Simulation State and Variables

In case of our shop, the state of the system consists of customers that are waiting in line at the cash register, resources that are free to help the customer, and resources that are busy helping a customer. Consequently, we can model the state of our simulation, by defining two variables as follows.

customers = shop.add_var("customers")
resources = shop.add_var("resources")

A simulation variable is different from a regular Python variable in two important ways. First, a simulation variable can contain multiple values, while a regular Python variable can only contain one value. Second, values of a simulation variable are available from a specific moment in (simulation) time. More about that later. So, with that in mind, let’s give our variables a value.

resources.put("cassier")
customers.put("c1")
customers.put("c2")
customers.put("c3")

We now gave the resources variable one value, the string cassier, but we gave the customers variable three values. You can probably understand why we did that: we now have one cassier and three customers waiting. This is the initial state of our simulation model.

Simulation Events

Simulation events define what can happen in the system and how the system (state variables) change when they do. We define simulation events as Python functions that take a system state and return a new system state. Remember that the system state is defined in terms of variables, so an event function takes (values of) state variables as input and produces (values of) state variables as output.

def process(customer, resource):
    return [SimToken(resource, delay=0.75)]

shop.add_event([customers, resources], [resources], process)

In our example we introduce a single event that represents a resource processing a waiting customer. First, let’s focus on shop.add_event in the code below. This tells the simulator that our event takes a value from the customers variable and a value from the resources variable as input, produces a value for the resources variable as output, and uses the process function to change the state variables. Describing that in natural language: it takes a customer and a resource and, when it is done, returns a resource.

The process function defines how the event modifies the system state (variables). Taking a value from the customers variable (and calling it customer) and a value from the resources variable (and calling it resource), the function returns the resource again. This return value will be put into the resources variable, as per the shop.add_event definition. However, as you can see, there are several things going on in the return statement.

First, the function does not return a single resource value, but a list of values. This is simply a convention that you have to remember: event functions return a list of values. The reason for this is that we defined the simulation event in shop.add_event as taking a list of values (consisting of one value from customers and one value from resources) as input and as producing a list of values (consisting of one value for resources) as output. Accordingly, we must produce a list of values as output, even if there is only one value.

Second, the function does not return the resource, but returns a SimToken containing the resource. That is because in simulation, values have a time from which they are available. A value with a time is called a token. This represents that the value is only available at, or after, the specified time. In this case, the resource value is made available after a delay of 0.75. You can consider this the time it takes the resource to process the customer. Since it takes 0.75 to process a customer, the resource is only made available again after a delay of 0.75. In the meantime no new process events can happen, because a value from resources, which is needed as input for such an event, is not available.

Putting it all together

Now we have modeled the entire system and we can simulate it. To do that, we call the simulate function on the model. This function takes two parameters. One is the amount of time for which the simulation will be run. The other is the reporter that will be used to report the results of the simulation. In our example we will run the simulation for 10. (Since we only have 3 customers, and each customer takes 0.75 to process, this should be more than enough.) We will use a SimpleReporter from the reporters package to report the result. This reporter simply prints each event that happens to the standard output.

from simpn.reporters import SimpleReporter

shop.simulate(10, SimpleReporter())

As expected, running this code leads to the following output. The event of (starting) processing customer c1 happens at time t=0. It uses value c2 for variable customers and value cassier for variable resources. The event of (starting) processing customer c2 happens at time t=0.75. This is logical, because our definition of the process event that the value cassier is only available in the variable resources again after 0.75. Accordingly, processing of c3 happens at time t=1.5.

process{customers: c1, resources: cassier}@t=0
process{customers: c2, resources: cassier}@t=0.75
process{customers: c3, resources: cassier}@t=1.5

For completeness, the full code of the example is:

from simpn.simulator import SimProblem, SimToken

shop = SimProblem()

resources = shop.add_var("resources")
customers = shop.add_var("customers")

def process(customer, resource):
    return [SimToken(resource, delay=0.75)]

shop.add_event([customers, resources], [resources], process)

resources.put("cassier")
customers.put("c1")
customers.put("c2")
customers.put("c3")

from simpn.reporters import SimpleReporter

shop.simulate(10, SimpleReporter())

Visualizing the Model

To help check whether the model is correct, it is possible to visualize it. To this end, there is a Visualisation class. You can simply create an instance of this class and call the show method to show the model as follows.

from simpn.visualisation import Visualisation

v = Visualisation(shop)
v.show()

The model will now be shown as a Petri net in a separate window. The newly opened window will block further execution of the program until it is closed. You can interact with the model in the newly opened window. Pressing the space bar will advance the simulation by one step. You can also change the layout of the model by dragging its elements around. After the model window is closed, you can save the layout of the model to a file, so that you can open it later. Use the method save_layout to save the model to do so. You can load the layout of the model from the file later, by passing the saved layout as a parameter to the constructor. If the layout file does not exist, the model will be shown with an automatically generated layout.

v = Visualisation(shop, "layout.txt")
v.show()
v.save_layout("layout.txt")