MODEL PAPER

B. Tech (IT) Degree Examination

Forth Year - First Semester

RANDOM PROCESSES AND ENGINEERING (ELECTIVE-I)

Effective from the admitted batch of 2004-2005

Time: 3 hrs
Max Marks: 70

First Question is Compulsory

Answer any four from the remaining questions

All Questions carry equal marks

Answer all parts of any question at one place

1. Answer all the following Questions:
a) Explain the classification of the Stochastic Process according to Time and State Space.
b) Bring out the interrelation between the Poisson Process and Exponential Distribution.
c) Distinguish between Morkovian and Non-Morkovian Queuing models.
d) Explain the Bath-Tub curve in Reliability analysis.
e) Mention Three important Properties of Spectral Representation of a Process.

2. a) Stating the Assumptions clearly obtain the system size distributions of a birth and death process.
≥ Explain the applications of Key renewal theorem in Computer Science.

3. a) Define stationary process and discuss its role in Forecasting.
≥ Explain ARMA Process with an example. Obtain the Correlation Function of ARMA (p,q).

4. a) Explain Box and Jinkins Model.
≥ Discuss the stages in periodogram analysis. Also explain how it is useful in finding the periodicity.

5. a) What do you mean by Non-Markovian Queuing Models? Derive Pollazek — Khinchine Formula.
b) Explain Gl/M/1 Queuing Model in the context of Computer Communications network.

6. a) Write a note on priority Queuing models and their impact on scheduling Algorithms.
b) Obtain the waiting time analysis of M/M/1 Queueing Model.

7. Define the following:
i) Reliability, (ii) Failure time distribution, (iii) Hazard rate functions, (iv)System reliability.
b) Explain about any one failure time distributions and find it Reliability.

8. a) What is meant by Maintainability and Availability!? Explain their importance in reliability Engineering.
b) If a device has a failure rate of λ (t) = (0.015 + 0.02 t)/Year, where t is in years.
(i) Calculate the reliability for a 5 year design life, assuming that no maintenance is performed.
(ii) Calculate the reliability for a 5 year design life, assuming that annual preventive maintenance restores the device to an as-good-as new condition.