Introduction to Computer Simulation

Computer Simulation

What is Computer Simulation:

A computer simulation is a computer program that attempts to simulate an abstract model of a particular system.
Computer simulations have become a useful part of mathematical modeling of many natural systems in physics (computational physics), astrophysics, chemistry and biology, human systems in economics, psychology, social science, and engineering.

Purpose of using computer simulations:

Computer simulations can be used to explore and gain new insights into new technology, and to estimate the performance of systems that are too complex for analytical (mathematical) solutions.

Types of simulations
- Types of simulations:

Continuous event simulations

Continuous event simulation:
Example real-life system: clear the air of a contaminated room

Continuous simulation system:

Note: (how it is done)

The concentation of gas is a chamber canbe modeled mathematically by some differential equation
The charge in a capacitor can also be modeled by a similar differential equation
The physical system is solved using differential equations
The parameters are translated to the electral system which will make it behave similarly as the real life system (only with respect to the contration of gas in the chamber)

Discrete event simulation

Why do we call it "Discrete event simulation":

In discrete event simulation, the state of the system changes discretely in time.
An event in the simulation occurs at some instant in time and the event causes a change of state in the system

Example real-life system: service center (buy a stamp)

Why the state is discrete:

Performance questions:
State = complete description of the important information of the system
(The state information is sufficient to allow you to determine the answer to your performance question

State in the dicrete-event simulation:

the number of customers in the system

The events that can change the state:

An arrival event changes the state as follows:
An departure event changes the state as follows:

Repeat for emphasis: characteristics of discrete event simulation

The event happens instantaneously (without any time duration) at some instance in time
(E.g., an arrival or departure happens instantaneously)
The system state changes in a descrete manner

Discrete event simulation techniques
- Techiqnues used to perform Discrete Event Simulations (Ref: click here)
- We will study the process-based technique
  Because:

Information mainatined by Discrete Event Simulation systems

Data structures used by Discrete Event Simulation systems:

Simulation clock

Events list

The Events list is a list of items of the form:
The Event time variable represents the simulation (virtual) time that the event will take place

The action (routine) is the program instructions that will be executed that simulate the event

Example:

In an arrival event, the action (routine) will increment the number of customers by 1.
In an departure event, the action (routine) will decrement the number of customers by 1.

Discrete Event Simulation Engine Logic

The structure of a discrete event simulation program is as follows:

/* -------------------------------------- Initialization step -------------------------------------- */ 1. Initialize system state variables (Events list = empty, etc) 2. Initialize (simulation) clock (usually starts at simulation time zero). 3. Schedule an initial event (i.e., put some initial event into the Events List). /* -------------------------------------- The actual simulation.... -------------------------------------- */ While (simulation has not ended) do { 1. Set (simulation) clock to time of the next event (advances clock) 2. Do the next event and remove the event from the Events List. }

Scheduling in Process-based Discrete Event Simulation

In process-based Discrete Event Simulation, the schedulable unit is a process (or co-routine)
A Process-based Discrete Event Simulation System will provide primitives for:

Example:

/* -------------------------------- Process 1 -------------------------------- */ void Proc1() { while (1) { Hold(1.2); /* Schedule a "resume" event at "Now + 1.2" */ printf("Proc1: Now = %lf\n", Now); /* Print current simulation time */ } } /* -------------------------------- Process 2 -------------------------------- */ void Proc2() { while (1) { Hold(1.5); /* Schedule a "resume" event at "Now + 1.5" */ printf("Proc2: Now = %lf\n", Now); /* Print current simulation time */ } } int main(int argc, char **argv) { /* ----------------------------------------------------- Initialize system variables in the simulation system InitProsim( #Processes, # ) ------------------------------------------------------ */ InitProsim(1000, 1000, 1000); /* ----------------------------------------------------- Create process "Proc1" ------------------------------------------------------ */ Generate("Name:Proc1", Proc1, 0); /* ----------------------------------------------------- Create process "Proc2" ------------------------------------------------------ */ Generate("Name:Proc2", Proc2, 0); /* ----------------------------------------------------- Run the simulation for 10 "virtual" seconds ------------------------------------------------------ */ StartSimulate(10); printf("DONE !\n"); }

Output of program:

Proc1: Now = 1.200000 Proc2: Now = 1.500000 Proc1: Now = 2.400000 Proc2: Now = 3.000000 Proc1: Now = 3.600000 Proc2: Now = 4.500000 Proc1: Now = 4.800000 Proc1: Now = 6.000000 Proc2: Now = 6.000000 Proc1: Now = 7.200000 Proc2: Now = 7.500000 Proc1: Now = 8.400000 Proc2: Now = 9.000000 Proc1: Now = 9.600000 Proc2: Now = 10.500000 DONE !

Example Program: (Demo above code)

Prog file: click here

Compile with:

cc -g -O -o main1 -I /home/cs558000/lib main1.c \ -L /home/cs558000/lib -lProSim4 -lOnAbort -lm