QEX2ANS - QUEUING EXERCISE 1 T w =FMIS 3301 1 A photo...

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Tw = FMIS 3301 QUEUING EXERCISE 1 1. A photo printing service has a single machine that processes pictures as they arrive. Arrivals occur an average of every 45 seconds (a rate of 80/hour), with a standard deviation of 27 seconds. The machine can print 1 picture in a constant 30 seconds. (Rp = 120/hr) a. What is the mean time in hours that a picture spends in the system? 0.68 min T a =45s; SD =27s; CV a =27/45 =0.6; CV P = 0; T P =30s.; SD = 0; S =1; U = Ra/Rp = 80/120 = 0.67; Service time factor 30/1 = 30s Utilization factor: (0.67 (√2*2)-1 )/(1-0.67) = (0.67)/(0.33) = 2 Variation factor: (0.6 2 + 0)/2 = 0.36/2 = 0.18 ALL: T W = 30*2*0.18= 10.8 seconds T = T W + T P = 10.8 + 30 = 40.8 seconds. b. How many pictures would be waiting to be printed? I B = R a T W = (80/3600)*10.8 = 0.24 2. Customers arrive at QuickNacho at an average rate of 0.75 per minute, and are served by a four servers at an average rate of 0.25 per minute. Assume Poisson arrival and service rates. a. What is the average waiting time in the queue? T a =1.33m; CV a =1; CV P = 1; T P =4m.; S =4; U = Ra/S*Rp = 0.75/4*0.25 = .75/1 = 0.75 Service time factor 4/4 = 1m Utilization factor: (0.75 √(2*4+2)-1 )/(1-0.75) = (0.75) 2.162 /(0.25) = 0.537/0.25 =2.15 Variation factor: 1.0 ALL: T W = 1*2.15*1= 2.15 minutes (129 seconds) b. What is the average number of customers at QN? 3.5
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