A Software Tool for the
Performability Evaluation
with Stochastic and Colored Petri Nets





Armin Zimmermann and Michael Knoke

Technische Universität Berlin
Real-Time Systems and Robotics Group

Faculty of EE&CS Technical Report 2007-13
ISSN-Nr. 1436-9915, August 2007

Contents

1  Introduction

1.1  History of the Tool

• an algorithm for the transient analysis of DSPNs
• a component for the steady-state and transient analysis of discrete time deterministic and stochastic Petri nets
• a component especially designed for manufacturing systems, including
  • modeling with hierarchically and colored stochastic Petri nets
  • independent models for structure and work plans
  • steady-state analysis and simulation
  • model based control
• a completely rewritten graphical user interface (Agnes), which integrates all different net classes and analysis algorithms

• a generic graphical user interface in JAVA based on an XML net class representation, easily extendable for most graph-like modeling formalisms
• user interface and evaluation algorithms run under Windows and Linux operating system environments
• modeling and simulation of stochastic colored Petri nets
• graphical display of SCPN simulation results
• independent components for modeling, simulation, analysis, and result output allowing the GUI to be run on a different computer than the analysis modules

1.2  Acknowledgments

2  TimeNET's Graphical User Interface

Figure 1: Graphical user interface of TimeNET 4.0

2.1  User Interface Genericity and Net Classes

2.2  Menus

Figure 2: Menu region of the graphical user interface

Figure 3: Menu File

New...

After selecting a net class from the upcoming selection window, a new model editor window for models of this class is opened. The drawing area is initially empty and the new model is called Untitled.xml until it is given a name with Save as.... The available set of net classes depends on the net class description files that are currently accessible for the user interface. The New... command can directly be invoked by pressing

Ctrl-N

 .

Open...

From the subsequent file selection menu (explained in Section 2.6) the model to be opened can be selected. A new window of the editor is opened with the model afterward. The extension .xml for the standard TimeNET 4.0 file format is set initially, but it can be changed as desired. The tool is also able to open models in the old .TN-format, which makes it possible to import models from older versions of TimeNET. The Open... command can directly be invoked by pressing

Ctrl-O

 .

Open Recent File

A list of recently opened model files is displayed. One of these models can be opened by selecting its name. If the GUI is started for the first time, the list is empty.

Save

Save changes of the current net under the model name that is shown in the title bar of the editor window. If in front of the net path (located in the title bar) an asterisk (*) is shown, the current net has been changed since the last Save.

Ctrl-S

  also saves the net.

Save as...

Save the current model under a new name, which has to be selected in a subsequent file selector window. The model is saved in the standard TimeNET 4.0 .xml format.

Print/Export Image

Exports the current figure to a drawing program Batik, from which it is possible to print, edit and save the picture. The exported file type is Scalable Vector Graphics (SVG) which is an XML markup language for describing two-dimensional vector graphics and is supported by an increasing number of open source and commercial tools. Because this module is directly based on the shape definitions contained in the net class definitions, it will work also for future net classes. Only the currently shown model page is exported for a hierarchical model. The menu entry opens a file selection window which allows to specify the desired filename.

Settings

Opens a settings window where some options of the GUI can be configured. This includes paths, fonts, colors, default simulation values as well as various other parameter.

Exit

Closes all editor windows and quits the user interface. If there are unsaved changes in any one of the open windows, it is possible to cancel the command. Keyboard access:

Alt-Q

 .

Figure 4: Menu Edit

Undo: < command >

Takes back the last change in the drawing area. All recent changes are stored and can be rolled back one after another. The last change (command) which can be taken back by applying Undo is shown on the right side of the Undo menu entry. Keyboard shortcut:

Ctrl-Z

 .

Cut

Copies the selected model objects into the internal buffer and deletes them from the model. For a description of selecting objects and other operations on model elements, refer to Section 2.5. Keyboard shortcut:

Ctrl-X

 .

Copy

Copies the selected model objects into the internal buffer. For a description of selecting objects and other operations on model elements, refer to Section 2.5. Alternative:

Ctrl-C

 .

Paste

Adds the model elements from the internal buffer to the current model. The elements are added in a position slightly away from the position of the copied/cut elements. They are still selected after the paste operation, and can therefore easily be moved to the desired position. Pasting can also be done by pressing

Ctrl-V

 .

Copying and pasting is also possible between different pages of a hierarchical model, and between open windows containing different nets. However, it is of course impossible to paste net objects into an incompatible model (belonging to another net class). In net classes where object names have to be unique, Paste renames the added objects automatically.

Hide Output

Hides any output of the simulation windows if this entry is selected.

Figure 5: Menu View

Create new view on file

Creates a new editor window with a copy of the model which can be selected by the shown file list. In Figure 5 is only one model opened, such that the file list contains only this model name as an entry (C:\Models\EDSPN\mmppd13.xml).

Grid activation

If this entry is selected, it activates an invisible grid for aligning objects. New objects are automatically aligned on the grid. Already drawn objects are kept in their current positions, but are aligned on the grid when being moved.

Sharp edges

If this entry is selected, arcs have sharp edges. Otherwise they have rounded edges.

Scale down Image

Each click scales down the image by 10 percent (zoom out), resulting in more space on the drawing area to add objects.

Scale up Image

Scales up the image by 10 percent (zoom in) per click.

Scale to normal size

Sets the size of the image back to the original size which is defined by the GUI.

Close

Closes the current model view which is the currently active window.

Close all views

Closes all views of the current model.

Figure 6: Menu Window

Cascade

Stacks all opened model views so that each window title bar is visible.

Tile

Displays all opened model views side by side, so that all windows are visible at once. The size of the windows is decreased but the model inside each window is not scaled down.

< Models >

This is a list of currently available model views. By selecting one model in this list, the corresponding view is selected and moved to the front of all other windows.

2.3  Command Buttons

Figure 7: Command button area

New

equal to File/New...: Creates a new model

Open

equal to File/Open...: Opens a model file

Save

equal to File/Save: Saves the active model

Undo

equal to Edit/Undo: Takes back the last model change

100%

equal to View/Scale to normal size: Sets the size of the image back to the original size

Scale Down

equal to View/Scale down Image: Scales down the image by 10 percent

Scale Up

equal to View/Scale up Image: Scales up the image by 10 percent

Delete

Deletes the selected objects

Grid Activation

equal to View/Grid activation: Activates a grid for aligning objects

2.4  Object Buttons

Figure 8: Object button example for net class EDSPN

Figure 9: Generic button to activate selection mode

2.5  Drawing Area

Figure 10: Popup Menu

2.6  File Selection Window

Figure 11: File Selection Window

2.7  Solution Monitor Windows

Figure 12: Solution Monitor Window

2.8  Startup

3  Extended Deterministic and Stochastic Petri Nets

3.1  Supported Model Types

3.2  Objects and Attributes

Figure 13: Model element buttons for net class eDSPN

• The text of a place is an identification string which is shown as a label nearby the place in the model. When a place is created, it gets an initial name P plus a number. All names of model elements must be unique.
• The initial marking of a place is a text, either specifying a natural number or containing the name of a marking parameter with the initial token number. Places have an initial marking of zero.

• Their firing delay is exponentially distributed. Its default value (i.e., the expectation of the exponentially distributed firing time) is 1. Please be aware that for consistency reasons, transition firing times are specified as delays for all transition types. Firing rates of exponential transitions have to be transformed into a delay by taking their reciprocal value.
• The serverType is either Ïnfinite Server" or "Single Server" (default value). It determines the way in which multiple customers are handled. Informally speaking, transitions with infinite server semantics can be enabled concurrently to themselves as many times as there are enough input token sets available. This server characteristic is known from queuing theory. In case of a single server type the firing times are determined sequentially.

• The priority is a natural number (default: 1), that defines a precedence among simultaneously enabled immediate transition firings. The default priority is 1, higher numbers mean higher priority.
• The weight is a real value (default: 1), specifying the relative firing probability of the transition with respect to other simultaneously enabled immediate transitions that are in conflict.
• The enablingFunction (also called guard) is a marking-dependent expression¹, which must be true in order to allow the transition to be enabled. Its default empty state means that the transition is allowed to fire.

• The fixed firing delay of this transition type is initially 1.

• The firing delay of a general transition is described by its probability mass function, and belongs to the class of expolynomial functions. Such a distribution function can be piecewise defined by exponential polynomials and has finite support. It can contain jumps, making it possible to mix discrete and continuous components. Many known distributions (uniform, triangular, truncated exponential, finite discrete) belong to this class. The default firing delay UNIFORM(0.0,1.0); of general transitions is uniformly distributed in the interval zero to one. The full available syntax definition can be found at page pageref under the term < pmf_definition > .

• The arc multiplicity text is 1 initially, but can be changed by selecting the arc and enter a different value in the attribute window. This value can be marking-dependent - an arc going from a place P1 to a transition with multiplicity #P1 would flush all tokens from the place when the transition fires.

• The inhibitor arc condition text is 1 initially, but can be changed by selecting the arc and enter a different value in the attribute window. The meaning of an inhibitor arc is that if the place has at least the number of tokens specified by the condition it will hinder the transition from firing, i.e., opposite to that of a normal arc.

• The name of the measure.
• An expression which should be evaluated.
• The computed result which is changed after a successful evaluation of the model. The meaning of a computed value may depend on the algorithm that computed it, e.g. there are different results for a transient and a steady-state evaluation for the same measures. A result can be cleared by deleting the result value in the attribute window.

• P{ < logic_condition > }; corresponds to the probability of < logic_condition >
• P{ < logic_cond_1 > IF < logic_cond_2 > }; computes the probability of < logic_cond_1 > under the precondition of < logic_cond_2 > (conditional probability)
• E{ < marc_func > }; refers to the expected value of the marking-dependent expression < marc_func >
• E{ < marc_func > IF < logic_condition > }; corresponds to the expected value of the marking-dependent expression < marc_func > ; only markings where < logic_condition > evaluates to true are taken into consideration

• The defType specifies the data type of a definition and can be ïnt" or "real".
• The name of the definition.
• An expression which is the definition value and is internally replaced for every occurrence of the definition name.

3.3  Specific Menu Functions

Figure 14: Main menu of graphical user interface for net class EDSPN

Figure 15: Menu Validate for net class EDSPN

Estimate Statespace

Computes an estimation of the number of reachable states that the current model has, based on the structure of the model. Figure 16 shows an example monitor window with the result output.

Figure 16: Result example of a state space size estimation

Traps

Computes the set of minimal traps (i.e. place sets that will never become unmarked in any subsequent marking after they are once marked). Figure 17 shows an example. Every trap is described by the corresponding places and their initial marking.

Figure 17: Result example for the trap computation

Siphons

Computes the set of minimal siphons (i.e. place sets that will never become marked again in any successive marking after they become unmarked). The output of this command is similar to the one of Traps.

Check Structure

Obtains minimal place invariants of the model and extended conflict sets of immediate transitions, showing them in two windows.

A place invariant (or semi flow) is informally a set of places for which a weighted sum of tokens remains the same for any reachable marking of the Petri net. Figure 18 shows an example of the output for the model in Figure 1 on page pageref, where the number of tokens in places HeavyTraffic plus LightTraffic is always 1 (the token count of the invariant), the number of tokens in places Queue plus QueueAvailable is always 3, and place NewPacket is not contained in any place invariant.

The extended conflict set (ECS) is the second output in Figure 18. An ECS is a set of immediate transitions, obtained by the transitive closure of transitions that are in structural conflict. This is important for the specification of firing probabilities, because they are relative to the other transitions in the same ECS. Adjust the priorities of immediate transitions to put transitions into different ECS, because transitions with differing priorities cannot be in conflict with each other and will therefore not be in the same ECS. Check the ECS and adjust the priorities also in the case of confusions, which are detected and notified by the structural analysis prior to the performance analysis algorithms.

Figure 18: Example of place invariant and extended conflict set results

Tokengame

Starts the so called token game of the Petri net model, which is an interactive simulation of the model behavior. The places shown in the drawing area contain their respective number of tokens in the current state, and enabled transitions flash. Please note that the firing times of the transitions are not taken into account. Double-clicking an enabled transition with the left mouse button causes it to fire, changing the marking accordingly. This is especially useful for debugging a model, checking whether it works as it is supposed to. To exit from the token game, select the menu entry again. The user decides between resetting the marking of the model back to the state before the token game was started, and keeping the current marking as the new initial marking before reaching the normal editing mode again.

3.4  Analysis Methods

Figure 19: Menu structure of EDSPN performance evaluation algorithms

Transient / Stationary (or Steady-State)

A transient evaluation analyzes the model behavior from the initial marking at time zero until a given end time. Consequently, it can e.g. for a reliability model be used to answer questions of the type: What is the probability that after one week of operation, the system is still operable? Or: How many parts have been produced one hour after a re-setup of a manufacturing system? The performance measures are computed for the final point in time, but several analysis algorithms compute and optionally show a figure for the transient evolution of the measures over time.

Steady-state or stationary evaluation assesses the mean system performance after all initial transient effects have passed, and a balanced operation mode has been reached. It is informally comparable to the transient solution for lim_{t ® ¥} in the normal case. Steady-state evaluation computes the mean for all performance measures, and can be used to answer typical questions like: What will be the maximum bandwidth of a communication channel? Or: What will be the expected number of parts in a manufacturing system's buffer?

The selection of either transient or steady-state evaluation is done separately for each evaluation methods in the menu Evaluation. Please note that not for all evaluation algorithms there are both available.

Analysis / Approximation / Simulation:

This selects the basic type of evaluation algorithm. Analysis means a direct and exact numerical performance evaluation with a full exploration of the reachability graph. Approximation algorithms are also direct numerical techniques, but try to avoid some of the costly evaluation parts by allowing some kind of inaccuracy. Simulation algorithms do not compute the reachability graph, but follow the standard Monte Carlo style simulation approach with some refinements (details see below). The term evaluation is used throughout this document as a synonym for any of the available performance evaluation algorithms, including all three types mentioned here.

Miscellaneous

remarks for performance evaluations:

Performance measures

must be defined to tell the analysis algorithms what to compute. One exception is the stationary analysis, which computes the throughputs for all timed transitions and the token distribution probabilities for all places. Performance measures have been explained before (see page pageref). The information on how to get the performance results is given in Section 3.5.

Option windows

appear every time the user selects one of the evaluation commands. The options for every algorithm are explained below and are kept by TimeNET until the next time the window is opened. The option windows have in common a set of buttons on the lower part of the window. Start begins the algorithm, showing the output in a monitor window. Default resets the option values back to their default. Load and Save can be used to store and retrieve sets of options in an option file *.opt, while Cancel closes the window without starting the evaluation.

Monitor windows

show the output of the evaluation algorithms which are running as background processes. Please refer to Section 2.7 for details.

Stopping a running evaluation

is possible by pressing the Close button of the monitor window. Sometimes an evaluation method cannot be stopped (especially on Windows based systems). In this case the running process must be killed manually by using the task manager on Windows or the kill command on Linux.

Stationary Analysis

computes the steady-state solution of the model with continuous time. Background information about this algorithm can be found in [9,6,7].

Figure 20: Option window for steady state continuous time analysis

Figure 20 shows the available options. The Overall solution method defines how the embedded Markov chain (EMC) is treated during the algorithm: normally, it is explicitly computed and stored (option EMC explicit). It is possible to avoid fill-ins in the EMC matrix (option fill-in avoidance). Independent parts of the subordinated Markov chains (SMC) can be computed sequentially or in parallel on a cluster of workstations (option Computation of SMCs: sequential / distributed). The overall precision is given as an error value, and the maximum allowed number of iterations for the analysis algorithm as an integer.

For the integration of matrix exponentials an arithmetic with arbitrary precision can be used (option Precision of arithmetics: arbitrary / double). The number of bits to store values can be specified in the case of arbitrary precision (option Bits for arbitrary precision), and the corresponding truncation error can be given (option Truncation error). If the EMC is computed explicitly, the obtained linear system of equations can either be solved directly or iteratively. For the fill-in avoidance method the initial iteration vector can either be uniformly distributed, random, or loaded from a file. To load the vector, one must have been saved during a previous analysis (last option). For the random initialization of the initial vector a seed value for the used random number generator can be given.

Please note that in every reachable marking of the model at most one timed non-exponential transition can be enabled. Otherwise the algorithm stops with an error message. Furthermore, no dead markings are allowed in a steady-state solution.

The Experiment option allows to run multiple analysis runs automatically with a given range of parameter values. Starting the analysis as an experiment opens another dialog window as shown in Figure 21 to define the parameter range and additional experiment options.

Varying Parameter

identifies the name of a definition in the model (explained on page pageref) whose values will be iterated.

From value

specifies the start value for the varying parameter of this experiment.

To value

specifies the stop value for the varying parameter of this experiment.

Step size

allows to define a linear or logarithmic step size. In the linear mode the Summand is added in each step whereas in the logarithmic mode the Exponent is multiplied.

Summand (linear) or Exponent (logarithmic)

The value which is added or multiplied in each step.

The results of an experiment are written to a file < modelname > .EXPRESULTS which is located in the model directory as described later in Section 3.5.

Figure 21: Option window for simulation/analysis experiment

Stationary Simulation / Standard

simulates the steady-state behavior of an arbitrary SPN, and for the estimates of the performance measures are derived. Background information on the implementation can be found in [13,12]. Figure 22 shows the applicable options.

Figure 22: Option window for steady-state continuous time simulation

For all measures defined in the measure editor, estimates are computed during the simulation run. To perform a simulation, at least one measure must be defined.

Since samples from the transient phase do not represent the steady-state behavior of the model, the length of this phase is detected automatically by the simulation component and the samples from this phase are discarded. The detection can be switched off by unchecking the detect initial transient button. The initial and recommended choice are simulation runs with the detection switched on. However, there are cases in which a performance measure has no variation during the simulation (like in a completely deterministic model), confusing the detection algorithm, which never signals the end of the transient phase. After switching it off, those models can be evaluated as well.

Usually a TimeNET simulation run stops after a user-specified accuracy of the results has been achieved, which is checked statistically. The accuracy can be controlled as follows. The confidence level defines the probability (in percent) that the real value of the performance measure lies in the confidence interval, which is computed during the simulation. The maximum relative half width of the confidence interval (Maximum relative error in percent) sets the relative size of the confidence interval.

For probability measures, a refined variance estimation is used since samples of probabilities cannot be assumed to be normally distributed. The precision of estimates close to 0.0 or 1.0 can be improved by specifying a smaller permitted difference for those measures. The default value allows 50% of the probability density function to be outside the interval [0.0, 1.0] which means no improvement at all. Smaller values improve accuracy for the cost of increasing simulation run time.

To start simulation runs with the same or a different set of random numbers, the initial Seed value of the random number generator can be adjusted.

The following four options can be used to limit the run length of a simulation, which normally depends only on the model, the performance measures and the required accuracy. The Maximum number of samples that are generated for a measure can be specified, after which the simulation stops (zero means no limit). The next option can be used to set a lower limit on the simulation run, because it requires every transition of the model to be fired at least the given amount of times. This may be useful in situations where the firing frequencies differ extremely, to assure that every model activity has been covered. The Maximum model time specifies an upper limit in terms of the simulated time, i.e. measured in model time units. The Maximum real time that the simulation may take can be specified in seconds. After the simulation has stopped for any of the reasons listed above, the reached accuracy is shown in the monitor window.

The standard simulation allows two types of variance estimation, which is necessary to detect the already reached accuracy. The normal case is the application of variance estimation based on spectral variance analysis [10]. In many cases, a variance reduction technique based on control variates can be applied successfully [11]. This can accelerate the simulation run, but requires a minimum number of 5 simulation processes to be executed either quasi-parallel on the host computer or distributed in a workstation cluster.

The Experiment option allows to run multiple simulation runs automatically with a given range of parameter values. Starting the simulation as an experiment opens another dialog window as shown in Figure 21 to define the parameter range and additional experiment options. These options are already described in the previous evaluation algorithm Stationary Analysis. The results of an experiment are written to a file < modelname > .EXPRESULTS which is located in the model directory as described later in Section 3.5.

Stationary Simulation / RESTART

is a variant of the steady-state simulation algorithm, which is especially useful for evaluating models with rare events (probabilities smaller than 10^-6) and is based on the RESTART method [17]. Estimation of those events is a well-known problem in simulation algorithms, and usually requires extremely long simulation runs. To use this method, exactly one measure representing a rare event must be defined. This measure must be of the form P{#Pi > = n}; or P{#Pi < = n}; to measure the (small) probability that there are at least n (or not less than n, respectively) tokens in place Pi in steady-state.

Figure 23: Option window for steady-state RESTART simulation

Figure 23 shows the option window for this evaluation algorithm. Most of the options are equivalent to the ones already explained for the standard simulation above. The max number of RESTART thresholds is an important parameter for the RESTART technique and can be computed by the expected order of magnitude of the rare event probability. A rule of thumb is to use the positive exponent of the expected small probability, i.e. choose thresholds = 8 if the measured probability is about 10^-8. Some parameters for the method are searched in a pilot simulation run, whose length can be adapted in the according field.

Transient Analysis

computes and displays the transient solution of DSPNs, the behavior of the net from the initial marking at time zero up to a specified point in time. No general transitions are allowed for this evaluation.

Figure 24: Option window for transient analysis

For the transient analysis of a DSPN at least one performance measure must be specified. Figure 24 shows the available options. The first and most important parameter is the time until the transient evaluation should be carried out, measured in model time units. The desired numerical Precision is given next. The output form tells the program whether a graphical output of the transient behavior is wanted (curve) or not (point). The values of the performance measures are computed and copied into the model results for the final point in time in both cases.

The stepsize for output controls the points for which intermediate results are computed and displayed. The result can be obtained in two ways, either by repeating Jensen's method or by storing and computing the matrix exponentials. The cluster size determines the number of steps for which one randomization is performed [5] in the case of repeated randomizations. The internal stepsize can be adjusted to control the internal discretization points.

Transient Simulation

estimates the initial behavior until a given time. It can be used for any type of model, but is restricted to basic measures. Figure 25 shows the corresponding option window.

Figure 25: Option window for transient simulation

The simulation is always running in sequential mode. The Number of sampling points can be specified to adapt the resolution of the generated curves. If the Percentage rule is on, only a decreasing percentage of all sampling points need to reach the predefined accuracy, otherwise this must hold for all sampling points. The remaining settings have equivalent meanings like the ones for the steady-state simulation.

3.5  Evaluation Results

AUX

Contains some auxiliary information of the performed evaluation. It contains the solution method, model name, type of analysis, and some important evaluation settings.

curves

Contains visualization data of all defined measures in the case of an experiment (a set of analysis). This file can be used to plot the results with external tools.

DEFINFO

Contains information about structural properties of the model, such as marking dependent arc multiplicities, enabling functions of transitions, and marking dependent transition weights.

ECS

Describes extended conflict sets of the model.

ese

Contains an estimation of the state space.

EXPRESULTS

Contains a tabular list of results of an experiment. This file contains the end result of each measure in each experiment step. It is possible to plot this file.

INV

Contains the place invariants of the model.

pid

Contains the list of software processes which are used to evaluate the model.

pmf

Contains the delay functions of all general transitions.

RESULTS

Lists detailed results of given performance measures. This file contains the end result of each measure as it is shown in the measure definition after a successful performance evaluation. Additional contents are the throughput values of timed transitions.

rrg

Contains the reduced reachability graph (RRG) of the model in binary form.

siphons

Contains the siphons of the model.

STAT_OUT

Contains results of the statistical analysis after a stationary simulation or detailed results of a transient simulation.

STRUCT

Contains structural information for internal usage.

tmark

Contains the numbering of tangible markings of the model.

TN

Contains the model in the .TN format, which has been used since TimeNET 2.0 and is still taken as input by some evaluation methods. The graphical user interface generates this file for an eDSPN model and starts the analysis afterward. The user interface is also able to import models in this format. A description is available in Section B.

traps

Contains the traps of the model.

4  Stochastic Colored Petri Nets

4.1  Colored Petri Nets

4.2  Objects and Attributes

Figure 26: Model element buttons for net class SCPN

• The text of a place is an identification string which is shown as a label nearby the place in the model. When a place is created, it gets an initial name P plus a number. All names of model elements must be unique.
• The queue of a place is the access strategy for the selection of tokens. Three different types exists: "Random" is the default strategy and returns tokens randomly. "FIFO" returns tokens in the order of arrival (just like in a queuing system). The opposite strategy is "LIFO".
• The capacity of a place is the maximum capacity. It is the maximum number of tokens the place can contain. A value of 0 represents an unlimited capacity and is the default value.
• The tokentype of a place specifies the type of tokens for that place. As tokens have types in a colored Petri net, it is useful to restrict the type of tokens that may exist in one place to one type, which is then also the type or color of the place. This type may either be a predefined base type or a model-defined structured type. The default type is 'int', the empty type is omitted.
• The watch attribute of a place denotes an automatic measure output. If this attribute is "true", the number of tokens over time is measured and automatically displayed in the result monitor (cf. Section 4.6) as a result measure.

• Their firing delay is given as a timeFunction. Its default value is an exponentially distributed firing time of 1.0. Currently, the following time functions are available:

  Det(a)

  specifies a deterministic (constant) firing delay with the real value 'a'. Because this is not really a function it is also allowed to write just a number into the field timeFunction. Examples for a deterministic firing delay are Det(10.0) and 20.0.

  Exp(a)

  specifies an exponentially distributed firing time with the mean (expected) real value 'a'. The rate of this distribution is then '1/a'.

  Uni(a, b)

  specifies a continuous uniform distribution in the range between the real values 'a' and 'b'.

  DUni(a, b)

  specifies a discrete uniform distribution in the range between the real values 'a' and 'b'.

  Norm(m, v)

  specifies a normal distribution, also called Gaussian distribution. The real parameter 'm' is the mean value and parameter 'v' is the variance (real value).

  LogNorm(m, v)

  specifies a log-normal distribution. The real parameter 'm' is the mean value, and parameter 'v' is the variance (real value), both of the underlying normal distribution.

  Wei(k, s)

  specifies the Weibull distribution with the real-valued shape parameter 'k' and the real-valued scale parameter 's'.

  Triang(a, b)

  specifies a triangular distribution with lower limit 'a' and upper limit 'b'. The triangle is isosceles.

  A firing delay may depend on the current marking of the model. Each parameter of the time function and the time function itself may thus contain references to definitions and places. A definition is replaced by its current value and a reference to a place is replaced by the number of tokens in this place. Page pageref provides a detailed description.
  It is also possible to define an arbitrary, user-defined time function by overwriting this function as described in Section 4.7. Please be aware that for consistency reasons, transition firing times are specified as delays for all transition types. Firing rates of exponential transitions have to be transformed into a delay by taking their reciprocal value.
• Their globalGuard is a global firing condition. A global guard function restricts the enabling of a transition. It is a boolean function that depends on the model state. A transition with global guard "#P1 > 0 && #P2 < 4" is only activated if there are tokens in place P1 and less than 4 tokens in place P2. The #-sign means the number of tokens in a place. A global guard function may contain references to definitions and places. A definition is replaced by its current value and a reference to a place is replaced by the number of tokens in this place. Page pageref has a detailed description.
• Their localGuard is a local firing condition. It is a boolean function that depends on the input arc variables. The transition is only enabled with a certain binding of tokens to variables in a model state if the guard function evaluates to "true" for this setting. A transition with an input arc variable Örder" and a local guard Örder.type == 3" is only activated for tokens in the corresponding place, whose "type" attribute is "3".
• Their takeFirst attribute can be used to speed-up the simulation in certain situations. Typically, a transition creates bindings by considering all tokens of all input places and selects one of these bindings randomly. If the takeFirst attribute is set to "true", only one valid binding will be created and used. Note that the semantic of the Petri net is changed. The takeFirst attribute is usable if there is no semantical assumption of the token order.
• The serverType is either Ïnfinite Server" or "Single Server" (default value). It determines the way in which multiple customers are handled. Informally speaking, transitions with infinite server semantics can be enabled concurrently to themselves as many times as there are enough input token sets available. This server characteristic is known from queuing theory. In case of a single server type the firing times are determined sequentially.
• Their timeGuard is a global firing condition based on the simulation time. It is a function which returns the duration (a positive real value with double precision) until the transition will be enabled. The transition is only activated if the value is 0.0. The current simulation time is provided by the "NOW" value. A simulation time is internally based on the DateTime class which has a lot of functions to create, manipulate, and calculate time and date values. A detailed description of the DateTime functions can be found in Section C.1. To enable a transition each Friday at 7:00:00 am, use the following timeGuard: "return (NOW.NextWeekDay(DateTime::fri, 7, 0, 0) - NOW);".
• The specType is either Äutomatic" (default value) or "Manual". An automatic transition uses the given attributes to generate the appropriate simulation code as described in Section 4.5. Sometimes it is necessary to overwrite the generated code manually to allow special actions or complex behavior. Template classes are generated for each manual transition if the simulation is started once. These templates can be used to overwrite some of the generated code. The location and structure of these template classes are described in Section 4.7.
• The manualCode attribute can be used to add manual code for overwriting the transition behavior as described in attribute specType.
• The watch attribute of a transition denotes an automatic measure output. If this attribute is "true", the number of firings over time is measured and automatically displayed in the result monitor (cf. Section 4.6) as a result measure.
• The logfileName is the name of an optional log file which will be written during a simulation run if a logfileExpression exists.
• The logfileDescription specifies the first line of the log file. It can be used to have textual headers for different logging columns. The headers can be separated by using a double quote. A logfileDescription "Delivered"ProducedÖrdered" writes these three strings separated by a TAB character to the log file.
• The logfileExpression contains expressions in C++-syntax which are evaluated on each firing of the transition. The following expression variables can be used:

  TAB

  produces the TAB character.

  NOW

  writes the current simulation time.

  < arcvariable >

  By using the name of an arc variable of one of the input arcs, the corresponding token of the current binding can be accessed. Note that the data type is equivalent to the type of the token.

  < arcvariable.attribute >

  Like in programming languages, attributes of a complex tokentype can be accessed by using a dot followed by the attribute name. If the attribute is a complex tokentype itself, another dot can be used to access their attributes and so on.

  Assume a transition with two input arcs, one named with Ä" (structured type, attributes: "name: string" and "time: DateTime") and the other with "B" (type integer, no attributes), then a valid logfileExpression is "NOW, TAB, A.name, TAB, B, TAB, (NOW - A.time)/(3600*24)".
• The displayExpression contains one expression in C++-syntax which is evaluated on each firing of the transition and is displayed as a result measure in the result monitor (cf. Section 4.6). The expression syntax the same as for logfileExpression.

• The priority is a natural number, that defines a precedence among simultaneously enabled immediate transitions. The default priority is 1, higher numbers mean higher priority. Timed transitions have always a lower priority than immediate ones.
• The weight is a real value (default: 1.0), specifying the relative firing probability of the transition with respect to other simultaneously enabled immediate transitions that are in conflict (compare [4] for the issue of how these values should be set correctly in the context of GSPNs).

• Attribute eval defines the type of this measure. Three different types are available:

  Instantaneous

  measures display the instantaneous value of the given expression over time.

  Cumulative

  measures display the cumulative value of the given expression over time.

  TimeAverage

  measures display the average value of the given expression over time, i.e. the cumulative value divided by the model time.
• If watch is true, then the measure will be automatically displayed as a result measure.
• The result is the name of the measure.
• An expression which should be evaluated.

• The result is the name of the definition.
• An expression which is the definition value and is internally replaced for every occurrence of the definition name.

Figure 27: Window to define a new tokentype in a SCPN model

4.3  SCPN Expressions

4.3.1  Constants

4.3.2  Functions

• References to places.
• References to definitions and measures.
• References to tokens and their attributes.

4.3.3  Place References

4.3.4  Definition and Measure References

4.3.5  Token and Attribute References

tokenX

References token tokenX.

tokenX.color

References attribute color of token tokenX.

tokenX.color.red

References attribute red of attribute color of token tokenX.

4.3.6  Operators

4.3.7  Basic Data Types

Integer

values are internally stored as int values. The range of values is between -2³¹ = -2147482648 and 2³¹ = 2147483647 on a 32 bit system. Integer values can by checked for equality and inequality (==, !=), can be compared ( > , < , > =, < =), and arithmetically combined (+, -, *, /, %).

Real

values are internally stored as double values with a codomain of about ±1.7*10³⁰⁸ with a precision of 15 digits. The same operators are defined as for integer values.

Boolean

values are internally stored as bool values which represent false or true. Possible operators are the checks for equality and inequality (==, !=), and the logical operators conjunction (&&), disjunction (||), and negation (!).

String

values are constant strings bordered by double quotes. The typical C escaping mechanism is applicable: Quotation marks and the backslash sign are prefixed by a backslash (\). A tabulator can be written as \t and a new line as \n.

Date/Time

values are internally stored as objects of the DateTime class. Appendix C.1 describes all methods of this class. The DateTime class internally uses a double value which makes the Date/Time values uncountable. But it provides for practical reasons the hh:mm:ss@MM/dd/yyyy format which is often used for input and output. The global variable NOW always represents the current simulation time. DateTime values can by checked for equality and inequality (==, !=), and can be compared.

4.3.8  Structured Types

4.3.9  Value Parameters

4.4  Specific Menu Functions

Figure 28: Main menu of graphical user interface for net class SCPN

Figure 29: Menu SCPN for net class SCPN

Descend

The last shown replication/implementation of the underlying submodel is displayed in the editor window. It is the same action as doubleclicking a substitution transition or module definition. Menu item Ascend is the reverse operation and displays the parent model of a submodel. This item is available if a substitution transition or a module definition is selected.

Ascend

The parent model of the submodel will be displayed. It is the reverse operation to menu item Descend. This item is available if a submodel of a substitution transition or an implementation of a module definition is currently displayed in the editor window.

Next Replication

The next replication/implementation is then displayed in the editor window. This item is available if a submodel of a substitution transition or an implementation of a module definition is currently displayed and several replications or implementations exists.

New Replication

A new replication/implementation is created and displayed in the editor window. This item is available if a submodel of a substitution transition or an implementation of a module definition is currently displayed.

Remove Replication

The currently shown replication/implementation is removed and the previous one is shown in the editor window. The first replication/implementation (replication 0) cannot be removed. This item is available if a submodel of a substitution transition or an implementation of a module definition is currently displayed.

Run Script

Opens a window to setup a Javascript environment and allows to run such a script which, e.g., controls a simulation. Detailed information about the TimeNET scripting engine can be found in Section 4.9.

Figure 30: Window to start a Javascript script for controlling a SCPN simulation

Figure 30 shows the setup window for the scripting engine. This window has the following entries:

Script file

Full path of the script file which should be started. Normally, scripts are stored in the directory TimeNET/SCPNScripts.

Source net file

Full path of the SCPN model which should be used. The default entry is the currently opened SCPN model. The given model file is passed through the Javascript engine and is available as arguments[0] in the script.

Destination net file

Full path of a temporary SCPN model which can be used in the script file to store the model modifications. The given destination filename is passed through the Javascript engine and is available as arguments[1] in the script.

Integration property file

This file is required to setup the OpenAdaptor framework which can be used by Javascript to access different database connections. A default integration property file (which is automatically set) can be found in TimeNET/etc/gpsc_conf/integration.props. Normally, this file does not need to be changed.

Log4j property file

This file is required to setup the Log4J framework which is internally used by OpenAdaptor. A default Log4J property file can be found in TimeNET/etc/gpsc_conf/log4j.props and is automatically set. Normally, this file does not need to be changed.

Open destination net file

If this option is enabled, the destination net file is opened after running the script.

Skip integration

If this option is enabled, the database integration is not performed. Activate this option if the script does not need database access.

Generate Template

Creates template files (.c and .h) for a manual transition which must be selected before. These template files can be used to overwrite the transition behavior such as guard functions. A detailed description of manual transition is given in Section 4.7. Both template files are created in a special directory named <modelname>.manual within the current model directory.

Edit Parameters

Opens a window to add and edit value parameters of a SCPN model as shown in Figure 31. A parameter consists of the following values:

Type

The data type of the parameter value. This must be a basic type.

Name

The name of the parameter. A parameter is referenced in expressions by using this name.

Default value

The default value which is normally used. If the parameter is assigned to a module, this value can be overwritten in each module instance.

Description

Optionally a parameter may store a short description which is otherwise not used.

Figure 31: Window to add/edit parameter values for SCPN models

Check net

Validates the model in the currently selected editor window. This is done by validating the underlying XML model against the given SCPN XML-schema. All XML schema definition files are located in TimeNET/etc/schemas. A lot of structural and syntactical properties are specified in the XML-schema. Most of the structural properties are automatically considered by the TimeNET GUI. Expressions and some more structural properties are also checked by using an internal ANTLR grammar scheme for SCPN which additionally validates the syntax of expressions. Note that not all expressions can be validated. Some of them might give errors when starting the simulation. An example of a syntax error is shown in Figure 32.

Figure 32: Example of a syntax error after Check net

4.5  Simulation

Figure 33: Menu structure of SCPN simulation

Start Simulation

simulates the selected SCPN model.

Figure 34 shows the applicable options which will be described in the following.

Start Time

Start time of the simulation in the format hh:mm:ss@mm/dd/yyyy. This time is used to initialize transitions and calculate their first firing times.

End Time

End time of the simulation in the format hh:mm:ss@mm/dd/yyyy. If the simulation has reached this time by firing a transition, the simulation is stopped.

Simulation Server IP

This is the IP address of the simulation kernel. If the simulation should run locally, the IP is "localhost". If another IP address is used, make sure that a simulation kernel is running on the target computer, as described in Section 4.10.

Simulation Server Portnumber

This is the port number which is used to connect to the simulation kernel. The default value is 4445 but this value can be changed in order to avoid conflicts with other ports.

Result Server IP

This is the IP address of the result monitor. If the Result monitor should run locally, the IP is "localhost". If another IP address is used, make sure that a Result monitor is running on the target computer, as described in Section 4.6.

Result Server Portnumber

This is the port number which is used to connect to the result monitor. The default value is 4444 but this value can be changed in order to avoid conflicts with other ports.

Random seed value

Can be used to specify a seed value for the random generator. The default value is 0, then the current milliseconds of the system clock is used. A value different from 0 is useful to get the same order of executions for multiple simulation runs.

Activate simulation logging

If this item is activated, several logfiles are produced during the simulation to analyze the simulation process. These logfiles will be stored in a newly created folder <modelname>.log in the model directory.

Figure 34: Option window for the SCPN simulation

The simulation starts when pressing the "Start" button and stops at the given End Time. If the result monitor is configured to run at the local computer ("localhost"), then it is automatically opened at the start of the simulation and shows all defined measures.

After a successful simulation a file results.log with the results of all measures is stored in <modelname>.result.

Stop Simulation

stops a currently running simulation. If this does not work, please use the TaskManager on Windows or the "kill" command on Linux to stop the simulation process. The name of a simulation process equals the name of the simulated model and has on Windows systems the file ending ".exe".

Tokengame

starts a step by step simulation of the selected model.

Figure 35 shows the applicable options which will be described in the following.

Start Time

Start time of the tokengame simulation in the format hh:mm:ss@mm/dd/yyyy. This time is used to initialize transitions and calculate their first firing times.

Simulation Server IP

This is the IP address of the simulation kernel. If the simulation should run locally, the IP is "localhost". If another IP address is used, make sure that a simulation kernel is running on the target computer, as described in Section 4.10.

Simulation Server Portnumber

This is the port number which is used to connect to the simulation kernel. The default value is 4445 but this value can be changed in order to avoid conflicts with other ports.

Activate simulation logging

If this item is activated, several logfiles are produced during the simulation to analyze the simulation process. These logfiles will be stored in a newly created folder <modelname>.log in the model directory.

Figure 35: Option window for the SCPN token game

Simulation and Tokengame Process

4.6  Result Monitor

Figure 36: Result monitor window which displays results from a simulation

Figure 37: Window with data values of a specific diagram

Figure 38: Main menu of the Result monitor

Figure 39: Menu File of the Result monitor

Open

Allows to open a set of data values. This function is currently not available.

Close

Closes the currently selected subwindow.

Close all

Closes all subwindows.

Export values

Allows to export the original values of the currently selected subwindow. This function opens a file dialog to choose the target location for the created file. The file is stored in the csv format, so it contains a list of semicolon (not comma) separated values which can be loaded into Microsoft Excel and other programs.

Export SVG Image

Allows to export the image of the currently selected subwindow in the SVG (scalable vector graphics) format. A SVG image is supported by some open source programs and also by a lot of commercial programs such as Adobe Illustrator.

Exit

Exits the result monitor.

Figure 40: Menu Display of the Result monitor

Property

Opens a dialog window to change the properties of one or all subwindows. This window is shown in Figure 41. All available options are described separately in this paragraph because they are also available as individual menu items. The property dialog allows to set specific properties for all chart windows in one step.

Figure 41: Dialog window to edit the display properties

Chart type

This menu item sets the type of the chart of the currently selected window. It is possible to select a line chart or a bar chart.

Line

If activated, a line is drawn in the diagram between all data values. This option is only available for line charts and is set by default.

Points

If activated, a point is drawn for each data value. This option is only available for line charts.

Mean Line

If activated, a line which represents the arithmetic mean is drawn for all data values. This line is drawn green colored. This option is only available for line charts.

Gliding mean line A/B

If activated, a line which represents the gliding mean is drawn for all data values starting with a specific time and date. A dialog window is opened to enter the start time. This option is only available for line charts.

Rectangle line

If activated, a rectangle line is drawn in the diagram between all data values. The line is drawn blue colored. This option is only available for line charts.

Legend

If activated, a legend is shown in the currently selected diagram. Some diagrams in Figure 36 have the legend activated.

Show full chart

If activated, the full chart is shown after receiving start and end time. Otherwise the horizontal axis grows after receiving new values.

Data values

Opens a separate window which shows the original data values in a table. Such a table is depicted in Figure 37.

Figure 42: Menu X-Axis of the Result monitor

Grid

If activated, a grid is shown in the selected diagram.

Axis format

Should be used to define the data type which is used to interpret and show the values on the axis. The following datatypes are possible: Number, Date, Time, and Date/Time. The default setting for the x-axis of a line chart is Date/Time and for the y-axis it is Number. Bar charts always show an integer number on the x-axis. Note that the x-axis of a bar chart is on the left side.

Range

Defines the value range of the axis. A new dialog is shown where the lower and upper boundary of the range can be specified. In the default settings, the x-axis shows the complete time range of the simulation run and the y-axis starts with the lowest value and stops at the highest value.

Autoview

Resets all properties of this axis to the default settings.

Figure 43: Menu Window of the Result monitor

Auto tile

If activated, the currently selected diagram window is automatically relocated to fit into the current tile structure.

Tile

Relocates all diagram windows in the main window by using a tile structure. The windows are displayed in tiles, one beside another.

List

Relocates all diagram windows in the main window by using a list structure. The windows are displayed at the full width, one after another.

Cascade

Relocates all diagram windows in the main window by using a cascaded structure. The windows are displayed staggered one behind another.

Window list

A list of all opened windows is displayed. By selecting one window from this list, the corresponding diagram window will be activated and moved to the front. The currently active window is shown by a checkmark.

4.7  Manual Transitions

< ignore >

Text which indicates that all characters that follow in the same line should be ignored and will be removed during code generation.

< comment >

Text which indicates the beginning of a block of one or more lines which will be ignored and removed during code generation. The comment region ends at the token < /comment > .

< classname >

Text for the class name.

< parent >

Text for the parent class name.

< headername >

Text for the name of the header file's define.

bool globalGuard()

Returns true if the global guard function is satisfied. This method is called after a change in an input or output place of the transition to check for enabling. It normally uses net->getPlace( < placename > ) to find a place in the model and checks the current marking size by using the method place->getMarkingSize().

void initGlobalGuards()

Registers this transition as a global guard listener of places and is called once in the beginning of the simulation. Each place which is referenced by the global guard function of this transition needs to be informed. The method net->getPlace( < placename > )->addGlobalGuardTransition(this) is used to register each place.

void moveTokens(TokenList &binding)

Moves tokens from places to other places. It is executed if a transition fires. The default implementation moves tokens from all input places to all output places according to the arc inscriptions. Parameter binding contains the current binding which is a set of tokens to be moved. Tokens can be removed from a place by calling place.removeToken(token) and added to a place by calling place.addToken(token).

TempBindingList* generateBindingList()

Generates a list of all possible bindings for this transition. It is called to create bindings if all preconditions to enable the transition are fulfilled. The default implementation uses a permutation of all tokens in all input places with respect to the transition attributes such as takeFirst. Each binding is a set of tokens which is represented by a TokenList.

bool hasTimeguard() const

Returns true if this transition has a time guard and is called to speed-up the check for the timeguard function.

Seconds_T Timeguard(const DateTime &now)

Returns the duration when the transition could be enabled based on the given time now. If this method returns 0.0 the time guard is satisfied and the transition can be enabled immediately. A detailed description of the DateTime class is given in Appendix C.1.

Seconds_T getFiringDelay() const

Returns a tangible firing delay. It is called when a binding is created. This method uses the class Delay as described in Section C.2 which contains some important delay functions such as exponential or normally distributed random delay. It is possible to implement an own delay distribution which not necessarily needs to be a continuous function.

double display(TokenList &binding)

Returns a value which is displayed as a result measure in the result monitor after each firing of this transition. The default implementation uses the attribute displayExpression. This method has access to the currently fired binding which can be evaluated to return a measure.

void log(TokenList &binding)

Writes a number of values to the logging output after each firing of this transition. The default implementation uses the attribute logExpression. This method has access to the currently fired binding which can be evaluated to write out the measure. The constant name translogfile has to be used as the output stream.

4.8  Parametrizable Module Concept

4.8.1  Modules

Figure 44: A module definition with two inputs and one output

4.8.2  Module Implementation

4.8.3  Module Instantiation

4.9  TimeNET Scripting Engine

4.9.1  Creating Javascript scripts

    var newNet = Net.create();

    var oldNet = Net.load(filename.xml);

4.9.2  Integration of external data

Figure 47: Adaptor Framework Editor window

Figure 48: Adaptor Framework Editor window with SQL connection

4.10  SCPN Simulation - System Architecture

Figure 49: Remote structure of TimeNET components

startRemoteServer < port number > < model path >

Starts the simulation server on the local machine which is listening on the given port number. The given model path needs to be a valid directory where the compiled model files will be stored and the simulation is executed.

startResultMonitor < port number >

Starts the result monitor on the local machine which is listening on the given port number. The ResultMonitor runs without opening a window. A window will be opened not until receiving data on the given port from a running simulation.

4.11  Database Access

5  Technical Notes

5.1  System Requirements

• Windows Windows XP (a version for Windows Vista will be compiled when a MinGW port for Vista is available)
• Linux on personal computers (recommended distribution: Debian 3.1)
• SunOS 5.6-5.9 (Solaris) on Sun workstations: TimeNET 3.0 runs in these environments

5.2  Downloading TimeNET

Technische Universität Berlin
Prozessdatenverarbeitung und Robotik
Armin Zimmermann
Sekr. FR 2-2
Franklinstr. 28/29
10587 Berlin, Germany
Fax: +49-30-31.42.11.16

5.3  How to Install the Tool

• Permenently remove TNETHOME and MODELDIR environment variables from your system which were required by previous versions of TimeNET. (Applies to users of older version only)
• Create a TimeNETinstall directory in C:\Program Files on Windows or in /usr/local/bin or /home/username on Linux.
• Copy the downloaded compressed archive (TimeNETxxxx_windows.zip or TimeNETxxxx_linux.tgz) into the newly created TimeNETinstall directory.
• Switch to the TimeNETinstall directory.
• On Linux, use tar to extract the directories and files from the archive. tar -xvzf TimeNETxxx_linux.tgz
• On Windows, right-click the archive TimeNETxxx_windows.zip (or use WinZip) and extract all files into the current directory.

5.4  Configure a multi-user installation

5.5  Starting the Tool

• On Linux: /usr/local/bin/TimeNETinstall/TimeNET/bin/startGUI
• On Windows: C:\Program Files\TimeNETinstall\TimeNET\bin\startGUI.bat

5.6  Configuring the User Interface

6  Upgrading to TimeNET 4.0

6.0.1  Conversion of old Model Files

• TimeNET 1.4 / 2.0 models
  Filename extension: .TN
  Format explanation: see Section B
  TimeNET 4.0 allows to import and export models in the old .TN format. After loading a model in the old .TN format, it is automatically converted to the new XML format. The internal analysis modules for eDSPN models still use the old .TN format, into which it is possible to export model files.
• TimeNET 3.0 models
  Filename extension: .net
  Format explanation: see manual of TimeNET 3.0
  TimeNET 3.0 stores models in a net class-independent format. It is not possible to load models in the .NET format of TimeNET 3.0 into TimeNET 4.9. Such models must be converted to the .TN format first using TimeNET 3.0 (File/Export and File/Import).
• TimeNET 4.0 Beta realease models
  The general XML format of TimeNET models has slightly changed, so that models created with the 4.0 beta version must be converted by following a few simple steps. Open the old model in your favourite text editor and change the first lines depending on the type of the model (this is also explained in the web pages, from where you can copy and paste the text).
  • GMPN models: Remove the first lines until GMPN.xsd''> and add the following lines at the same place:

      <net id="0" netclass="SCPN" 
      xmlns="http://pdv.cs.tu-berlin.de/TimeNET/schema/SCPN" 
      xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
      xsi:schemaLocation="http://pdv.cs.tu-berlin.de/TimeNET/schema/SCPN 
      etc/schemas/SCPN.xsd">
      
    
  • eDSPN models: Remove the first lines until eDSPN.xsd"> and add the following lines at the same place:

      <net id="0" netclass="eDSPN" 
      xmlns="http://pdv.cs.tu-berlin.de/TimeNET/schema/eDSPN" 
      xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 
      xsi:schemaLocation="http://pdv.cs.tu-berlin.de/TimeNET/schema/eDSPN 
      etc/schemas/eDSPN.xsd">
      
    

A  Model File Format .XML

eDSPN.xsd

This schema definition is used for DSPN and eDSPN netclasses.

SCPN.xsd

This schema definition is used for stochastic colored Petri nets (SCPN).

B  Model File Format .TN

Footnotes: