Discrete event models

In a discrete-event simulation, all change occurs at instants in time, rather than over periods. The fundamental components are states and events. States can change as a result of events, and events can occur at pre-set times or be triggered by other events, conditionally on states, possibly after a delay.

Pure discrete-event models do not need a regular time step. Instead, the time of the next event can be calculated after each event, and the simulation jumps directly to that time. Typical domains for discrete event simulation include network, traffic and queueing systems.

Simile can run pure discrete-event models, but allows their components to be mixed with system dynamics components to build hybrid models. Obviously values can be passed between states and system-dynamics components, but there are special constructs for integrating events themselves with system dynamics:

• The limit event, triggered when the value of an equation including dynamic values reaches a threshold
• The squirt, allowing an event to instantaneously change the level of a compartment.

An example of a simple system requiring hybrid modelling is a bouncing ball. While the ball is flying, its behaviour is governed by continuous processes modelled with system dynamics, but bouncing is an event involving instantaneous change, and calculating the time of the bounce involves a continuously varying quantity reaching a limit. If the ball eventually comes to rest as a result of friction losses, an infinite series of infinitely-small bounces can be avoided by including a state that switches from 'bouncing' to 'at rest' when the ball's energy drops below a certain level.