SimB

SimB is a simulator built on top of ProB. It is available in the latest SNAPSHOT version in the new JavaFX based user interface ProB2-UI (https://github.com/hhu-stups/prob2_ui), The modeler can write SimB annotations for a formal model to simulate it. Examples are available at https://github.com/favu100/SimB-examples. Furthermore, it is then possible to validate probabilistic and timing properties with statistical validation techniques such as hypothesis testing and estimation.

Using SimB

Start SimB via "Open Simulator" in the "Advanced" Menu after opening a machine.

Now, you can open a SimB file (JSON format) controlling the underlying formal model.

A SimB file consists of probabilistic and timing elements to simulate the model. Within these elements, the modeler can user B expressions which are evaluated on the current state.

In the following, an example for a SimB file controlling a Traffic Lights for cars and pedestrians is shown:

{
 "activations": [
  {"id":"$initialise_machine", "execute":"$initialise_machine", "activating":"choose"},
  {"id":"choose", "chooseActivation":{"cars_ry": "0.8", "peds_g": "0.2"}},
  {"id":"cars_ry", "execute":"cars_ry", "after":5000, "activating":"cars_g"},
  {"id":"cars_g", "execute":"cars_g", "after":500, "activating":"cars_y"},
  {"id":"cars_y", "execute":"cars_y", "after":5000, "activating":"cars_r"},
  {"id":"cars_r", "execute":"cars_r", "after":500, "activating":"choose"},
  {"id":"peds_g", "execute":"peds_g", "after":5000, "activating":"peds_r"},
  {"id":"peds_r", "execute":"peds_r", "after":5000, "activating":"choose"}
 ]
}

Probabilistic and Timing Elements in SimB

The SimB file always contains an activations field storing a list of probabilistic and timing elements to control the simulation. Probabilistic values are always evaluated to ensure that the sum of all possibilities is always 1. Otherwise an error will be thrown at runtime. There are two types of activations: direct activation and probabilistic choice. All activations are identified by their id.

Direct Activation

A direct activation activates an event to be executed in the future. It requires the fields id, and execute to be defined. All other fields can be defined optionally.

execute identifies the activated event by its name.
after defines the scheduled time (in ms) when activating an event. By default, it is set to 0 ms, e.g., when this field is not defined explicitly.
activating stores events that will be activated when executing the event defined by execute. Missing definition leads to the behavior that no other events are activated. The modeler can either write a String (to activate a single event) or a list of Strings (to activate multiple events)
activationKind stores the kind of activation for execute. Possible options are multi, single, single:min, and single:max. The default value is multi
- multi means that the activation will be queued for execution.
- single means that the activation will only be queued if there are no queued activations with the same id
- single:min means that the activation will only be queued if (1) there are no queued activations for the same id or (2) there is a queued activation with the same id whose value for the scheduled time is greater. In the case of (2), the already queued activation will be discarded.
- single:max means that the activation will only be queued if (1) there are no queued activations for the same id or (2) there is a queued activation with the same id whose value for the scheduled time is lower. In the case of (2), the already queued activation will be discarded.
additionalGuards stores optional guards when executing the event stored in execute
fixedVariables stores a Map. Here, a variable (parameter, or non-deterministic assigned variable) is assigned to its value.
probabilisticVariables stores either a Map or a String. Concerning the Map, a variable (parameter, or non-deterministic assigned variable) is assigned to another Map defining the probabilistic choice of its value. The second Map stores Key-Value pairs where values are mapped to the probability. The modeler can also assign probabilisticVariables to first or uniform.
- first means that the first transition is chosen for execution.
- uniform means that a transition is selected from all alternatives uniformly.
priority stores the priority for scheduling execute. Lower number means greater priority.

{
   "id":  ...
   "execute": ...
   "after": ...
   "activating": ...
   "activationKind": ...
   "additionalGuards": ...
   "fixedVariables": ....
   "probabilisticVariables": ....
   "priority": ...
}

Probabilistic Choice

A probabilistic choice selects an event to be executed in the future. It requires the two fields id, and chooseActivation. chooseActivation is a Map storing Key-Value pairs where activations (identified by their id) are mapped to a probability. It is possible to chain multiple probabilistic choices together, but eventually, a direct activation must be reached.

{
   "id":  ...
   "chooseActivation": ...
}

Real-Time Simulation

Using a SimB file, the modeler can play a single simulation on the underlying model in real-time. The modeler can then manually check whether the model behaves as desired. Combining VisB and SimB, a simulation can be seen as an animated picture similar to a GIF picture. This gives the domain expert even a better understanding of the model.

A Traffic Light example (based on the SimB file shown in Using_SimB ) simulating the first 21 seconds is shown below.

Timed Trace Replay

Based on a single simulation, the modeler can generate a timed trace which is also stored in the SimB format. Afterwards, it can be used to replay a scenario. similar to real-time simulation.

Below, the resulting timed trace for the scenario in Real-Time Simulation is shown

{
  "activations": [
    {
      "execute": "$initialise_machine",
      "after": "0",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": {
        "tl_cars": "red",
        "tl_peds": "red"
      },
      "probabilisticVariables": null,
      "activating": [
        "cars_ry_1"
      ],
      "id": "$initialise_machine"
    },
    {
      "execute": "cars_ry",
      "after": "5000",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": [
        "cars_g_2"
      ],
      "id": "cars_ry_1"
    },
    {
      "execute": "cars_g",
      "after": "500",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": [
        "cars_y_3"
      ],
      "id": "cars_g_2"
    },
    {
      "execute": "cars_y",
      "after": "5000",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": [
        "cars_r_4"
      ],
      "id": "cars_y_3"
    },
    {
      "execute": "cars_r",
      "after": "500",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": [
        "peds_g_5"
      ],
      "id": "cars_r_4"
    },
    {
      "execute": "peds_g",
      "after": "5000",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": [
        "peds_r_6"
      ],
      "id": "peds_g_5"
    },
    {
      "execute": "peds_r",
      "after": "5000",
      "priority": 0,
      "additionalGuards": null,
      "activationKind": null,
      "fixedVariables": null,
      "probabilisticVariables": null,
      "activating": null,
      "id": "peds_r_6"
    }
  ],
  "metadata": {
    "fileType": "Timed_Trace",
    "formatVersion": 1,
    "savedAt": "2021-03-03T11:04:08.460477Z",
    "creator": "User",
    "proB2KernelVersion": "4.0.0-SNAPSHOT",
    "proBCliVersion": null,
    "modelName": null
  }
}

Monte Carlo Simulation

It is also possible to apply Monte Carlo simulation to generate a certain number of simulations. Here, all simulations are played without real time. However, it is possible for the user, to replay the generated scenarios with real-time afterwards.

The input parameters are:

Number of Simulations defines the number of simulations to be generated.
Starting Condition defines condition to simulate until before taking Ending Condition into account. It is either defined by a Number of Steps, Starting Time or Starting Predicate.
Ending Condition defines condition to simulate until after taking Starting Condition into account (defines the last transition of the simulation). It is either defined by a Number of Steps, Ending Time or Ending Predicate

SimB

Contents

SimB

Using SimB

Probabilistic and Timing Elements in SimB

Direct Activation

Probabilistic Choice

Real-Time Simulation

Timed Trace Replay

Monte Carlo Simulation

Hypothesis Testing

Estimation