ACE Tutorial. October, 2013 Byoung K. Choi and Donghun Kang
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1 ACE Tutorial October, 2013 Byoung K. Choi and Donghun Kang
2 Objective This document aims to provide a minimum tutorial guide for a beginner to get started with the activity-based simulation tool kit ACE. It gives a procedural description of how to build an ACE simulation program that ranges from creating a blank activity transition table to running the simulation. Recommendation Prior to reading this document, the readers are recommended to read and understand Chapter 6 ( 6.6) of the textbook, Modeling and Simulation of Discrete-Event Systems by Choi and Kang. History of This Document Date Version Reason Person(s) in charge 05/10/ Initial Draft Byoung K. Choi <bkchoi@kaist.ac.kr> 05/16/ Second Draft Donghun Kang <donghun.kang@kaist.ac.kr> Donghun Kang <donghun.kang@kaist.ac.kr> 02/13/ Third Draft with modeling with canceling arc 02/19/ Final Document Byoung K. Choi <bkchoi@kaist.ac.kr> 2
3 Table of Contents 1. Basic Features of ACE Modeling of a Single Server System Create a blank ATT (Activity Transition Table) Declare Queues C, M and Q with initial values (C=1, M=1, Q=3) Building the Activity Transition Table (ATT) Initialize Enabled Activities = {Create} Run the Simulation Declaring Variables Modeling with Canceling Arcs Additional Modeling Features Random Variate Generation Functions Syntax for Specifying Conditions and Actions
4 1. Basic Features of ACE ACE is an ACD-model executor whose input is a formal ACD model specified in the form of an activity transition table. The main window of ACE is divided into three regions: Main Menu, Activity Transition Table (ATT) Window, and Spreadsheet Window. Also provided are three tool bars: ATT Tool Bar in the ATT Window, and Queue Tool Bar and Variable Tool Bar in the Spreadsheet Window. The procedure of building an ACE simulation program consists of the following: 1) Create a blank Activity Transition Table. 2) Declare all Queues and Variables in the Spreadsheet Window 3) Build the Activity Transition Table in the ATT window 4) Initialize Enabled Activities 5) Run the simulation The above procedure will be explained with the Activity Transition Table of a single server system given below. ACE supports a number of random variate generation functions including Exp (μ), Erlang (α, λ), Beta (α, β), and Uni (α, β). The procedure for declaring Variables will be described with another example. 4
5 2. Modeling of a Single Server System 2.1 Create a blank ATT (Activity Transition Table) 1) At the Main Menu, click File New to create a blank ATT. 2.2 Declare Queues C, M and Q with initial values (C=1, M=1, Q=3) 1 In the Spreadsheet Window, select the Queue tap to bring up the Queue Tool Bar and then (a) click Add-queue ( ) button to (b) create a new row (Queue1) for the queue C as shown below: 2 In the Spreadsheet Window, specify the attribute values of Queue1 as follows: (a) Name = C; (b) Type = Creator; (c) Initial Value = 1. 3 At the Queue Tool Bar, (a) Click Add-queue ( (Queue2) for the queue M as shown below: ) button to (b) append a new row 5
6 4 In the Spreadsheet Window, specify the attribute values of Queue2 as {Name = M; Type = Resource; Initial Value = 1}. 5 At the Queue Tool Bar, Click Add-queue ( ) button to append a new row for the queue Q. 6 In the Spreadsheet Window, specify the attributes in the appended row as {Name = Q; Type = Entity; Initial Value = 3} and then provide the queue names in the Description fields as follows: 7 In the ATT Window, check if the queues C, M and Q are properly initialized. 2.3 Building the Activity Transition Table (ATT) 1 In the ATT Window, (1) select Activity1 and (2) click Add-arc ( an additional arc for the activity Activity1. ) button to create 6
7 2 In the ATT Window, set the name of Activity 1 to Create and specify all the data for the selected activity. 3 In the ATT Window, (1) select Create and (2) click Add-activity ( append another activity Activity2 after the Create activity. ) button to 4 In the ATT Window, set the name of Activity 2 to Process and specify all the data for the selected activity. 2.4 Initialize Enabled Activities = {Create} 1 In the ATT Window, (1) select Create and (2) click Enabled-activity ( ) button to make Create an Enabled Activity as shown below. Now the ATT is completely defined! 7
8 2.5 Run the Simulation 1 At the Main Menu, click File Save As as shown below, and give the folder name and file name to store the completed ATT (activity transition table). 2 At the Main Menu, click Run Run Options to open the Run Options dialog box and then specify run options as shown below: EOS (end of simulation) time = 500; Random (number) Seed = 12345; and check the System Trajectories box. 3 At the Run Options dialog box, click Save & Run to run the simulation. Check the Output Report and Output Plots as shown below. 8
9 3. Declaring Variables In ACE, all variables are regarded as 2-dimensional array. A simple (non-array) variable is regarded as a 1x1 array. All variables are initially set to zero as a default. Methods of declaring an integer k and an integer array N[12] = {0, 0, 0, 0, 3, 3, 3, 5, 3, 1, 1, 0} will be described. 1 In the Spreadsheet Window, (1) select the Variable tap to bring up the Variable Tool Bar and (2) click Add-variable ( ) button to create a new row with Name = Variable1 as shown below. 2 In the Spreadsheet Window, set the Name field to k and click 0 rows button to bring up the Initial Values window with a default value of 0. When the type of the variable is not integer, its type is selected from the fold-down menu as shown below. 3 At the Variable Tool Bar, Click Add-variable ( = Variable2 as shown below. ) button to append a row with Name 9
10 4 In the Spreadsheet Window, (1) set Name to N, (2) set Columns to 12 (Rows and Type are not changed), (3) click 0 rows button to bring up the Initial Values window having 12 columns, and (4) set the entries of the Initial Values window to the given initials values as shown below. 4. Modeling with Canceling Arcs In Chapter 10 ( 10.3) of the textbook, it was shown that the use of the canceling arc in an ACD proved to be quite convenient when modeling reneging, resource failures, and time-constrained processing. The canceling arc in ACD is denoted by a circle-tailed arrow, which indicates that whenever the originating activity is completed, the target activity is canceled if it is active. How to model an ACD with canceling arcs using ACE will be described with the ACD in Fig of the textbook and it s ATT given below. In this single server system with reneging, the customers waiting for a service in a line may leave if they have waited more than Uni(10,15) minutes. 10
11 First step is to build an ATT (see below) from the above input ATT by following the ACE program building procedure described in Section 2 of this tutorial. Once the ATT is built, the simulation is run by clicking Run Run Options at the Main Menu to open the Run Options dialog box and then specify run options as {EOS time = 500, Random number seed = 12345, and the System Trajectories box marked}: At the Run Options dialog box, click Save & Run to run the simulation. Check the system trajectory of the Output Report. Observe that a Waited event listed in the Future Event List {Created( ), Waited( )} at Clock is canceled by the Processed event where Q=1 > 0 at Clock
12 Also, as time goes by, the queue length at the Q queue increases. Therefore, at a certain time, a job gets started to renege. Observe that at Clock , the Waited event is executed where Q=4 and M=0 (busy), which means that a job waiting at the Q queue will renege the system. 5. Additional Modeling Features 5.1 Random Variate Generation Functions The ACE supports a number of random variate generation functions that can be used in specifying inter-arrival times, service or processing times, etc. As shown in the table below, the supported distribution functions are Normal, Beta, Exponential, Weibull, Erlang, Student-T, Uniform, and Triangular. All the random variate generation functions return a floating point random number. Therefore, the system variable to which the returned value of a random variate generation function is assigned, should be declared as a type double. Probabilistic Distribution Function Description 12
13 Normal normal (μ, σ) Beta beta (α, β) Exponential exp (μ) Weibull weib (α, λ) Erlang erlang (α, λ) Student-T student (ν) uni () Uniform uni (α, β) Triangular tri(α, β, γ) Returns a floating point random number that follows the normal distribution having parameters μ and σ where - < μ <, 0 σ <. Returns a non-negative floating point random number less than or equal to 1.0 with the parameters α and β where 0 < α, β <. Returns a floating point random number that follows the exponential distribution having a parameters μ. Returns a floating point random number that follows the weibull distribution having two parameters α and λ where 0 < α, λ <. Returns a floating point random number that follows the Erlang distribution having two parameters α and λ where 0 < α < and λ {1,2, }. Returns a floating point random number that follows the Erlang distribution having a parameter ν where ν {1,2, }. Returns a non-negative floating point random number less than 1.0; that is, the range of return values includes 0.0 but not 1.0. Returns a floating point random number within the specified range; that is, the range of return values (X) includes α but not β (α X < β). Returns a floating point random number that follows triangular distribution within the specified range; that is, the range of return values include α and β where - < α < β <, α γ β. The random variate generation functions may be utilized as follows: 1 Specifying the BTO-event s time: In the following ATT Window, the BTO-event Time column for the activity Create is specified with the random variate generation function, Exp(15) or alternatively, exp(15). All the random variate generation function may start with a capital letter, but the rest should be lower case letters. 2 Assigning a random value to a system variable in the At-begin/At-end Actions Prior to assign a random value to a system variable, the system variable should be declared (as type double ). In the following Spreadsheet Window, the system variable U is declared as a type of double. 13
14 Then, in the following ATT Window, the At-begin Action of the activity Inspect is to assign a uniform random number to a system variable U, namely, U = Uni(0, 1), in order for a probabilistic branching. 5.2 Syntax for Specifying Conditions and Actions When specifying At-begin/At-end Conditions/Actions, the syntax described in the following should be used (Mostly, it follows the syntax of Microsoft C# programming language. Please, refer to the C# Programmer s Reference located at MSDN website). 1 Naming of a Variable or Queue The name of a queue or a variable should begin with a letter that could be followed by a sequence of letters, digits (0-9) or underscore. The first character cannot be a digit. The name of a queue or a variable must not contain any embedded space or symbol like? - # % ^ & ( ) [ ] { }. ; : / and \. 2 Operators The following operators are permitted to use in the conditions and actions. Operator category Operators Description Arithmetic + Add two operands: A + B - Subtract seconds operand from the first: A - B * Multiply both operands: A * B / Divide numerator by de-numerator: B / A % Computes the remainder after dividing its first operand by its second: A % B 14
15 Logical Increment/decrement Relational Assignment && Logical AND of its bool operands: A && B (true or false) Logical-OR of its bool operands: A B (true or false)! Negates its operand:!a (true if A is false, false if A is true) ++ Increase integer value by one: A++ -- Decrease integer value by one: A-- == Returns true if the values of tis operands are equal, false otherwise: A == B!= Returns false if its operands are equal, true otherwise: A!= B <,>,<=,>= = += A += B is equal to A = A + B -= A -= B is equal to A = A B *= A *= B is equal to A = A * B /= A /= B is equal to A = A / B %= A %= B is equal to A = A % B Less than, greater than, less than or equal, greater than or equal operators. Stores the value of its right-hand operand to the left-hand operand: A = B 3 Statements When specifying At-begin/At-end Actions, each statement should end with a semicolon ; to separate the statements. The semicolon at the end of a last statement of an Action may be omitted. For example, the following actions are all valid: A-- A--; P1--; M1--; When specifying the Influence Activity column, the adjacent activities should be separated by a comma,. The syntax of the conditional statement if-else in an Action follows that of the C# language, as can be seen in the following example. 15
16 In the ATT Window given below, a type casting operator is used to prevent illegal type casting error. The type of the variable k is integer, but the type of the right-hand side operand (Clock / 120) double. Therefore, an explicit type cast from double-type to integer-type using (int) is enforced in the statement. 4 Array Variable The ACE supports array-type variables. In order to access an element of an array-type variable, the symbol [] is used to give a specific position of the element. If the variable is a two-dimensional array, [][] is used. In the ATT Window given below, the variables N and R are declared as array-type variables (Remember that a onedimensional array should have 1 for Rows column). For example, the 5 th element of the variable N can be accessed via N[4] because the array index starts from zero. 16
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