Anna University, Chennai Department of Computer Science Engineering ( Common to I.T) Fourth Semester MA Probability and Queueing. Subject Code: MA Subject Name: Probability and Queuing Theory Type: Question Bank Edition Details: Kings Edition Syllabus. MA — PROBABILITY AND QUEUEING THEORY (Regulation ). ( Common to Information Technology) Time: Three hours Answer ALL Questions PART.

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A man either drives a car or catches a train to go to office each day. Customers spend an average of 15 min.

What are the differences between Markovian and non Markovian queueing model? The arrival pattern with 12cars per day. Find the rth moment of X about the 2 origin. V with mean 0 and 1 i.

## Probability and Queueing Theory(question with answer)

Define open Jackson networks. System independent of time t. When do you say the Markov chain is regular?

Find all the marginal distributions and conditional probability distributions. Write the Physical conditions of Binomial distribution. Also find the probability that he drives to work in syllaus long run. The service station for which the utilization factor is maximum among all the other service stations of the network is called the bottle neck of a network.

Define Birth and Death process. Out of the 2 salesman, one is incharge of billing and receiving payment while other salesman is incharge of weighing and delivering the items. Blades are supplied in packets of 5 each. Construct the Transition Probability Matrix. Thus T is the random service time, which is a continuous random variable. There are four types of random process 1. Define First order stationary and Second order stationary process. Find the probability that 11 particles are counted in 4 minutes.

Define i Continuous time random process 2 Discrete random process. Determine whether the given matrix is irreducible or not. The clinic has 4 phases each having different service nature in series as follows: Probability and Queueing Theory Subject Code: The Markov chain is irreducible if all states communicate with each other at some time. A random sample of size is taken from a population whose mean is 60 and variance is Assume that the inter arrival time follows an exponential distribution and the service time distribution is also exponential with an average of 36 minutes.

The time required to repair a machine is exponentially distributed with parameter St. He never goes two days in a row by train but if he drives one day, then the next day he is just as likely to drive again as he is to travel by train.

In a certain locality the daily consumption of water in millions of litres, can be treated as a random variable having a gamma distribution with an average of 3 million litres.

When do you say the Markov chain is homogeneous? A random process is said to be stationary to order one if the first order density functions defined for all the random variables of the process are same. Service time distribution follows any general distribution. Due to lack of space, Only one customer is allowed to enter the shop, only if the billing clerk is free. In discrete random process, X is. What is the probability that out of 5 workers, at the most two contract that disease.

Prove that the sum of two independent Poisson process is a Poisson process. In steady state the arrival rate and departure rate at the respective sllabus coincide.

Find the probabilities that: Continuous Random sequence 3.

### SEM 4 QUESTION PAPERS – CSE TUBE

If the one-step transition probability does not depend on the step i. Assuming the system behavior can be approximated by the two stage tandem queue find the bottle neck of the repair facility. Find a the mean life time of the component b the probability that such syllabks component will be more than hours.

A housewife buys 3 kinds of cereals A, B and C.