PROBABILITY AND QUEUEING THEORY QUESTION BANK WITH ANSWERS PDF

Where is the Menu? Here Pij denote the one step transition probability. Mathematics 1 — January and May Question Anna University—Chemistry 1—January Question A random process is called stationary if orobability its statistical properties do not change with time. There are four types of random process.

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Find the marginal and conditional distributions. Find cov X,Y. Show that it is not stationary. 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 go by car again as he is to travel by train. Now suppose that on the first day of the week, man tossed the fair dice and went by car to work if and only if a 6 appeared. V repairman finds that the time spent on his job has an exponential distribution with mean 30 minutes.

If he repair sets in the order in which they came in and if the arrival of sets is approximately Poisson with an average rate of 10 per 8 hour day. If the service time for each customer is exponential with mean 4minutes and if people arrive in Poisson fashion at the rate of 10 per hour, find the following: 1 What is the probability of having to wait for service?

OR B Customers arrive at a one man barber shop according to a Poisson process with a mean inter arrival time of 20 minutes.

Customers spend an average of 15 minutes in the barber chair. The service time is exponentially distributed, If an hour is used as a unit of time then What is the probability that a customer need not wait for a hair cut?

What is the expected number of customer in the barber shop and in the queue? How much time can a customer expect to spend in the barber shop? Find the average time that a customer spend in the queue?

Estimate the fraction of the day that the customer will be idle? What is the probability that there will be 6 or more customers? OR B A car wash facility operates with only one bay. The parking lot is large enough to accommodate any number of cars. Find the average number of cars waiting in the parking lot , if the time for washing and cleaning a car follows.

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