number 2

Problem Set 7: SIMULATION Simulate by hand the single server Post Office situation described in lectures for the first 20 customers arriving in the Post Office after 8 a.m. where the arrival time distribution and service time distribution are as follows (all times are in minutes): Customer arrivals gap probability 0.45 0.24 0.16 0.08 5 0.04 0.02 0.01 Service time duration probability 0.20 0.35 0.30 0.15 MON Use the following random numbers: to generate customer arrival times: 97, 02, 80, 66, 96, 55, 50, 29, 58, 51, 04, 86, 24, 39, 47, 60, 65, 44, 93,20 to generate service times: 95, 92, 67, 24, 76, 64, 02, 53, 16, 16, 55, 54, 23, 36, 44, 71, 88, 74, 10, 46 What is the average time customers wait in line? What is the server utilization? Why is this not a fully satisfactory simulation? Ans: a) 3.85 minutes Repeat the simulation of Q1 above for the first 50 customers. Use the Excel random number generator for arrival and service times. Run your simulation model at least 30 times calculating for each run: 9 the average time in line the average time the server is idle the server utilization Then calculate the overall averages for each of (a), (b), (c) after your runs. Would you support opening up another server? Explain your recommendations carefully. Ans: (approx., after 30 trials): __a) 10 mins (b) 0.12 mins (c) 96%