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SJSU ISE 230 - Simulation with Process Model

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Chapter 22 Simulation with Process ModelDescription22.1 Simulating an M/M/1 Queuing System22.2 Simulating a M/M/2 System22.3 A Series SystemExampleSlide 8SolutionThe Effect of a Finite Buffer22.4 Simulating Open Queuing Networks - ExampleSlide 12Slide 13Slide 1422.5 Simulating Erlang Service TimesSlide 1622.6 What Else Can Process Model Do?Chapter 22Simulation with Process Modelto accompanyOperations Research: Applications and Algorithms 4th editionby Wayne L. WinstonCopyright (c) 2004 Brooks/Cole, a division of Thomson Learning, Inc.2DescriptionIn Chapter 9 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.322.1 Simulating an M/M/1 Queuing SystemAfter installing Process Model you can start it by selecting Start – Programs – Process Model.You will see the process model screen appear. The book contains a labeled diagram showing key icons.Process Model is an easy to use software that allows you to simulate queuing systems.To simulate a M/M/1 queuing systems having λ=10 arrivals/hour and µ=15 customers/hour. (See the file MM1.igx on the cd from the book.)4 The book walks you through the steps of creating the model.During the simulation an on-screen scoreboard tracks the following quantities:Quality Processed-Total Number of units to leave systemCycle Time-Average time a unit spends in systemValue Added Time-Time which a unit spends in serviceCost Per Unit-If costs are associated with the resources, the cost incurred per unit serviced is computed.After completing the simulation you are asked if you want to view the output. Sample output can be seen in the book.522.2 Simulating a M/M/2 SystemLet us suppose that we had two telephone operators who can handle calls.To modify the previous example we simply need to change the number of operators to 2 and ensure that up to 2 operators can be working on calls at the same time.See the file MM2.igx. The book contains the output of running this file for 1000 hours.622.3 A Series SystemThis section uses Process Model to simulate a series queuing system.The auto assembly line example used previously will be used.7ExampleThe last two things that are done to a car before its manufacture is complete are installing the engine and putting on tires.An average of 54 cars per hour arrive requiring these two tasks.One worker is available to install the engine and can service an average of 60 cars per hour.After the engine is installed, the car goes to the tire station and waits for its tires to be attachedThree workers server at the tire station.8 Each works on one car at a time and can put tires on a car in an average of 3 minutes.Assume interarrival times and service times are exponential.Simulate this system for 400 hours.9SolutionSee the file Carassembly.igx.The key to creating a queuing network with Process Model is to build the diagram one service center at a time.Begin by creating arrivals in Example 1 and then create the engine production center and the tire center.The tire center will need to have the number of servers changed.The system is flexible and can be modeled to accommodate changes in Move Time and other factors.10The Effect of a Finite BufferThe output form this model can be found in the book.Suppose we only have enough space for two cars to wait for Tire installation. This is called a buffer of size 2.To model this change the Input Capacity in the Tire Activity dialog box needs to be changed to 2.Running the simulation shows the average wait is 6 hours. Clearly we need more storage space.1122.4 Simulating Open Queuing Networks - ExampleAn open queuing network consists of two servers: Server 1 and Server 2.An average of 8 customers per hour arrive from outside at Server 1.An average of 17 customers per hour arrive from outside at Server 2.Interarrival times are exponential.Server 1 can server at an exponential rate of 20 customers per hour and Server 2 can serve at an exponential rate of 30 customers per hour.12 After completing service at Server 1, half the customers leave the system and half go to Server 2.After completing Service at Server 2 75% of the customers complete service and 25% return to Server 1.Simulate this system for 400 hours.13SolutionSee the file Open.igx.To begin we create two arrival entities: one arrival entity representing external arrivals to Server 1 and one arrival entity representing external arrivals to Server 2.After creating the Servers we use the connector tool to create a link from Server 1 to Server 2, a link Server 2 to Server 1, and a link from Server 2 to Server 1, and a link from Server 1 and 2 to the exiting system.14 We input the arrival and service rates, move times along with the routing information into the software.The project diagram can be seen in the book.Note as the simulation runs some calls move between the servers and some exit the system!Seeing this movement really makes the concept of an open queuing network come alive!1522.5 Simulating Erlang Service TimesService times often do not follow exponential distribution.Usually the Erlang distribution is used to model nonexponential service times.An Erlang distribution can be defined by a mean and a shape parameter k.The shape parameter must be an integer.It can be shown that Standard Deviation of Erlang = kMean16 Therefore is we know the mean and the standard deviation of the service times we may determine an appropriate value of k.The syntax for generating Erlang service times in Process Model is ER(Mean, k).1722.6 What Else Can Process Model Do?A brief description of other modeling features included in Process Model follows:Bulk Arrivals and ServicesOften at a restaurant people arrive in groups. This arrival pattern is called bulk arrivals.RenegingPerhaps people hang up when calling an 800 number if they are put on hold more than 5 minutes. Process Model can model such balking or reneging behavior.Variation in Arrival patternAt a restaurant or bank arrival rate varies substantially over the course of the day. Variable arrival rate patterns can easily be modeled with Process Model.18 Variation of Number of ServersDuring the day workers take breaks and go to lunch. Also many companies


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