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1、? Simulation with Process ModelIn Chapter 21, we learned how to build simulation models of many different situations. In this chapter, we will explain how the powerful, user-friendly simulation package Process Model can be used to simulate queuing systems.22.1Simulating an M/M/1 Queuing SystemAfter
2、installing Process Model from the books CD-ROM, you can start Process Model by selecting Start Programs Process Model 4. You will see the screen shown in Figure 1, where some key icons have been labeled. It is simple to simulate an M/M/1 queuing system having l ? 10 arrivals/hour and m ? 15 customer
3、s/hour. See file MM1.igx. Assume that these are calls for directory assistance.Step 1Click on one of the arrival icons (a person or a phone) and drag the icon to the blank part of the screen (called the Layout portion). We have chosen to use the phone icon. Your screen should look like Figure 2.Step
4、 2Select the Process rectangle and drag it right over the arrival icon. Click on it and drag it to the right. You will now have a double-arrowed connection between the arrival icon and the Process rectangle. The double-arrowed icon indicates the arrival of entities into the system. Later we will tel
5、l Process Model that interarrival times are exponential with mean 6 minutes. After Taking Calls is typed within the Process rectangle, the Lay- out window looks as shown in Figure 3.Step 3Choose one of the server icons to represent a telephone operator (say, the person with the computer) and drag th
6、is icon to the Layout window above the Take Calls Process rectangle. Then type the word “operator” to indicate a phone operator. Next, click on the Connector Line tool in the Toolbox and place the cursor over the operator. We then click once and drag a connection down to the Take Calls activity. Thi
7、s indicates that the oper- ator can take calls. The Layout window should now look as shown in Figure 4.Step 4Next, tell Process Model to make interarrival times exponential. Process Model works off the mean interarrival time or service time, not the arrival or service rates. Process Model supports m
8、any distributions, including the triangular, normal, and Erlang random variables. For now, we will use the exponential distribution. Since the average time between arrivals is 6 minutes, we will model the interarrival times as E(6). (E stands for exponential.) To enter the interarrival time distribu
9、tion, click on the double arrow con-necting Call to Take Calls and fill in the dialog box as shown in Figure 5. Entering Peri- odic and E(6) ensures that interarrival times will be generated over and over as indepen- dent exponential random variables with mean 6.MM1.igx1192C H A P T E R2 2Simulation
10、 with Process ModelStep 5We now need to tell Process Model that service times are exponential with mean4. To do this, click on the Take Calls Process rectangle and fill in the dialog box as shown in Figure 6.Step 6We have now completed the model setup. Select File Save As and save the model.(All mod
11、els have the suffix .igx.)Step 7To run the simulation, select Simulation and then Options and fill in the dialog box as shown in Figure 7.We have chosen to run the system for 4,000 hours. Choosing a Warmup length of 1 hour, the first hour of running the simulation will not be used in the collection
12、of sta- tistics. To start the simulation, choose Simulation Save and Simulation. As the simulationprogresses, telephone calls moving through the flowchart illustrate the flow of calls through the process. Resources or servers will show a green light when the resource is being utilized and a blue lig
13、ht when idle. Counters above and to the left of each activity represent the number of calls waiting to be processed. The speed of the simulation can beConnector lineArrivals or resources ProcessrectangleServers F I G U R E 12 2 . 1Simulating an M/M/1 Queuing System1193F I G U R E 2F I G U R E 31194C
14、 H A P T E R2 2Simulation with Process Modelcontrolled by moving the Speed Control bar, left for slower and right for faster. By choos- ing Simulation End Simulation, you may stop the simulation at any time. During the sim- ulation, an on-screen scoreboard tracks the following quantities:IQuantity P
15、rocessed (total number of units to leave the system)ICycle Time (average time a unit spends in the system)F I G U R E 4F I G U R E 5F I G U R E 62 2 . 2Simulating an M/M/2 System1195IValue Added Time (time a unit spends in service)ICost Per Unit (if costs are associated with the resources, the cost
16、incurred per unit serviced is computed)After completing the simulation, you are asked if you want to view the output. If so, youwill see an output similar to Figure 8, and the output may be saved as a text file. Figure 8 includes comments (in boldface) to explain the key portions of the output. If we treat this output as representative of the systems steady state, we have the fol- lowing parameter estimates:I?0? .3363I?0? ?1? .5634IWs?
