SIGMA Tutorial. March, 2013 VMS Technology, Inc.

Transcription

1 SIGMA Tutorial March, 2013 VMS Technology, Inc. This SIGMA tutorial aims to provide a minimum but sufficient guide for a beginner to get started with SIGMA. For more details, the reader is recommended to refer to the SIGMA website ( or the book Event Graph Modeling Using SIGMA, 4 th Ed., by Schruben and Schruben. SIGMA version 3.5 is used throughout this tutorial.

2 1. Basic Features of SIGMA SIGMA is an event graph based discrete event simulation software, and supports the full simulation modeling life cycle that consists of (1) model building & testing, (2) output analysis, (3) animation & graphical data tracking, and (4) documentation and report writing. While simulation is running, simulation model can be created, enriched and edited. 2. Installation of Educational Release of SIGMA You can download the latest educational release (free copy) of SIGMA from the link below. You have to provide your address so that they can send you a serial number. When installing SIGMA, you enter your address and serial number as shown below 3. Main Menu of SIGMA 3-1. Menu bar File Menu Bar - New to create a new model at the Create Event mode - Open Event Graph Model to open (bring in) an existing model - Save to save the current model under the same name - Save As to save the current model with a new name 2

3 Edit Menu Bar - Cut to copy & cut away the selected entities (Events & Edges) - Copy to copy the selected entities - Paste to paste the copied entities - Delete to delete the selected entities Run Menu Bar - Start to start a simulation-run of the current model - Options to set options for making a simulation-run Variables Menu Bar - Create/Edit Variables to define (declare) state variables 3-2. Tool bar Back to Edit Create Event Create Single Edge Start Run 4. SIGMA Program Building Procedure If clicked during a Create mode, the mode is changed back to Edit Create graphical components of an event graph model in sequence Add an edge between two vertices (or edge-vertex to a vertex) Run the simulation of the defined event graph model The procedure of building a SIGMA program for simulation consists of the following steps: 1) Create a SIGMA Event Graph (consisting of vertices and edges) on the main screen. 2) Declare all the variables introduced state variables at the dialog box 3) Define Run vertex: Variables are initialized or listed as parameters to be initialized later in the Run Options dialog box. 4) Define Event vertices: State changes and the parameter variable of each event vertex are described at an Edit Vertex dialog box. 5) Define Edges: the time delay, edge condition, and attribute (parameter value) of each edge are defined at an Edit Edge dialog box. 6) Run Options: The condition for terminating the simulation run ( Stop on condition) and variables to be traced are specified, and state variables are initialized. The modeling procedure will be explained for the single server event graph model: 3

4 5. SIGMA Modeling and Simulation Example (Single Server System) 5-1. Create SIGMA Event-Graph 1) At the Edit mode, click File New (left-button) to get into the Create Event mode. 2) Now, a cursor appears to indicate that we are in the Create Event mode (Cursor ) 3) Click at the cursor to create Vertex#1 and drag the curser to the next node location 4) Repeat the above event-vertex creation operation to obtain the Vertices 1~4. 5) Click Vertex#3 to create an edge 4 3, and click right button to return to the Edit mode. 6) Click the tool bar to get into the Create Single Edge mode (cursor: ). 4

5 7) Double-click Vertex#2 to create a self-edge, and click right button (back in Edit mode) 8) Double-click Vertex#1 to get the dialog box Edit Vertex 1: - Enter Run in the Name field of the dialog box: - Press the OK button of the dialog box to change its name to Run: 9) Double-click Vertex#2 to get the dialog box Edit Vertex 2: - Enter Arrive in the Name field of the dialog box: - Press the OK button of the dialog box to change its name to Arrive: 10) Double-click Vertex#3 to get the dialog box Edit Vertex 3: - Enter Load in the Name field of the dialog box: - Press the OK button of the dialog box to change its name to Load: 5

6 11) Double-click Vertex#4 to get the dialog box Edit Vertex 3: - Enter Depart in the Name field of the dialog box: - Press the OK button of the dialog box to change its name to Depart: 5-2. Declare State Variables (Enter Q and M) 1) Click Variables Create/Edit Variables at the Edit mode to open the State Variable Editor: 2) - Enter Q (Name field); enter Number of jobs (Description field); click Add button; - Enter M (Name field); enter Machine status (Description field); click Add button: 5-3. Define Run Vertex (Enter Q, M as its Parameter Variables) 1) Double-click Vertex#1 to get the dialog box Edit Vertex 1: 2) - Enter Q, M in the Parameter field of the dialog box: 6

7 5-4. Define Event Vertices (Describe State Changes) 1) Double-click Vertex#2 and enter Q= Q+1 in the State Change field of the dialog box: 2) Double-click Vertex#3 and enter Q=Q 1, M=M 1 in the State Change field: 3) Double-click Vertex#4 and enter M=M+1 in the State Change field: 7

8 5-5. Define Edges (Enter Delay time and Edge condition) 1) Double-click Run Arrive Edge and enter 0 and True in the Delay and Condition fields: 2) Double-click Arrive Load Edge and enter 0 and M>0 in the Delay and Condition fields: 3) Double-click the double edge Load Depart to get a Select a Sub-edge dialog box (1) Select the Load Depart edge and enter 2*ERL{1} and True : (2) Select the Depart Load edge and enter 0 and Q>0 : 8

9 4) Double-click Arrive Arrive Edge and enter 5*ERL{1} and True : 5-6. Define Run Options (Random# seed, Stop-on, Trace variable, Initial values) - Click Run Options to define run options in the Run Options box. (1) Enter in the Random Seed field as the random number generator seed. (2) Check the Time button and enter 100,000 in the Stop time field. (3) Enter Q, M in the Trace Variables field. (4) Enter 0, 1 (as the initial values of Q, M) in the Initial Values field Make a simulation run - Click Run Start to start a simulation run 9

10 6. SIGMA Functions SIGMA supports a number of built-in functions which may be grouped into 1) random variate generation functions, 2) statistical functions, 3) simulation clock, 4) list handling functions, 5) data reading function, and 6) mathematical functions Random Variate Generation Functions 1) U = RND ~ U(0,1): standard uniform random variate 2) X = ERL{K} ~ Erlang(k,1): standard k-erlang random variate 3) X = NOR{M;S}: normal random variate with mean=m and variance=s Statistical Functions (X and Q have to be declared as traced state variables) 1) A = AVE{X}: cumulative average of the sampled variable {X t } 2) B = TAV{Q}: cumulative time-average of the time-dependent variable Q(t) 10

11 6-3. Simulation Clock Function 1) T = CLK: current simulation clock 6-4. Ranked-List (Priority Queue) Handling Functions SIGMA supports built-in ranked-lists. A ranked-list, which is a list of ENT[] records and is identified by its list-index L, is constructed by the PUT{O;L} function, and its record is removed by the GET{O;L} function. The array ENT[] is used exclusively as a buffer for storing/removing a record (data about an entity) to/from a ranked-list using the PUT{}/GET{} function. For example, ENT[0] = Arrival-time, ENT[1]= Job-type, ENT[2]= Due-date, etc. The array RNK[L] contains the index of the element of ENT[] that is to be used for ranking the records in the ranked-list L. Namely, the records of the ranked-list L is ranked (or sorted) by the data field ENT[RNK[L]]. For example, if the jobs in the ranked-list 5 are to be ranked by their arrival-times ENT[0], we set RNK[5]=0. 1) GET{O;L} removes a record from L according to O and places it in the ENT[] array. (1) O=FST: removes the first record of the ranked-list L and places it in ENT[]; (2) O=LST: removes the last record of the ranked-list L and places it in ENT[]; (3) O=KEYT: removes the first record of L, if any, whose REC[0] matches ENT[0]; 2) PUT{O;L} places the current contents of ENT[] into L according to the option O: (1) O=FIF(first-is-first) inserts ENT[] after the last record of L (2) O=LIF(last-is-first) inserts ENT[] before the first record of L (3) O=INC inserts ENT[] in an increasing order of ENT[RNK[L]] (4) O=DEC inserts ENT[] in a decreasing order of ENT[RNK[L]] Both PUT{O;L} and GET{O;L} return 1 if successful and 0 otherwise. Thus, let Q[L] denote the size of the ranked-list L, then the enqueue operation Q++ is expressed as: Q[L] = Q[L] + PUT{FIF;L} And, the dequeue operation Q-- is expressed as: Q[L] = Q[L] GET{FST;L} 6-5. Data Reading Function 1) DISK {F; I} reads the I-th data from the text file F. If I=0, the file is read sequentially to wrap around (After reaching the end of the file, reading starts again at the beginning). For example, X = DISK{DATA.DAT; 9} will read the 9 th data of the file DATA.DAT and assign it to X Mathematical Functions 1) H= MOD{X;M} returns the integer remainder of X/M where X and M are real expressions. 2) MAX{X;Y}/ MIN{X;Y}: maximum/ minimum of X and Y. 3) COS{X}/ SIN{X}: cosine/sine of Y (in radians) 11