Question: Measures of Performance with a single capacity unit NOTE: IF THE ARRIVAL PROCESS IS EXPONENTIAL, THEN THESE EXPRESSIONS PROVIDE EXACT ESTIMATES OF SYSTEM PERFORMANCE. IF

Measures of Performance with a single capacity unit NOTE: IF THE ARRIVAL PROCESS IS EXPONENTIAL, THEN THESE EXPRESSIONS PROVIDE EXACT ESTIMATES OF SYSTEM PERFORMANCE. IF NOT, THEN THESE EXPRESSIONS PROVIDE APPROXIMATE (BUT "GOOD") ESTIMATES OF SYSTEM PERFORMANCE. THIS WORKSHEET IS USED ONLY WHEN m=1. a s p s I_q I_p I T_q T = = = = = = = = = average interarrrival time standard deviation of average interarrival time average service time standard deviation of average service time Inventory in queue Inventory in service Inventory in system cycle time for queue cycle time for system Enter a (average interarrival time) Enter s (standard deviation of average interarrival time) Enter p (average service time) Enter s (standard deviation of average service time) Average Capacity Utilization Inventory in system Inventory in queue Inventory in service Cycle Time in system Cycle time for queue OVIDE EXACT ESTIMATES XIMATE (BUT "GOOD") 4.00 4.00 3 3 75.00% 3.00 2.25 0.75 12.00 9.00 Enter inputs in these yellow cells Read results in these orange cells. s in these yellow cells. Measures of Performance with multiple capacity units - approximations NOTE: THESE EXPRESSIONS PROVIDE APPROXIMATE ESTIMATES FOR SYSTEM PERFORMANCE FOR THE CASE WHEN THE ARRIVAL AND SERVICE PROCESSES DO NOT NECESSARILY FOLLOW AN EXPONENTIAL DISTRIBUTION AND THERE ARE 1 OR MORE CAPACITY UNITS. THIS WORKSHEET IS MORE USEFUL WHEN m > 1. a s p s I_q I_p I T_q T m Pn Enter a Enter s Enter p Enter s Enter m = = = = = = = = = = = (average interrarival time) (standard deviation of average interrarival time) (average service time) (standard deviation of average service time) (number of capacity units - m > 1) Average Utilization per capacity unit Inventory in system Inventory in queue Inventory in service Cycle time in system Cycle time in queue res of Performance with multiple capacity units - approximations HESE EXPRESSIONS PROVIDE APPROXIMATE ESTIMATES FOR SYSTEM PERFORMANCE CASE WHEN THE ARRIVAL AND SERVICE PROCESSES DO NOT NECESSARILY FOLLOW AN NTIAL DISTRIBUTION AND THERE ARE 1 OR MORE CAPACITY UNITS. THIS HEET IS MORE USEFUL WHEN m > 1. average interarrrival time standard deviation of average interarrival time average service time standard deviation of average service time Inventory in queue Inventory in service Inventory in system cycle time for queue cycle time for system number of capacity units probability of exactly n customers being in the system (average interrarival time) (standard deviation of average interrarival time) (average service time) (standard deviation of average service time) (number of capacity units - m > 1) Utilization per capacity unit 4 4 3 3 4 18.75% 0.75618 #VALUE! Read the results of 0.00618 the model from 0.75000 these orange cells. 3.02473 0.02473 Enter inputs in the yellow cells. Single Capacity Unit and Throughput Losses NOTE: This analysis only holds when both the interarrival and service times follow an exponential distribution. Further in this case, there is a predefined limit on the number of customers who can wait for service (defined as N-1 where N -1 > 0). a p I_q I_p I T_q T N Enter a Enter p Enter N = = = = = = = = average interarrrival time average service time Inventory in queue Inventory in service Inventory in system cycle time for queue cycle time for system System capacity (queue capacity = N-1) (average interrarival time) (average service time) (maximum number of customers in system (N-1 is the max number allowed in queue)) Traffic Intensity -- r Effective Utilization Probability of system being idle -- P(0) Inventory in queue Inventory in service Inventory in system Cycle time in system Cycle time in queue Probability that there are N customers in the system Throughput Loss per unit time 4 3 2 0.75000 56.76% 0.43243 0.24324 0.56757 0.81081 #VALUE! 4.28571 1.28571 0.24324 0.06081 Enter inputs in these yellow cells. Read the results from these orange cells. uts in these ells. With an exponential arrival process and 1 or more capacity units NOTE: It is assumed that the if all the capacity units are "busy" serving customers, then demand which occurs when this is the case is lost. a p m Enter a Enter p Enter m = = = average interarrrival time average service time number of capacity units (average interrarival time) (average service time) (number of capacity units) Probability that all m capacity units are busy Effective Utilization per capacity unit Effective Flow Rate per unit time Customers lost per unit time 3 2 5 Enter inputs in the cells. 0.00056 yellow 13.33% 0.33315 Read the results in 0.00019 #VALUE! these orange cells. Table used to calculate P_m(r) for the m cap units - throughput losses model. No user input required. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Total 1.66666667 1.88888889 1.93827160 1.94650206 1.94759945 1.94772138 1.94773300 1.94773396 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 PLEASE PLEASE DO DO NOT NOT CHANGE CHANGE 1 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 2 3 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 47 48 49 50 51 52 53 54 55 56 57 58 59 60 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 1.94773404 l From m cap units & N-m=0 m From m cap units & N-m=0 r (calculated) 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.66666667 0.333333 0.5 0.666667 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.22222222 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 0.04938272 LEASE LEASE DO DO NOT NOT CHANGE! 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