Classification of Simulation Models

1. Classification of Simulation Models • Static vs. Dynamic Simulation Model • Static Simulation Model is a representation of a system at a particular point in time (i.e., time plays no role) • Examples: Monte Carlo Simulation (will discuss later) • Estimating the probability of winning a game in a casino machine. • Estimating the value of π. • Dynamic Simulation Model is a representation of a system as it evolves over time • Examples include models of a bank, a processor

2. Deterministic Simulation Model does not contain any probabilistic components. • Example: a system of differential equations representing a chemical reaction. • Output are also deterministic • Stochastic Simulation models: those having at least some random input components. • Examples include Queuing models (Interarrival times between two consecutive customers and service times are usually random) • They produce output that are also random. • Deterministic vs. Stochastic Simulation Models

3. Continuous vs. Discrete Simulation Models. • Discrete Simulation models those representing systems whose state changes at discrete points of time. • Changes of the system occur continuously as the time evolves

4. Discrete-event Simulation Model • Simulation models we consider in this course are discrete, dynamic, and stochastic. Such models are called Discrete-Event Simulation Models • Changes occur at a separate points of time • i.e., The system can change only at a countable number of points in time. • What does it change the system state? Events • Event:is an instantaneous occurrence that changes the state of the system Examples:Arrival of a new customer, a Departure of a customer from a queuing model

5. Time-Advance Mechanism • Simulation Clock: is a variable in the simulation model that keeps track of the current simulation time (does not depend on the computer time) 0 Simulation clock • There are 2 approaches for advancing the simulation clock: • Next-event time advance • Fixed-increment time advance 0 Dt 2 Dt 3 Dt 4 Dt

6. Next-Event Time Advance • The most common used approach : • The simulation clock is initialized to zero. • Time of occurrence of future events are determined. • The simulation clock is then advanced to the time of the occurrence of the next event (the event that is scheduled to occur first). • The system is updated taking in account that the event has occurred. • Update the time of the occurrence of the next events. • Go to step 3. • Repeat until a stopping criterion is satisfied.

7. Example: A single server Queuing system • e.g., one-operator barbershop, a cashier in a supermarket, etc. • Define: • ti = time of arrival of the ith customer. • Ai =ti –ti-1 = the interarrival time between the (i-1)st and the ith customer. • Si = the service time of the ith customer • Di = the delay time in queue of the ith customer. • ci = ti + Di + Si = departure time of the ith customer. • ei = The time of the occurrence of the ith event.

8. The next-event time-advance approach illustrated for the single-server queuing system.