Definition
In Modeling and Simulation, a Stochastic Process is a probabilistic mechanism used to address aleatory uncertainty by representing systems with inherent random variation (e.g., air currents, coin flip irregularities).
Why It Matters
In the real world, deterministic models almost always fail because they ignore “noise”; stochastic processes provide the mathematical language to model this inherent randomness, allowing for robust system design that survives environmental variability.
Core Concepts
- Aleatory Uncertainty: Inherent randomness in the environment that is modeled using stochastic distributions rather than deterministic values.
- Probabilistic Arrival/Service: In queuing models, arrival and service patterns are often modeled as stochastic processes (e.g., Poisson arrivals) to reflect real-world variability.
- Analytic Solutions: Stochastic processes are the foundation of analytical modeling, such as using Markov Chains to solve simple queues.