Question Paper: Computer Simulation And Modelling Question Paper - May 18 - Information Technology (Semester 8) - Mumbai University (MU)

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## Computer Simulation And Modelling - May 18

### Information Technology (Semester 8)

Total marks: 80

Total time: 3 Hours
INSTRUCTIONS

(1) Question 1 is compulsory.

(2) Attempt any **three** from the remaining questions.

(3) Draw neat diagrams wherever necessary.

**1.a.**Elaborate the steps involved in simulation study. Why is it necessary to have program and process documentation?

**1.b**The sequence of numbers 0.63, 0.49, 0.24, 0.89 and 0.71 has been generated. Use the Komogorov-Smirnov test with $\alpha$= 0.05 to determine if the hypothesis that the numbers are uniformly distributed on the interval[0,1] can be rejected. Use D$_{0.05}$= 0.565

**2.a**A firm sells bulk rolls of newsprint. The daily demand is given by the following probability distribution:

Daily Demand (Rolls) | 3 | 4 | 5 | 6 |
---|---|---|---|---|

Probability | 0.20 | 0.35 | 0.30 | 0.15 |

Lead time is a random variable given by the following distribution:

Lead Time (Days) | 1 | 2 | 3 |
---|---|---|---|

Probability | 0.36 | 0.42 | 0.22 |

Determine the lead-time demand for 5 cycles of simulation. Random digits for lead time and demand are as follows:

R.D for Lead Time | 46 | 75 | 86 | 27 | 63 | |||||
---|---|---|---|---|---|---|---|---|---|---|

Probability | 4 | 5 | 4 | 5 | 6 | 3 | 4 | 4 | 6 | 4 |

**2.b**Draw the flowchart for arrival and departure event. Compare event-scheduling, process interaction and activity scanning algorithms.

**3.a**Ace Heating and Air Conditioning service finds that the amount of time a repairman needs to fix a furnace is uniformly distributed between 1.5 and 4 hours. i) Find the probability that a randomly selected furnace repair requires more than 2 hours. ii) Find the probability that a randomly selected furnace repair requires less than 3 hours. iii) Find the mean and standard deviation.

**3.b**The number of customers arriving at Costa Coffee is Poisson distributed with mean 4. Generate Poisson variate. Use random numbers 0.5389, 0.0532, 0.3492 in sequence.

**4.a**Given the following data for utilisation and time spent in system for the Able-Baker carhop problem. Calculate the overall point estimators, standard error and 95% confidence interval for the same. Given t$_{0.025,3}$=3.18

Run r | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Able's Utilization $\rho _r$ | 0.808 | 0.875 | 0.708 | 0.842 |

Average system time w$_r$ (mins) | 3.74 | 4.53 | 3.84 | 3.98 |

**4.b**What do you understand by calibration and validation of models? How can one increase the face validity of a model and validate the model assumptions.

**5.a**Customers arrive at random to the passport center at a rate of 40 customers per hour. Currently, there are 20 clerks, each serving 4 customers per hour on the average. Estimate the average utilisation of a server and the average number of busy servers. Can we decrease the number of servers?

**5.b**Describe briefly Queueing, Inventory and Reliability systems.

**6 Write short notes on (any two):**

**6.a**Multivariate and Time Series Input Models

**6.b**Areas of applications of simulation

**6.c**Initialization bias in steady state simulation

**6.d**Simulation of Manufacturing & Material Handling System.