ESI4523 Exam 1

Resource Module

mange resources used in a simulation model; set queue capacity and patter of failure

Simulation

method to mimic real systems under virtual environment

Steps in Simulation

1. Problem Formulation 2. Set Objective 3. Model Conceptualization and Data Collection 4. Model Translation 5. Verify and Validate 6. Experimental Design 7. Production Runs and Analysis 8. Documentation and Reporting 9. Implementation

NR

number of busy resources

NQ

number of entities in the queue

Event Calendar

place where future events are stored; Arena places newly scheduled events to event calendar in increasing order of event times

Verification

process to check whether the model works properly

Decide Module

provides branch points by condition or by chance

Sample Path

record of time depended behavior of the system

Process Module

represents the processes such as machine drilling; resources, queues, entity delay time defined

MR

resource capacity

Resources

seized and released by entities; entities compete with eachother for service from resources

Route/Station Transfer

send an entity from one station to another without direct connection

Entity Module

sets different types of entities in simulation model

P-value

significance level at which we can reject the null hypothesis; large p-value = good fit, small p-value = bad fit If p-value is smaller than alpha reject the null

Events

something that happens at an instant of time that might change a system state

Dispose Module

terminates entities; records entity stats

Stopping Rule

time or number of parts produced; stops simulation from running forever

When to Use Simulations?

to evaluate the behavior of the system under different sets of conditions. Dynamic, complex, and uncertain systems need simulation.

Event Routine

updates system state and statistical counters

Station Module

used as an entry point to sections of model logic. It provides location information of entities to simulation logic.

Statistical Accumulators

used to estimate desired performance measures

Resource Failures

used to model unplanned, random downtimes; can be time-based or count-based

Resource Schedules

vary capacity of a resource over time; can be idle, busy, inactive or failed

Dynamic Plots

visualize states of system, trace variables or queues as simulation runs, disappear after run ends

Scheduled Utilization

∫B(t)dt/∫M(t)dt B(t)-busy resources M(t)-schedule resources

Instantaneous Utilization

∫U(t)dt/t U(t) = B(t)/M(t) B(t)-busy resources M(t)-schedule resources

Continuous Function

CONT(CDF value, X value,....)

Chi Square Test

Chi Square = sum(nj -ej)^2/ej If Chi Square is small then it is a good fit

Continuous vs Discrete Simulation

Continuous - state of the system changes continuously over time Discrete - state of the system changes only at discrete points

Komolgrov-Smirnov Test

D=greatest vertical distance between empirical distribution and theoretical distribution

Discrete Function

DISC(CDF value, X value,...)

Deterministic vs Stochastic Simulation

Deterministic - No probabilistic components Stochastic - random behavior on components

Little's Law

Length of queue = arrival rate * wait time

Normal Distribution

NORM(mean,standard deviation)

Static vs Dynamic Simulation

Static- at a particular time or time plays no role Dynamic - evolves over time

Tradeoff between System and Model

Systems are more costly and complex, but they have a higher fidelity. Whereas models are less costly and simpler but have a lower fidelity.

Triangular Function

TRIA(Min,Mode,Max)

Uniform Distribution

UNIF(min,max)

Linear Congruential Method

Zi = (aZi-1 + c) mod m Ui = Zi/m Full period if m = period

Queues

a place where entities can wait when no resource is available

Record Module

able to collect and report various kinds of statistics(e.g., user defined statistics)from within model run as entities pass through it.

Counter Statistics

accumulated sums of something; accumulation of number that are not all 1; total production

Assign Module

assigns certain characteristics to different entities

Schedule Rule - Wait

capacity decrease waits until entity releases the resource; full break but may start and end late

Schedule Rule - Ignore

capacity goes down immediately for stat collection, but work goes on until finished; could shorten break

Schedule Rule - Preempt

capacity goes down immediately; processing is interrupted and break starts immediately

Time-persistent Statistics

continuous time statistics; statistics obtained from trajectory of system state over time; utilization of a machine

TNOW

current simulation time

Timing Routine

determines the next event type and advances the simulation clock

Tally Statistics

discrete time statistics; taking average, minimum, maximum; average waiting time, max waiting time

Entities

dynamic objects in the system; something moving throughout the system

TFIN

final simulation time

Create Module

generates entities

Storage Module

holds a non-ordered set of entities that are waiting for an event to occur the conclusion of a predefined delay time and arrival of a requested transporter that is en route.

Variables

information that reflects some characteristics of the system

Simulation clock

keeps track of the current value of simulated time

Attributes

local variable characterizing entities