Probability and queueing theory important questions with answers pdf

Academic Scheduled Even Semester Timetable Anna University Chennai. How to reduce the cost of next-generation solar modules. Soft robots that mimic human muscles. All Conferences Symposiums. International Conference St. Print This Post. Please enter your comment! Please enter your name here. You have entered an incorrect email address! Find the mean and variance of the following distributions : Geometric and Exponential Refer B : page no, Prove that Poisson distribution is the limiting form of Binomial distribution.

For a triangular distribution Find the mean, variance and moment generating function. Refer C: page no : 1. It is known that the probability of an item produced by a certain machine will be defective is 0.

If the produced items are sent to the market in packets of 20, fine the no. The city has a daily stock of 35, gallons. Multiple queues condition of arrival in one queue and departure from different queues is also well handled by the Monte Carlo SSM. SSM consist of replacing the actual universe of the item with its theoretical counterpart , which is the universe described by some assumed probability distribution.

A random number table is then used for sampling from this theoretical population. Computerization use makes easy storage and retrieval of a large amount of data for months and years. Manipulation of those factors which can be controlled. It then calculates results over and over, each time using a different set of random values from the probability functions.

Monte Carlo simulation helps the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action. Queuing theory Queuing theory is the mathematical study of waiting for a queue. A queueing model is constructed so that queue lengths and waiting times can be predicted. Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service.

Answer Detailed Solution Below Option 2 : 3. Poisson distribution Normal distribution Exponential distribution Binomial distribution. Explanation: In queuing theory, The arrival rate or arrival pattern follows the Poisson distribution service rate or service pattern follows Exponential distribution.

The average service rate is less than the average arrival rate Output rate is linearly proportional to input Output rate is constant and the input varies in a random manner All of the above. Queuing theory or waiting line theory is primarily concerned with processes characterized by random arrivals i. If we assume there are costs associated with waiting in line, and if there are costs of adding more channels i.

The computations will lead to such measures as the expected number of people in line, the expected waiting time of the arrivals, and the expected percentage utilization of the service facilities. These measures can then be used in the cost computations to determine the number and capacity of service facilities that are desirable.

Answer Detailed Solution Below Option 3 : 5. Answer Detailed Solution Below Option 4 : 24 per hour. Answer Detailed Solution Below Option 1 : service time distribution and queue discipline. Answer Detailed Solution Below Option 2 : waiting time and length of the queue in a queuing system. Answer Detailed Solution Below Option 2 : 0. Answer Detailed Solution Below 2.