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Unformatted text preview: Homework Set #10 Solutions IE 336 Spring 2011 1. (a) This is the M/M/1 queue. The transition diagram is shown in Figure 1. Figure 1: Transition Diagram for Problem 1a (b) If there are 5 customers in the queue at steadystate, then there must be 6 customers in the system. q 5 = 6 = 6 (1 ) where = . (c) In the M/M/1 queue, there is only one server. In steadystate, the server is always busy if there is at least one customer in the system. b 1 = 1 + 2 + = 1 = 1 (1 ) = (d) In the M/M/1 queue, there is only one server. Therefore, the probability that three servers are busy is zero. (e) The average waiting time in the queue is: W q = 1 1 2. (a) This is the M/M/1/N queue, where N = 7. The transition diagram is shown in Figure 2. (b) We want to compute 5 . 5 = ( 5 h 1 1 8 i for 6 = 1 1 8 for = 1 (c) The average number of customers in the system at steadystate is: L = ( 1 h 1 7 1 8 i 7 8 1 8 for 6 = 1 7 2 for = 1 1 Figure 2: Transition Diagram for Problem 2a (d) Using Littles Law, the average waiting time in the system at steady state is:...
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 Spring '08
 Xangi

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