min[Ri(1 ] = min[20(1 0.1007), 24] = 17.99 calls/hour R = Pb), Rp – – and the average server utilization will be = = 17.99/24 = 0.7495 u Thus, the CSR is busy only about 75% of the time and idle for about 25% of the time. Because of variability, however, there will be an average of 1.23 callers on hold and 10% of all callers (or two per hour) will get a busy signal, resulting in lost sales. To study the effect of adding more telephone lines, we simply change the value of and K see how it affects key performance measures. Table 8.1 summarizes the results (rounded up to two decimal places). Table 8.1 Effect of Buffer Capacity on Process Performance Number of telephone lines 5 6 7 8 9 10 n Number of servers 1 1 1 1 1 1 c Buffer capacity = c 4 5 6 7 8 9 K n – Blocking probability (%) 10.07 7.74 6.06 4.81 3.85 3.11 Pb Throughput (units/hour) 17.99 18.46 18.79 19.04 19.23 19.38 R Average number of calls in queue 1.23 1.52 1.79 2.04 2.27 2.48 Ii Average wait in queue (minutes) 4.10 4.95 5.73 6.44 7.09 7.68 Ti Capacity utilization 0.75 0.77 0.78 0.79 0.80 0.81 u Note that, as the buffer capacity (number of telephone lines) is increased, the blocking probability declines, and more callers are able to get into the system. Interestingly, however, the average waiting time of the callers who do get in increases. Thus, increasing the buffer capacity has two opposing effects: increasing the process throughput but also increasing the average
R = min[Ri(1 – Pb), Rp ] = min[20(1 – 0.1007), 24] = 17.99 calls/hour and the average server utilization will be u = = 17.99/24 = 0.7495 Thus, the CSR is busy only about 75% of the time and idle for about 25% of the time. Because of variability, however, there will be an average of 1.23 callers on hold and 10% of all callers (or two per hour) will get a busy signal, resulting in lost sales. To study the effect of adding more telephone lines, we simply change the value of K and see how it affects key performance measures. Table 8.1 summarizes the results (rounded up to two decimal places). Table 8.1 Effect of Buffer Capacity on Process Performance Number of telephone lines n 5 6 7 8 9 10 Number of servers c 1 1 1 1 1 1 Buffer capacity K = n – c 4 5 6 7 8 9 Blocking probability Pb (%) 10.07 7.74 6.06 4.81 3.85 3.11 Throughput R (units/hour) 17.99 18.46 18.79 19.04 19.23 19.38 Average number of calls in queue Ii 1.23 1.52 1.79 2.04 2.27 2.48 Average wait in queue Ti (minutes) 4.10 4.95 5.73 6.44 7.09 7.68 Capacity utilization u 0.75 0.77 0.78 0.79 0.80 0.81 Note that, as the buffer capacity (number of telephone lines) is increased, the blocking probability declines, and more callers are able to get into the system. Interestingly, however, the average waiting time of the callers who do get in increases. Thus, increasing the buffer capacity has two opposing effects: increasing the process throughput but also increasing the average
BufferCapacityChopra.docx