assignment modeling & simulation (1)

7/26/2019 Assignment Modeling & Simulation (1)

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MODELING & SIMULATION

Assignment-1

1. A) With an example, define models of a system. Give the classification of different types

of models of a systemb) With necessary example, state any 2 situations where simulation is not appropriate tool

to use.c) With a neat flow chart, briefly explain the different steps involved in simulation study.

2. A) Explain any four characteristics of a ueuin! system

") A small !rocery stores has only one chec#out counter. $ustomers arrive at this

counter at random from 1 to 1% minutes apart. Each possible value of interarrival time

has the same probability of occurrence eual to %.1%. the service times vary from 1 to

& minutes apart with probabilities shown below.

'ervice time 1 2 ( * &

+robability %.1% %.2% %.(% %.% %.1% %.%*

evelop simulation table for 1% customers and find the followin!-

a) he avera!e time between arrivals.

b) he probability that a customer has to wait in the ueue.c) he avera!e service time /andom di!its for arrivals- 01, 2. 1*, 0, (%, 02, *, 2(, (%

/andom di!its for service times- , 1%, , *(, 1, 0, 01, &, 0, (.

(. A) What are pseudo random numbers 3 4ist the errors which occur durin! the !eneration

of pseudo random numbers.

") 5se linear con!ru mential method to !enerate a seuence of three random members

for 6%72, a7, c7 and m71%%. a) iscuss in brief the various problems or errors which occur while !eneratin! pseudo

random numbers.

b) Explain the two 8Goodness of fit9 test by usin! an appropriate example

*. :or the followin! seuence can the hypothesis that the numbers are independent can be

re;ected on the basis of len!th of rans up < down when = 7 %.%*

%.( %.0% %.2* %.0 %. %.12 %.21

%.& %.& %.( %.0 %.& %.& %.1

%.0 %. %.22 %.0& %.00 %. %.&

%.*& %.1 %.*2 %.00 %.%2 %. %.(%


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%.1 %.2 %.*& %.00 %.%2 %. %.(%

%.1 %.2 %.*& %.* %.(1 %. %.%*

%.0 %.1 %.2( %.2 %.0( %.&* %.(

%.(0 %.2

Assignment-2

*. a) Example the concept of system with any me live examples

b)iscuss the various ways of modelin! of a s3m

c) repeat&. a) iscuss in brief the various problems or errors which occur while !eneratin! pseudo

random numbers.

b) Explain the two 8Goodness of fit9 test by usin! an appropriate example

. a) Explain how < what for the inverse transform techniue is used to sample from two

discrete distributions.

b) iscuss how the sample mean is estimated under normal < poisson distributions

. a) Explain in detail about the model buildin!, verifyin! < validation in the model

buildin! process throu!h a dia!ram.0. a) What is sytem < system environment > Explain the components of a system with

examples.b) what are the advanta!es of simulations>c) iscuss the types of models of a system.

1%. a) What is the role of maximum density < maximum period in !eneration of random

numbers> With !iven seed *, constant multiplier 21, increment 0, < moduleus %,

!enerate a seuence of five random numbers.b) :or the followin! seuence can the hypothesis that the numbers are independent can be


%.( %.0% %.2* %.0 %. %.12 %.21

%.& %.& %.( %.0 %.& %.& %.1

%.0 %. %.22 %.0& %.00 %. %.&

%.*& %.1 %.*2 %.00 %.%2 %. %.(%


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%.1 %.2 %.*& %.00 %.%2 %. %.(%

%.1 %.2 %.*& %.* %.(1 %. %.%*

%.0 %.1 %.2( %.2 %.0( %.&* %.(

%.(0 %.2

11. a) A seuence of 1%%% four di!it numbers has been !enerated < analysis indicates the

followin! combinations < freuencies

$ombination ?bserved freuency

?i

:our different *&*

i!its

?ne pair (02

wo pairs 1

hree li#e di!its 2

:our li#e di!its 2

"ased on po#er test chec# whether the numbers are independent, else =7%.%*b) Explain inverse transform techniue for exponential distribution. 'hown the

correspondin! !raphical interpretation.

12. a) Explain the acceptance @ re;ection techniue. Generate * poissons variates with mean

=7 %.2*

b) Explain chisuare !oodness of fit test. Apply it to poissons assumption with =7 (&

data siBe 7 1%% and observed freuency ?i 12 1% 10 1 1% * * ( ( 1

1(. a) Explain with a neat dia!ram model buildin! verification and validation1. a) What is the role of maximum density < maximum period in !eneration of random

numbers> With !iven seed *, constant multiplier 21, increment 0, < moduleus %,

!enerate a seuence of five random numbers.b) :or the followin! seuence can the hypothesis that the numbers are independent can be


%.( %.0% %.2* %.0 %. %.12 %.21


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%.& %.& %.( %.0 %.& %.& %.1

%.0 %. %.22 %.0& %.00 %. %.&

%.*& %.1 %.*2 %.00 %.%2 %. %.(%

%.1 %.2 %.*& %.00 %.%2 %. %.(%

%.1 %.2 %.*& %.* %.(1 %. %.%*

%.0 %.1 %.2( %.2 %.0( %.&* %.(

%.(0 %.2

1*. a) A seuence of 1%%% four di!it numbers has been !enerated < analysis indicates the

followin! combinations < freuencies

$ombination ?bserved freuency

?i

:our different *&*

i!its

?ne pair (02

wo pairs 1

hree li#e di!its 2

:our li#e di!its 2

"ased on po#er test chec# whether the numbers are independent, else =7%.%*

b) Explain inverse transform techniue for exponential distribution. 'hown the

correspondin! !raphical interpretation.1&. a) Explain the acceptance @ re;ection techniue. Generate * poissons variates with mean

=7 %.2*

b) Explain chisuare !oodness of fit test. Apply it to poissons assumption with =7 (&data siBe 7 1%% and observed freuency ?i 12 1% 10 1 1% * * ( ( 1

Assignment-3

1. a) Explain with a neat dia!ram model buildin! verification and validation

1. a) efine simulation, simulation model, entities, measures of performance and activities.

b) 4ist ( circumstances under which simulation is the appropriate tool and two

circumstances under which simulation is not the appropriate tool.


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c) Explain in brief with a neat fi!ure the steps involved in a simulation study

10. a) Explain in brief a simple ueuin! model < represent it usin! ueuin! notation.

b) 4ist < describe in brief in five elements3characteristics of the ueuin! system.c) A !rocery has one chec#out counter. $ustomers arrive at this chec# out counter at

random from 1 to minutes apart < each inter arrival time has the same probability of

occurrence. he service times vary from 1 to & minutes with probabilities as !iven below.

'ervice Cminutes) 1 2 ( * &

+robability %.1% %.2% %.(% %.2* %.1% %.%*

'imulate the arrival of * customers < caluculate

i) avera!e waitin! time for a customer

ii) probability that a customer has to waitiii) probability of a server bein! idle

iv) avera!e services time

assignment modeling & simulation (1)

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