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Unformatted text preview: queue, this allowed us to show that if the average interarrival time Eti = 1/ , the average service time Esi = 1/µ, the average waiting time in the queue is L, the long run rate at which customers enter the system is the average waiting time in the system is W , and the fraction of time the queue is empty is ⇡ (0) a, then we have L= aW ⇡ (0) = 1 a µ In the M/G/1 case, the expected duration of busy periods and the average waiting time in the queue satisfy: ⇡ (0) = 1/ 1/ + EB WQ = E (s2 /2) i 1 /µ The ﬁrst formula is a simple consequence of our result for alternating renewal. The more sophisticated second formula uses “Poisson Arrivals See Time Averages” along with cost equation reasoning. 3.5 Exercises 3.1. The weather in a certain locale consists of alternating wet and dry spells. Suppose that the number of days in each rainy spell is a Poisson distribution with mean 2, and that a dry spell follows a geometric distribution with mean 7. Assume that the successive durations of rainy and dry spells are i...
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