Anna University Chennai 2008 M.Sc Software Engineering XCS 472 – MODELING AND SIMULATION - Question Paper

5 Year M.Sc., DEGREE EXAMINATION, NOVEMBER / DECEMBER 2008.

Seventh Semester

Computer Technology

XCS 472 – MODELING AND SIMULATION

(Common tot M.Sc., software Engineering)

(Regulation 2003)

Time: 3 hours Maximim: 100 marks

ans ALL ques..

PART A – [10 X two = 20 MARKS]

1. Mention two situations where simulation is improper and two situations where it is inappropriate.

2. Differentiate discrete and continuous system using examples.

3. a latest survey indicated that 80% of men aged 30 years old are married. obtain the probability that two or three out of a random sample of 20 men of 30 years old are not married.

4. Life time of a satellite is provided by the pdf f(x) = 0.4e-0.4x when x = 0 and f(x) = 0 otherwise. What is the probability that satellite is functional after five years?

5. using a linear congruential generator generate 5 two digit numbers. Mention any 2 desirable properties of random number generator.

6. briefly define a runs test.

7. mention any 3 important factors in the selection of simulation software.

8. write any 3 significant features of a simulation language.

9. point out the difference ranging from validation and verification.

10. write the 4 steps involved in modeling an input data.

PART B – [5 X 16 = 80 MARKS]

11. (a) (i) Draw a flow chart describing the steps of simulation study. [8]

(b) (ii) Construct a table of inter arrival times, service times for 10 customers for a single server queue. compute avg. of non zero wait times, avg. idle time of server, avg. queue length. presume times so that all of the above statistics are non zero. [8]

OR

(b) (i) define the components of a simulation system using three various examples. [8]

(ii) Simulate a single item inventory system for 10 days. Suppose that the demands are 12, 23, 17, 34, 28, 31, 27, 18, 11, 25. Reorder size = 50. Reorder point = 25. Lead time = two days. Only 1 outstanding order allowed. Initial inventory = 40. compute the avg. shortage. [8]

12. (a) (i) Arrivals at a bank teller’s cage are Poisson at the rate of 1.2 in a minute. obtain the probability of (1) no arrival in the next one minute and (2) two to3 arrivals in next two minutes. [5]

(ii) A compound has exponential time to failure with mean of 10,000hrs. The compound has already been in operation for 10,000 hrs. What is the probability that it will fail by 15,000 hrs? [3]

(iii) If arrivals are Poisson, then show that inter arrivals are exponential [8]
OR

(b) (i) obtain mean and variance of Poisson distributed random variate. [8]

(ii) Using Monte Carlo Simulation obtain v3 and ?. [8]

13. (a) (i) provided finve random numbers 0.44,0.8, 0.12, 0.007, 0.9 perform a test of uniformity using Kolmogorov Smirnov test with a=0.05. [8]

(ii) Drive random number generator that generates random numbers according to the distributions (1) exponential and (2) uniform in (10, 20).

(OR)

(b) (i) Perform runs test on the subsequent sequence of numbers:
0.08, 0.09, 0.43, 0.29, 0.42, 0.53, 0.68, 0.10, 0.76, 0.98 [8]

(ii) Develop random number generator for the generation of numbers that has the distribution: F(t)=(t-1/2)/6 when 0 = t = nine and 0 elsewhere. Also generate five random numbers. [8]

14. (a) (i) Using a Simulation Language or otherwise make a flow chart for the subsequent simulation:
A parent volunteers to remind other parents to come to school meeting next week. It takes five two 2nd to obtain the next number to call, seven two 2nd to place the call and 30 five seconds to provide the message for every parent on the list. The chance of reaching a parent is 35%. How many were reached out of 100 parents? Hoe long does it take? [12]

(ii) Write any 4 features of a simulation language you are familiar with. [4]

(OR)

(b) (i) Construct a flow chart to perform simulation of single server queue to collect statistics of weue length ,wait times. [12]

(ii) Briefly define the output analyzer of Arena.

15. (a) (i) Records pertaining to monthly number of job related injuries in a mine are provided beneath. (Values for past 100 months are given)

Injuries per month: 0 1 2 3 4 5 6

Frequency : 35 40 13 6 4 1 1

Apply x2 test to that the distribution is Poisson with mean = 1.0. [12]

(ii) What do you mean by face validity? [4]

OR

(b) (i) provide examples of input data that could be (1) Normal (2) Exponential (3) Poisson (4) Triangular. [8]

(ii) explain validation of input output transformation. [4]

Earning:   Approval pending.