simulation

BASIC SIMULATION MODELING 129 customer type, and not by whether the checker is the regular or express one. Initially, the system is empty and idle and the simulation is to run lor exactly 8 hours. Compute the average delay in each queue, the time-average number in each queue, and the utilization of each checker. What recommendations would you have for further study or improvement of this system? (On June 21, 1983, the Cleveland Plain pealer, in a story entitled \"Fast Checkout Wins over Low Food Prices,\" reported that \"Supermarket shoppers think fast checkout counters are more important than attractive prices, according to a survey [by] the Food Marketing Institute.... The biggest group of shoppers, 39 percent, replied 'fast checkouts,' ... and 28 percent said good or low prices... [reflecting] growing irritation at having to stand in line to pay the cashier.\")1.28. A one-pump gas station is always open and has two types of customers. A-police car arrives every 30 minutes (exactly), with the first police car arriving at time 15 minutes. Regular, (nonpolice) cars have exponential interarrival times with mean 5.6 minutes, with the first regular car arriving at time O. Service times at the pump for all cars are exponential with mean 4.8 minutes. A car arriving to find the pump idle goes right into service, and regular cars arriving 10 find the pump busy join the end of a single queue. A police car arriving to find the pump busy, however, goes to the front of the line, ahead of any regular cars in line: [If there are already other police cars at the front ofthe line, assume that an arriving police . car gets in line ahead of them as well. (How could this happen?)] Initially the system is empty and idle, and the simulation is to run until exactly 500 cars (of any type) have completed their delays in queue. Estimate the'expected average delay in queue for each type of car separately, the expected time-average number of cars (of either type) in queue, and the expected utilization of the pump.1.29. Of interest in telephony are models of the following type. Between two large cities, A and B, are a fixed number, n, of long:.distance lines or circuits. Each line can operate in either direction (Le., can carry calls originating in A or B) but can carry only one call at a time; see Fig. 1.97. If a person in A or B wants to place a ~ call to the other city and a line is open (i.e., idle), the call goes through: immediately on one of the open lines. If all n lines are busy, the person gets a . recording saying that she must hang up and try later; there are no facilities for queueing for the next open line, so these blocked callers just go away. ,The ,times between attempted calls from A to B are exponential with mean 10 seconds, and the times between attempted calls from B to A are exponential with mean 12 seconds. The length of a conversation is exponential with mean 4 minutes, regardless of the city of origin. Initially all lines are open, and the simulation is to run for 12 hours; compute the time-average number of lines that are busy, the time-average proportion of lines that are busy, the total 'number of attempted calls (from either city), the number of calls that are blocked, and the proportionLine '1Line 2City • City·A B··Line n FIGURE 1.97 . A long-distance telephone system.

130 SIMULATION MODEUNG AND ANALYSIS_ _ 0 0 0 0 0Inspectio~n~O.:..-.7_ _ _ _ _ _... ./\"00- 00 \.00 • RepairFIGURE 1.98A bus maintenance depot. of calls that are blocked. Determine approximately how many lines would be needed so that no more than 5 percent of the attempted calls will be blocked.1.30. City busses arrive to the maintenance facility with exponential interarrival times with mean 2 hours. The facility consists of a single inspection station and two identical repair stations; see Fig. 1.98. Every bus is inspected, and inspection times are distributed uniformly between 15 minutes and 1.05 hours; the inspection station is fed by a single FIFO queue. Historically, 30 percent of the busses have been found during inspection to need some repair. The two parallel repair stations are fed by a single FIFO queue, and repairs are distributed uniformly between 2.1 hours and 4.5 hours. Run the simulation for 160 hours and compute the average delay in each queue, the average length of each queue, the utilization of the inspection station, and the utilization of the repair station (defined to be half of the time-average number of busy repair stations, since there ,are two stations). Replicate the simulation five times. Suppose that the arrival rate of busses ,quadrupled, i.e., the mean interarrival time decreased to 30 minutes. Would the facility be able to handle it? Can you answer this question without simulation?REFERENCESBanks, J., and J. S. Carson: Discrete-Event System Simulation, Prentice-Hall, Englewood Cliffs, N.J. (1984).Braun, M.: Differential 'Equations and Their Applications, Applied Mathematical Sciences, Vol. 15, Springer-Verlag, New York (1975).Chandrasekaran, U., and S. Sheppard: Discrete Event Distributed Simulation-A Survey, Proc. Conference on Methodology and Validation, Orlando, Fla., pp. 32-37 (1987).Chandy, K. M., and J. Misra: Distributed Simulation: A Case Study in Design and Verification of Distributed Programs, IEEE Trans. Software Eng., SE-5: 440-452 (1979).Chandy, K,M., and J. Misra: Asynchronous Distributed Simulation .via a Sequence of Parallel Computations, Commun. Assoc, Comput. Mach., 24: 198-206 (1981).Chandy, K.M., and J, Misra: Distributed Deadlock Detection, Assoc. Comput, Mach. Trans. Computer Systems, 1: 144-156 (1983).Chandy, K. M., and C. H. Sauer: Computer Systems Performance Analysis, Prentice-Hall, Englewood Cliffs, N.J. (1981):

BASIC SIMULATION MODELING 131Comfort, J. C.: The Simulation of a Master-Slave Event-Set Processor, Simulation, 42: 117-124(1984).Davis, G. B., and T. R. Hoffmann: FORTRAN 77: A Structured, Disciplined Style, 3d ed.,McGraw-Hill, New York (1988).Fayek, A.-M. M.: Introduction to Combined Discrete-Continuous Simulation Using PCSIMSCRIPT 11.5, CACI Products Company, La Jolla, Calif. (1988).Fishman, G. S.: Principles of Discrete Event Simulation, John Wiley, New York (1978).Forgionne, G. A.: Corporate Management Science Activities: An Update, Interfaces, 13:3: 20-23(1983). .Gordon, G.: System Simulation, 2d ed.,- Prentice-Hall, Englewood Cliffs, N.J. (1978).Orogono, P.: Programming in Pascal, 2d ed., Addison-Wesley, Reading, Mass. (1984).Gross; D., and C. M. Harris: Fundamentals of Queueing Theory, 2d ed., John Wiley, New York(1985).<Q Halton, J. H.: A Retro·spective and Prospective Survey of the Monte Carlo Method, SIAM Rev.,12: 1-63 (1970).o Hammersley, 1. M., and D. C. Handscomb: Monte Carlo Methods, Methuen, London (1964).Harpell, J. L., M. S. Lane, and A. H. Mansour: Operations Research in Practice: A LongitudinalStudy, Interfaces, 19:3: 65-74 (1989).Heidelberger, P.: Discrete Event Simulations and Parallel Processing: Statistical Properties, SIAM1. Statisl. Comput., 9: 1114-1132 (1988).Jefferson, D. R.: Virtual Time, Assoc. Comput. Mach. Trans. Programming Languages and.Systems, 7: 404-425 (1985).Jensen, K., and N. Wirth (revised by A. B. Mickel and J. F. Miner): Pascal User Manual andReport, 3d ed., Springer-Verlag, New York (1985).Kernighan, B. W., and D. M. Ritchie: The C Programming Language, 2d ed., Prentice-Hall,Englewood Cliffs, N.J. (1988).Kleinrock, L.: Queueing Systems, Vol. I, Theory, John Wiley, New York (1975).Kleinrock, L.: Queueing Systems, Vol. II, Computer Applications, John Wiley, New York (1976).Koffman, E. B., and F. L. Friedman: Problem Solving and Structured Programming in FORTRAN77, 3d ed., Addison-Wesley, Reading, Mass. (1987).Lavenberg, S., R. Muntz, and B. Samadi: Performance Analysis of a Rollback Method forDistributed Simulation, Performance '83 (A. K. Agrawala and S. K. Tripathi, eds.):117-132 (1983).Law, A. M., and M. G. McComas: Pitfalls to Avoid in the Simulation of Manufacturing Systems,Ind. Eng., 21: 28-31 (May 1989).Law, A. M., and M. G. McComas: Secrets of Successful Simulation- Studies, Ind. Eng., 22: 47-48,51-53, 72 (May 1990).Wi;~ / Misra, J.: Distributed Discrete-Event Simulation, Computing Surveys, 18: 39-65 (1986). Morgan, B. J. T.: Elements of Simulation, Chapman & Hall, London (1984)., Naylor, T. H.: Computer Simulation Experiments with Models of Economic Systems, John Wiley,New York (1971).Pegden, C. D.: Introduction to SIMAN (January 1989 version), Systems Modeling Corp.,Sewickley, Pa. (1989).Pratt, C. A.: Catalog of Simulation Software, Simulation, 49: 165-181 (1987).Pritsker, A. A. B.: Introduction to Simulation and SLAM II, 3d ed., Systems Publishing Corp.,West Lafayette, Ind. (1986). .Rasmussen, J. J., and T. George: After 25 Years: A Survey of Operations Research Alumni, CaseWestern Reserve University, Interfaces, 8:3: 48-52 (1978). Ross, S. M.: Introduction to Probability Models, 4th ed., Academic Press, San Diego, Calif.j (1989). Rubinstein, R. Y.: Simulation and the Monte Carlo Method, John Wiley, New York (1981).Sargent, R. G.: Event Graph Modelling for Simulation with an Application to Flexible Manufac-turing Systems, Management Sci., 34: 1231-12.51 (1988).

132 SIMULATION MODELING AND ANALYSISSchmidt, J. W., and R. E. Taylor: Simulation and Analysis ofIndustrial Systems, Richard D. Irwin,Homewood, Ill. (1970).Schruben, L.: Simulation Modeling with Event Graphs, Commun. Assoc. Comput. Mach., 26:957-963 (1983).Shannon, R. E.: Systems Simulation: The Art and Science, Prentice-Hall, Englewood Cliffs, N.J.(1975). .Shannon, R. E., S. S. Long, and B. P. Buckles: Operations Research Methodologies in Industrial Engineering, AIlE Trans;; 12: 364-367 (1980).Sheppard, S., R. E. Young, U.,Chandrasekaran, and M. Krishnamurthi: Three Mechanisms for Distributing Simulation, Proc. 12th Conference of the NSF Production ,Research and Technology Program, Madison, Wis., pp. 67-70 (1985).Solomon, S. L.: Simulation of Waiting-Line Systems, Prentice-Hall, Englewood Cliffs, N.J. (1983).Som, T. K., and R. G. Sargent: A Formal Development of Event Graphs as an Aid to Structuredand Efficient Simulation Programs, ORSA J. Comput., 1: 107-125 (1989).Stidham, S: A Last Word on L = Aw, Operations Res., 22: 417-421 (1974).Swart, W., and L. Donno: Simulation Modeling Improves Operations, Planning, and Productivity for Fast FOQd Restaurants, Interfaces, .11:6: 35-47 (1981).Thomas, G., and J. DaCosta: A Sample Survey of Corporate Operations Research, Interfaces,9:4: 102-111 (1979).

CHAPTER 2 MODELING COMPLEX SYSTEMS Recommended sections for a first reading: 2.1 through 2.52.1 INTRODUCTIONIn Chap. 1 we looked at simulation modeling in general, and then modeled andcoded two specific systems . Those systems were very simple, and it waspossible to program them directly in a general-purpose language , without usingany special simulation software or support programs (other than a random-number generator) . Most real-world systems, however, are quite complex, andcoding them without supporting software can be a difficult and time-consumingtask. In this chapter we first discuss an activity that takes place in mostsimulations, list processing. A group of FORTRAN support routines, SIMLIB ,is then introduced, which takes care of some standard list-processing tasks aswell as several other common simulation chores, such as processing the eventlist, accumulating statistics, generating random numbers and observations froma few distributions, and writing out results. SIMLIB is then used in fourexample simulations, the first of which is just the single-server queueing systemfrom Sec. 1.4 (induded to illustrate the use of SIMLIB on a familiar model) ;the last three examples are of somewhat greater complexity. 133