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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If the pumping station of the locality has a daily supply capacity of a millions litres. The length of the shower in a tropical island in a rainy season has an exponential distribution with parameter 2, time being measured in minutes. A random sample of 8 lamps is taken for inspection. Are X and Y independent? Determine whether the given matrix is irreducible or not.
Ma226 depends on time t, Steady state: The clinic has 4 phases each having different service nature in series as follows: 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.
However if she buys B or C the next week she is 3 times as likely to buy A as the other cereal. Find the probability that among a sample of jobs there are no jobs that have to wait until weekends. So he made a. Each typist can type an average of 6 letters per hour. What are the applications of Weibull distribution? Probability and Queueing Theory 3 1 Subject Code: This is a multiple server model with finite capacity.
Network of queues can be described as a group of nodes, where each of the nodes represents a service facility of the same type. The number of monthly breakdown of a computer is a r. If letters arrive for being typed at the rate of 15 letters per hour, find the traffic intensity.
Probability and Queueing Theory(question with answer)
What do you mean by transient state and steady state queueing system? In open Maa2262 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. Sylllabus is the probability that of 2 days selected at random the stock is insufficient for both days?
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.
Define Mw2262 and Death process. Service time distribution follows Poisson distribution. V with syllabs 0 and 1 i. Joseph had a little overcoat. Define stationary process A random process is called stationary if all its statistical properties do not change with time.
Write down Pollaczek-khintchin formula. The customers may enter the system at some node, can traverse from node to node in the system and finally can leave the system from any node.
Write down the moment generating function of Gamma distribution. In discrete random process, X is. It is a non Markovian queueing model. Joseph The Dreamer – christ connect church.
Find the probability that i no one joins the queue in a particular minute ii 2 or more persons join the queue in the minute. What do you mean by traffic intensity? The waiting room does not accommodate more than 14 patients. Write the Physical conditions of Binomial distribution. Prove that the sum of two independent Poisson process is a Poisson process. A housewife buys 3 kinds of cereals A, B and C.
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. Discrete Random sequence 2. Here Pij denote the eyllabus step transition probability. What are the differences between Markovian and non Markovian queueing model?
MA Probability and Queuing Theory – Question Bank Kings Edition
It has found that most types of major news stories occur as Poisson processes. 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.
The basic characteristics of queueing system are Arrival time pattern, Service time pattern, Number of services channels, Capacity of the system, Service discipline.
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. Also customers can return to the nodes already visited. Calculate the probability that the yard is empty. The service time is not following exponential distribution.
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? The service time is constant.
syllahus Show that X t is not wide sense stationary. Assuming that the system behavior may be approximated by the two-stage tandem queue, determine the average repair time. November 19, 0. Assuming the system behavior can be approximated by the two stage tandem queue find the bottle neck of the repair facility. A man either drives a car or catches a train to go to office each day.