ieng461 systems modeling and simulation

Eastern Mediterranean University

Department of Industrial Engineering

IENG461

Systems Modeling and Simulation

Computer Lab ARENA(Input Analysis)

DATA COLLECTIN ACTIVITIES

Consider modeling a painting workstation where

jobs arrive at random, wait in a buffer until the

sprayer is available, and having been sprayed,

leave the workstation. Suppose that the spray

nozzle can get clogged— an event that results in

a stoppage during which the nozzle is cleaned or

replaced.

SIMULATION MODELING

Suppose that you are asked to simulate this

painting workstation. List the required data to

estimate the expected job delay in the buffer for

this simple system

DATA COLLECTION

• Collection of job interarrival times. – Clock times are recorded on job arrivals and

consecutive differences are computed to form the requisite sequence of job interarrival times.

– If jobs arrive in batches, then the batch sizes per arrival event need to be recorded too.

– If jobs have sufficiently different arrival characteristics (depending on their type), then the analyst should partition the total arrival stream into substreams of different types, and data collection (of interarrival times and batch sizes) should be carried out separately for each type.

DATA COLLECTION

• Collection of painting times.

– The processing time is the time it takes to spray a job. Since nozzle cleaning or replacement is modeled separately (see later), the painting time should exclude any downtime.

DATA COLLECTION

• Collection of times between nozzle clogging. – This random process is also known as time to

failure.

– Observe that the nozzle clogging process takes place only during painting periods, and is suspended while the system is idle. Thus, the observations of the effective time to failure should be computed as the time interval between two successive nozzle cloggings minus the total idle time in that interval (if any).

DATA COLLECTION

• Collection of nozzle cleaning/replacement times.

– This random process is also known as downtime or repair time.

– Observations should be computed as the time interval from failure (stoppage) onset to the time the cleaning/replacement operation is complete.

DATA COLLECTION

Suppose we collected the following sample data

for repair times (nozzle cleaning/replacement

times for painting station given above) and

recorded them in a file named as “repair.txt”:

SAMPLE DATA FOR REPAIR TIMES

12.9 27.7 13.5 13.7 22.2 20.9 26.6 29.1 22.4 10.7 30.0 27.4 18.8 25.3 15.0 17.0 21.7 13.7 15.5 23.2 11.0 27.5 22.5 27.1 25.2 10.3 18.0 11.5 14.1 24.0 10.9 27.0 24.2 25.6 22.4 21.0 21.3 23.1 15.8 13.2 22.8 25.9 22.4 13.8 16.6 10.8 10.3 15.1 19.0 27.9 20.5 19.4 10.9 24.1 10.9 22.2 25.5 17.2 10.9 15.6 14.3 29.9 17.8 19.8 17.6 13.3 24.0 29.7 18.1 28.4 28.6 26.9 20.7 22.0 16.8 19.4 27.4 22.5 28.3 27.1 18.9 11.9 13.2 10.9 22.1 16.7 28.5 19.9 18.5 16.5 12.7 18.1 15.0 21.0 25.7 19.5 11.9 22.9 23.2 18.9

Save as “repair.txt” than change file extension as “.dst”

CHI-SQUARE TEST for Uniform Distribution (Repair Data) Cell number Cell Interval # of Observations Relative Frequency Theoretical Probability 1 [10,12) 13 0.13 0.10 2 [12,14) 9 0.09 0.10 3 [14,16) 8 0.08 0.10 4 [16,18) 9 0.09 0.10 5 [18,20) 12 0.12 0.10 6 [20,22) 8 0.08 0.10 7 [22,24) 13 0.13 0.10 8 [24,26) 10 0.10 0.10 9 [26,28) 10 0.10 0.10 10 [28,30) 8 0.08 0.10

k -s -1 = 10-2-1=7, α = 0.10

2 2

0.10,73.6 12

2

0.10,7 12

Can not reject the null hypothesis

Why ?

ARENA INPUT ANALYZER

• Arena provides built-in data analysis facilities via its Input Analyzer tool, whose main objective is to fit distributions to a given sample.

• Keep in mind that Arena provides built-in facilities for fitting distributions to independent empirical data, however, Arena does not provide any built-in facility for fitting dependent (time series) random processes.


The Input Analyzer is accessible from the Tools menu in the Arena home screen. After opening a new input dialog box (by selecting the New option in the File menu in the Input Analyzer window), raw input data can be selected from two suboptions in the Data File option of the File menu: 1. Existing data files can be opened via the Use Existing option. 2. New (synthetic) data files can be created using the Generate New

option as iid samples from a user-prescribed distribution. Once the subsequent Input Analyzer files have been created, they can be accessed in the usual way via the Open option in the File menu


The Arena Input Analyzer functionality includes fitting a distribution to sample data in two ways: 1. The user can specify a particular class of distributions and request the Input Analyzer to recommend associated parameters that provide the best fit.

2. The user can request the Input Analyzer to recommend

both the class of distributions as well as associated parameters that provide the best fit.


• Distribution Arena name Arena parameters • • Exponential EXPO Mean • Normal NORM Mean, StdDev • Triangular TRIA Min, Mode, Max • Uniform UNIF Min, Max • Erlang ERLA ExpoMean, k • Beta BETA Beta, Alpha • Gamma GAMM Beta, Alpha • Johnson JOHN G, D, L, X • Log-normal LOGN LogMean, LogStdDev • Poisson POIS Mean • Weibull WEIB Beta, Alpha • Continuous CONT P1, V1, . . . a • Discrete DISC P1, V1, . . . • • a The parameters P1, P2, . . . are cumulative probabilities.

Table displays the distributions supported by Arena and their associated parameters.

ARENA INPUT ANALYZER When you open this

file via “Use

Existing Option” ,

the Input Analyzer

automatically

creates a histogram

from these sample

data, and provides

a summary of ,

sample statistics, as

shown in the

figure .


• The Options menu in the Input Analyzer menu bar allows the analyst to customize a histogram by specifying its number of intervals through the Parameters option and its Histogram option’s dialog box. Once a distribution is fitted to the data (see next section), the same menu also allows the analyst to change the parameter values of the fitted distribution.

• As mentioned above, either the user can specify a

particular distribution and request the Input Analyzer to recommend associated parameters for this distributon or use the “ best fit” option to decide which distribution to use for these sample data.

ARENA INPUT ANALYZER Specifying Uniform Distribution

ARENA INPUT ANALYZER Fit All Summary:

ieng461 systems modeling and simulation

Documents