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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Network of queues can be described as a group of nodes, where each of the nodes represents a service facility of the same type. Find the Marginal probability densty of X. Find the syllabux that this computer will function for a month with only one breakdown.

Find a The mean number of stories of any of these types in each day. If the pumping station of the locality has a daily supply capacity of a millions litres.

Find i The proportion of customers who enter the supermarket. System depends on time t, Steady state: Define open Jackson networks. Identify the regression equation on y on x: This is a multiple server model with finite capacity. The Markov chain is irreducible if all states communicate with each other at some time. Probability and Queueing Theory 8 Subject Code: What is the probability that it will last for atleast one more minute?

The source emits zyllabus at the rate of 6 per minute.

There are four types of random process 1. Define stationary process A random process is called stationary if all its statistical properties do not change with time. Networks preserving the following characteristics are called Jackson networks.

If the one-step transition probability does not mw2262 on the step i. Thus T is the random service time, which is a continuous random variable. What fraction of the potential customers are turned away? Find the correlation coefficient between X and Y x on y: Also find the probability that he drives to work in the long run.

### MA Probability and Queuing Theory – Question Bank Kings Edition

Prove that the sum of two independent Poisson process is a Poisson process. She never buy the same cereal in successive weeks. A random process or Stochastic process X s,t is a function that maps each element of a sample space into a time function called sample function.

If she buys cereal A, the next week she buys B. A random sample of size is taken from a population whose mean is 60 and variance is A housewife buys 3 kinds of cereals A, B and C. Where the arrival pattern M is Poisson, the Service time distribution G follows syllabhs general distribution and the number of servers is one.

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.

The customer who has finished is billing job has to wait until the delivery section becomes free. The message arrivals are modelled as two independent Poisson processes, with rates 20 per hour for the syllbus messages and 15 per hour for the long messages.

In steady state the arrival rate and departure rate at the respective nodes coincide.

Construct the Transition Probability Matrix. Joseph The Dreamer – christ connect church.

MA Question Bank – 2 3 2. The maximum temperature of a place at 0,t.

## Probability and Queueing Theory(question with answer)

Write down the applications of network queues. Define wide sense stationary process. Find the probability that on a randomly selected day. The cumulative failure rate of all the machines is 0. Define series queues Tandem queues with an example. A regular Markov chain is defined as a chain having a transition matrix P such that for some power of P, it has only non-zero positive probability values.

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The town has a daily stock of 35, litres. Number of telephone calls in 0,t. What is the joint probability that there are m customers at station 1 and n customers at station 2 for a 2 stage series queue? Are X and Y independent? In discrete random process, X is. Find the value of k. The doctor takes on the average 4 minutes for each phase mx2262 the check up and the time taken for each phase is exponentially distributed. Pn1n2 represent the probability that there are n1 customers in station 1 sylllabus n2 customers in station 2.