Tutorial 9 Erindale: Thu@3pm 970320 ========== St George: Thu@6pm CSC354, Spring 1997 Tutorial notes, T9 ========================================================================= Announce: - ps3 due in 2 weeks (Apr 3) Topics: - Take up 5 questions from Law & Kelton Chapter 9 (9.1, 9.5, 9.7, 9.8, 9.10) - Answer questions about problem set 3 and explain how the simulation works, in general - Walk them through a trace of the simulation ========================================================================= For week 10 tutorials in CSC 354S, we offer some review questions in the area of output data analysis of a single system. The questions at the end of Chapter 12 in BCN are not all that great, so here are some questions from L&K 9.1 Argue heuristically that comparable output random variables from replications using different random numbers should be independent. 9.5 Why is determining the number of tellers for a bank different from determining the hardware requirements for a computer or communications system? 9.7 For the following systems, state whether you think a terminating or a non-terminating simulation would be more appropriate. In the terminating cases, state the terminating event E. a) Consider a telephone system for which an arriving call may experience a delay before obtaining a line. Suppose that the goal is to estimate the mean delay of the 100th arriving call. b) Consider a military inventory system during peacetime, which is assumed to have a long duration. Assume that system parameters (e.g., the interdemand distribution) do not change over time and we are interested in the output process C1, C2, ..., where Ci is the total cost in the ith month. Suppose further that we want a measure of the mean cost. c) Consider a manufacturing system for food products. A production schedule is issued, the system produces output for 13 days, and then the system is completely cleaned out on the 14th day. Then a new production schedule is issued and the 2-week cycle is repeated, etc. The goal is to estimate the mean throughput over a cycle. d) Consider an air freight company that provides overnight delivery of packages. Aircraft loaded with packages start arriving at the hub operations at approximately 11 p.m. The packages are unloaded and then sorted in a warehouse according to the destination zip code (postal code). Packages with similar zip codes are placed on one aircraft, and the last plane departs at approximately 5 a.m. It is desired to estimate the mean (across departing planes) amount of time that planes are late in departing. e) Consider a manufacturing system that operates in a similar manner 7 days a week. Suppose, however, that 6 machines operate during the first 2 shifts each day, but only 4 machines operate during on the third shift. Let N1, N2, ... be the output process of interest, where Ni is the number of parts produced in the ith shift. We are interested in a measure of mean throughput. 9.8 For a small factory, suppose the system operates 24 hours a day for 5 days and then is completely cleaned out. Thus, we have a terminating simulation of length 120 hours. We have done 5 replications and obtained the following values for mean throughput: X1 = 7221, X2 = 7155, X3 = 7250, X4 = 7260, X5 = 7260. Construct a point estimate and 95 percent confidence interval for the mean weekly throughput. Approximately how many replications would be required to obtain an absolute error of 50? A relative error of 5 percent? (related to) 9.10 How do you obtain a point estimate of the median of an empirical distribution? Assume that you have 10 values in your distribution. ^ Solution: x (0.5) = X (5) The estimator of the median of the empirical distribution is the data value that falls in the middle of the sorted data values. If there are 10 data values as in the original question 9.10, then X sub (5) is the order statistic that falls in the 5th position when the data values are sorted.