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Unformatted text preview: M/M/1 Queue Chuan Shi We learned M/M/1 queue in Queueing lectures. For an M/M/1 queue, there is one server with an exponential service rate . The arrival rate to the system is < . In addition, the waiting area is infinite. Particularly, we derive that the average number of customers in the system (both queue and server!!) is L s = = 1 where = / is the utilization of the server. Note, this L s is the average number of customers in the entire system, NOT the queue (buffer)! By Littles law L = W , we know that the average time a customer spends in the system is 1 W s = In other words, this W s already contains the time that a customer spends in the queue as well as the time that customer spends at the server! If you are not sure about the results above, please re-visit slide 46 of the Queueing lecture. Recall that, when we derived this, we built an Markov process model. In that model, our state space is the number of customers in the system...
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- Fall '10