Classes for Connectors, Places and Transitions

1 Petri Nets

Petri Nets are bipartite graphs that only allow connection of different kinds of nodes, places to transitions or transitions to places. The Modelica type system can ensure that only legal connections are made if we define two different connector classes, one class PTPort for for places to transitions-with class prefix and variable suffixes PT, and another class TPPort for transitions for places - with class prefix and variable suffixes TP. Since variable names are different, the connector types are different in the Modelica type system, even though the connector classes in both cases represent the same kind of variables:state and firing information.

In order to have slightly different connector icons for the input version (filled triangle) and the output version (unfilled triangle), we also define otherwise identical input and output versions of these connector classes, see below. There is also a ConditionPort connector class for specifying an optional input condition to a Transition.

connector PTPort "Connecting Places to Transitions" Boolean sPT "state information"; Boolean fPT "firing information"; end PTPort;
connector PTPortIn = PTPort; // Input version of PTPort
connector PTPortOut = PTPort; // Output version of PTPort
connector TPPort "Connecting Transitions to Places" Boolean sTP "state information"; Boolean fTP "firing information"; end TPPort;
connector TPPortIn = TPPort; // Input version of PTPort
connector TPPortOut = TPPort; // Output version of PTPort
connector ConditionPort "Optional condition to a Transition" Boolean c(start=true); end ConditionPort;

We now define Place and Transition classes.

class Place constant Integer nIn = 1 "Number of input transition ports"; constant Integer nOut = 1 "Number of output transition ports"; TPPortIn inTrans[nIn] "Vector of input transition connectors"; PTPortOut outTrans[nOut] "Vector of output transition connectors"; Boolean state; Boolean ostate; Boolean d1, d2; // Dummy variables equation ostate = pre(state); // ostate is the current state // Report state to input transitions, vector equation cat(1,inTrans.sTP,{d1}) = cat(1,{ostate},inTrans.sTP or inTrans.fTP); // Report state to output transitions, column matrix equation [outTrans.sPT,{d2}] = [{ostate},outTrans.sPT and not outTrans.fPT]; // Compute new state for next Petri net iteration state = (ostate and not anyTrue(outTrans.sPT)) or (anyTrue(inTrans.sTP)); end Place;
class Transition ConditionPort condition "Optional condition"; constant Integer nIn = 1; constant Integer nOut = 1; PTPortIn inPlaces[nIn] "Vector of input place connectors"; TPPortOut outPlaces[nOut] "Vector of output place connectors"; Boolean fire; equation fire = condition and allTrue(inPlaces.sPT) and not anyTrue(outPlaces.sTP); // Report firing info to input places, vector equation inPlaces.fPT = fill(fire,nIn); // Report firing info to output places, vector equation outPlaces.fTP = fill(fire,nOut); end Transition;

We also need utility Boolean reduction functions anyTrue and allTrue.

function anyTrue "True, if at least one element is true in a vector" input Boolean inp[:]; output Boolean result; algorithm result := false; for i in 1:size(inp,1) loop result := result or inp[i]; end for; end anyTrue;
function allTrue "True, if all elements are true in a vector" input Boolean inp[:]; output Boolean result; algorithm result := true; for i in 1:size(inp,1) loop result := result and inp[i]; end for; end allTrue;

All classes and functions are collected into a package called NormalPetriNet:

encapsulated package NormalPetriNet
connector PTPort ...;
connector PTPortIn ...;
connector PTPortOut ...;
connector TPPort ...;
connector TPPortIn ...;
connector TPPortOut ...;
connector ConditionPort ...;
class Place ...;
class Transition ...;
function anyTrue ...;
function allTrue ...;
end NormalPetriNet;

2 A Modelica Petri Net Model and Simulation of a Job Shop System

We now return to our job shop system example. Its Petri net graph is shown once more below in Figure 1, with the difference that the token has advanced, representing the condition C3 that a job is currently being processed.

Figure 1: The job shop system Petri Net graph once more. The job is in the stage of being processed.

We would now like to build a Modelica Petri net model of the job shop system, using our recently developed NormalPetriNet package. We need modified instances of the general Place and Transition classes in order to reflect the different numbers of input and output ports.The JobShopSystem model follows below, containing these modified instances of places and transitions, as well as connection equations.

model JobShopSystem Transition arrival(nIn = 0, nOut = 1); // E1 Place inwait(nIn = 1, nOut = 1); // C2 Transition synchronize(nIn = 2, nOut = 1); // E2 Place processing(nIn = 1, nOut = 1); // C3 Transition parallel(nIn = 1, nOut = 2); // E3 Place idle(nIn = 1, nOut = 1); // C1 Place outwait(nIn = 1, nOut = 1); // C4 Transition delivery(nIn = 1, nOut = 0); // E4 equation connect(arrival.outPlaces, inwait.inTrans); connect(inwait.outTrans[1], synchronize.inPlaces[1]); connect(idle.outTrans[1], synchronize.inPlaces[2]); connect(synchronize.outPlaces[1], processing.inTrans[1]); connect(processing.outTrans[1], parallel.inPlaces[1]); connect(parallel.outPlaces[1], outwait.inTrans[1]); connect(parallel.outPlaces[2], idle.inTrans[1]); connect(outwait.outTrans[1], delivery.inPlaces[1]); end JobShopSystem;

2.1 Simulation of JobShopSystem

Finally we simulate the job shop system model using the above default settings, for a job that passes through the system and is processed.

loadModel(Modelica)

Simulation of the model fails as of October 2015, Will be fixed in the near future

simulate( JobShopSystem, stopTime = 1 )
plot( inWait.state )

No data found plot( process.state )

No data found plot( idle.state )

No data found plot( outWait.state )

No data found