Chapter 11 Queueing Theory Q-2: (Is it better to train or hire more employees?) Consider a supermarket that has one girl running up sales at the counters. Let the time between arrivals and service time follow traingular distributions as shown below: C b Arrival 8 9 11 minutes Service 3 4 5 minutes h = = = ts = (1) Compute ta, va, 1, ca?, ts, VS, 4, cs? and p for arrival and service processes. (ii) Determine L, W, Lq and Wq. (iii) Now suppose that you employ girls so that you have m girls at the counters, compute L, W, Lq and Wq for m = 2, 3, 4 and 5. Solution: Q-2: (i) For arrival: For Service: h = ta = min min? 2 = min min 22 p= (ii) For GI/G/1 model: (because we have one girl) La persons W= min persons Wq = min (iii) For GI/G/m model: (because we have more than one girl) min min? va = VS = = = 2 ca CS? = Lq= m k /! Kk! *k! "/k! L W La Wq 1 0 Chapter 11 Queueing Theory Q-2: (Is it better to train or hire more employees?) Consider a supermarket that has one girl running up sales at the counters. Let the time between arrivals and service time follow traingular distributions as shown below: C b Arrival 8 9 11 minutes Service 3 4 5 minutes h = = = ts = (1) Compute ta, va, 1, ca?, ts, VS, 4, cs? and p for arrival and service processes. (ii) Determine L, W, Lq and Wq. (iii) Now suppose that you employ girls so that you have m girls at the counters, compute L, W, Lq and Wq for m = 2, 3, 4 and 5. Solution: Q-2: (i) For arrival: For Service: h = ta = min min? 2 = min min 22 p= (ii) For GI/G/1 model: (because we have one girl) La persons W= min persons Wq = min (iii) For GI/G/m model: (because we have more than one girl) min min? va = VS = = = 2 ca CS? = Lq= m k /! Kk! *k! "/k! L W La Wq 1 0