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 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. It is vivid from the expressions of moments of poisson process that they are time dependent. The doctor takes on the average 4 minutes for each phase of the check up and the time taken for each phase is exponentially distributed.
Find i The proportion of customers who enter the supermarket. If the pumping station of the locality has a daily supply capacity of a millions litres.
Find the probability that on a randomly selected day. Because of space constraints, only 4 cars are accepted for servicing. What is the probability that this water supply will be inadequate on any given day? If the average service time is cut to 8. The arrival pattern with 12cars per day.
Each typist can type an average of 6 letters per hour. Suppose the length of life of an appliance has ma226 exponential distribution with mean 10 years. The parking lot is large enough to accommodate any number of cars. MA Question Bank – 2 3 2. Check whether it is regular.
Write down the applications of network queues. If she buys cereal A, the next week she buys B. The source emits particles at the rate of 6 per minute.
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. No customer may leave the system.
Engineering : ALL SEMESTER MATHS QUESTION BANK WITH ANSWERS AND MODEL
There are four types of random process 1. In discrete random process, X is In discrete random process, X is discrete and the time set is continuous. Let M be the number of customers arriving in the system during service time T. Probability and Queueing Theory MA Question Bank – Find the average response time for a sylkabus tandem open network with feedback. What are the applications of Weibull distribution?
Let X be the power consumption in millions of kilowatt hours. Write down the flow balance equation of closed Jackson network. Check whether or not the process is wide sense stationary.
What are the differences between Markovian and non Markovian queueing model? Here Pij denote the one step transition probability. In discrete random process, X is discrete and the time set is continuous. However if she buys B or C the next week she is 3 times as likely to buy A as the other cereal. The message arrivals are modelled as two independent Poisson processes, with rates 20 per hour for the short messages and 15 per hour for the long messages.
Probability and Queueing Theory(question with answer)
A man either drives a car or catches a train to go to office each day. Write any two properties of regression coefficients. A random process is called stationary if all its statistical properties do not change with time. If the arrivals of the patients at the clinic are approximately Poisson at the average rate of 3 per hour, what is the average time spent by a patient i in the examination ii waiting in the clinic?
If jobs syllabsu at a rate of 5 per hour and the time to complete each job varies according to an exponential distribution with mean 6 min. Find the average number of cars in the service station, the average number of cars waiting for service and the average time a car spends in the system.
Probability and Queueing Theory Subject Code: The maximum temperature of a place at 0,t. In open Jackson networks, the arrivals from outside to the node i is allowed and once a customer gets the service completed at node ijoins the queue at node j with probability Pij or leaves the system with probability Pi0. A random sample of size is taken from a population whose mean is 60 and variance is If customers arrive at the barber shop in a Poisson fashion at an average rate of one every 40 minutes, how long on the average a customer in the spends in the shop.
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. Number of telephone calls in 0,t.