6.1 Principles and Rationale for Continuous Simulation

In direct contrast to Discrete-Event Simulation, Continuous Simulation is a paradigm used for systems where the state variables change continuously over time. The behavior of these systems is not described by events, but rather by a set of mathematical differential equations that govern the rates of change of the state variables. The simulation progresses by solving these equations over time, resulting in a smooth trajectory of the system’s state rather than a series of discrete jumps.

The primary rationale for using continuous simulation is that the system’s behavior is best captured by the language of calculus and differential equations. This approach is chosen when the analyst is interested in the smooth, aggregate flow of system components rather than the actions of individual entities. The focus is on the continuous evolution of quantities, not the timing of discrete events.

Continuous simulation is applied across a wide range of fields where systems are governed by physical laws or flow dynamics. Key application areas include:

• Civil Engineering:
  • Modelling water levels and structural stress in dam embankments.
  • Simulating geological pressures during tunnel construction.
• Military Applications:
  • Calculating the trajectory of a missile under the continuous influence of gravity and atmospheric drag.
  • Creating high-fidelity fighter aircraft training simulators.
• Logistics:
  • Analyzing the smooth flow of traffic through a toll plaza design.
  • Simulating the aggregate flow of passengers through an airport terminal.
• Business Development:
  • Modelling market dynamics in a product development plan.
  • Analyzing aggregate trends for a market study.

We now turn to our third major paradigm, which is distinct from both DES and continuous simulation and is fundamentally rooted in the principles of randomness and statistical sampling.