System Modelling and Simulation - June 2015

VTU Computer Science (Semester 8)

Total marks: --
Total time: -- INSTRUCTIONS
(1) Assume appropriate data and state your reasons
(2) Marks are given to the right of every question
(3) Draw neat diagrams wherever necessary 1 (a) List any five circumstances, when the simulation is the appropriate tool and when it is not. 10 marks

1 (b) Explain the steps in simulation study, with the flow chart. 10 marks

2 (a) Explain the following:
i) System
ii) Event list
iii) Entity
iv) Event. 10 marks

Write the flow chart with respect to single channel queue:

2 (b) (ii) Execution of the departure event. 10 marks

2 (c) One company uses 6 trucks of haul manganese ore from kolar to its industry. There are two loaders, to load each truck. After loading, a truck moves to the weighing scale to be weighted. The queue discipline is FIFO. When it is weighed, a truck travels to the industry and returns to the loader queue. The distribution of loading time, weighing time and travel time are as follows:
Depict the simulation table and estimate the loader and scale utilization. Assume 5 trucks are at the loaders and one is at the scale, at time'0'. Stopping time T_E=76 min.

3 (a) Explain discrete random variable and continuous random variable with example. 10 marks

3 (b) Explain the following discrete distribution:
i) Binomial distribution
ii) Poisson distribution 10 marks

3 (c) Explain the following continuous distribution:
i) Uniform distribution
ii) Exponential distribution. 10 marks

4 (a) Explain queue behaviour and queue discipline and list queuing notation for parallel server systems. 10 marks

4 (b) What is network of queue? Mention the general assumption for a stable system with infinite calling population. 10 marks

5 (a) Explain combined linear congruential generator. 10 marks

5 (b) Explain inverse-transform technique of producing random variates for
i) Exponential distribution
ii) Weibull distribution 10 marks

5 (c) Generate three Poisson variates with mean α=0.2.
[Random number: 0.4357, 0.4146, 0.8353, 0.9952, 0.8004]. 10 marks

6 (a) The sequence of numbers 0.44, 0.81, 0.14, 0.05, 0.93 has been generated. Use the Kolmogonov-Smirnov test with α=0.05 to determine if the hypothesis that the numbers are uniformly distributed in the interval [0, 1] can be rejected. Compare F(x) and S_N(x) on a graph. [N=5, D_0.05'=0.565]. 10 marks

6 (b) Explain chi-square goodness of fit test. Apply it to Poisson assumption with α=3.64. Data size=100 and observed frequency
O_i=12, 10, 19, 17, 10, 8, 7, 5, 5, 3, 3, 1] [x²_0.05.5=111]. 10 marks

7 (a) What are pseudo random numbers? What are the problems that occur while generating pseudo random number? 10 marks

7 (b) Enlist the steps involved in development of a useful model of input data and number of ways to select input models without data. 10 marks

7 (c) List any 6 suggested estimators for distributions often used in simulation. 10 marks

8 (a) Explain with a neat diagram, model building, verification and validation. 10 marks

8 (b) Explain the iterative process of calibrating a model. 10 marks