## 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) (i)**Execution of the arrival event. 10 marks

**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.

Loading time: | 10 | 5 | 5 | 10 | 15 | 10 | 10 |

Weigh time: | 12 | 12 | 12 | 16 | 12 | 16 | |

Travel time: | 60 | 100 | 40 | 40 | 80 |

**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] [x^{2}_{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