the M/G/1 queueing system being operated under the FIFO service rule, we derive the expres- sions of the following quantities in terms of the arrival rate λ , the mean service time E [ S ], and the variance of service time σ 2 S . W : the average time a randomly arriving customer will spend in the system, which is com- posed of the waiting time in the queue and the service time. L : the average number of people in the system that a randomly arriving customer ±nds, which is composed of the number of people in the queue and the person in service. ρ : the long run fraction of time the server is busy, which is equivalently the probability that the server is busy at a random point in time. B : the long run average duration of a server busy period. Recall that the M/G/1 queueing system is a single server queueing system in which the customer arrival process is Poisson with rate λ and the service time, S , for each customer follows a general distribution with PDF f S ( s ), mean E [ S ], and variance σ 2 S . Let us ±rst compute ρ and B . Suppose
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class12mg1q - Urban Operations Research Supplementary Notes...

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