6. Key Simulation Methodologies
Discrete-Event Simulation
In discrete systems, system state changes are discontinuous events. A model uses a state descriptor (a set of numbers) to represent the system’s state.
Key Features:
- Entities: Representation of real elements like machine parts.
- Relationships: Links between entities.
- Simulation Executive: Controls the advance of time and executes events.
- Random Number Generator: Simulates various data inputs.
- Results & Statistics: Provides performance measures and validates the model.
Time Advancement:
- Time Slicing: Time advances in fixed increments until no events remain.
- Next Event: Time advances directly to the next scheduled event, which is more efficient.
Queuing System Simulation: A queue consists of entities being served and those waiting to be served.
| Parameter Symbol | Description |
| λ | Arrival rate (number of arrivals per second) |
| Ts | Mean service time for each arrival (excluding queue wait time) |
| ρ | Server time utilization |
| u | Traffic intensity |
| r | Mean number of items in the system |
| Tr | Mean time of an item in the system |
| w | Mean number of items waiting in the queue |
| Tw | Mean waiting time of all items |
| N | Number of servers in a system |
- Single Server Queue: A system with one server. Items are served if the server is idle; otherwise, they join a waiting queue.
- Multi Server Queue: A system with multiple identical servers and a common queue. An incoming item is served if any server is available.
Queuing Relationships:
| General Terms | Single Server | Multi-server |
| r = λTr (Little’s) | ρ = λTs | ρ = λTs/N |
| w = λTw (Little’s) | r = w + ρ | u = λTs = N |
| Tr = Tw + Ts | r = w + Nρ |
Continuous Simulation
A continuous system is one where activities complete smoothly without delays or queues. The state variables are controlled by continuous functions and are often modeled using differential equations. This type of simulation is used when the underlying system dynamics are continuous.
Application Areas:
- Civil Engineering: Dam embankment and tunnel construction.
- Military: Missile trajectory simulation, fighter aircraft training.
- Logistics: Airport passenger flow analysis, toll plaza design.
- Business: Product development planning, market study analysis.
Monte Carlo Simulation
This is a computerized mathematical technique used to generate random sample data based on a known distribution for numerical experiments. It is applied to quantitative risk analysis and decision-making problems.
Characteristics:
- Its output must generate random samples.
- Its input distribution must be known.
- Its result must be known during the experiment.
| Advantages | Disadvantages |
| Easy to implement. | Time-consuming, as it requires a large number of samples. |
| Provides statistical sampling for numerical experiments. | Results are approximations of true values, not exact figures. |
| Offers approximate solutions to mathematical problems. | |
| Usable for both stochastic and deterministic problems. |