I will rephrase your question, as to "What relationship does queueing theory and probability therory?" Queueing theory is the mathematical study of waiting lines See: http://en.wikipedia.org/wiki/Queueing_theory Wait times, by their nature, are uncertain but can be represented by probability distributions. From a distribution, I may be able to tell that the chance of waiting more than 5 minutes for service is 10%, or that there is a 95% chance that my complete time in a facility (service time and wait time) is less than 15 minutes. On the other side, queueing theory may determine how often those responsible for service have no customers. The theory has broad applications, ranging from computer networks, telephony systems, delivery of goods and services (such as mail, home repair, etc) to an area and customer service in any location where people might stand in line. Traffic analysis uses queueing theory extensively. The "forward" analyses begins with an assumed probability distribution. Given probability distributions that are thought to describe certain activities (number of customers arriving in a particular time span, time spent with each customer and special events -frequency of events and time spent on special events), the distribution of waiting times can be determined mathematically. Thus, probability theory provides the basis (distribution and mathematical theory) for queueing applications. Today, more complex queueing problems are solved by Monte-Carlo simulation, which after thousands (or hundreds of thousands) of repeated runs, can provide nearly the same accuracy of statistics and distributions as those generated from purely mathematical solution. More broadly, queueing modeling and theoretical solutions are within stochastic process analysis.
how theory of probability used in real life
The answer is: WORK THEM OUT
Blaise Pascal and Pierre de Fermat started corresponding over an issue on mathematics of gambling, from which the theory of probability developed in 1654.
I can not give you a simple answer. It is very individual and subjective. I will assume that you are referring to probability theory. Statistics is based on an understanding of probability theory. Many professions require basic understanding of statistics. So, in these cases, it is important. Probability theory goes beyond mathematics. It involves logic and reasoning abilities. Marketing and politics have one thing in common, biased statistics. I believe since you are exposed to so many statistics, a basic understanding of this area allows more critical thinking. The book "How to lie with statistics" is a classic and still in print. So, while many people would probably say that probability theory has little importance in their lives, perhaps in some cases if they knew more, it would have more importance.
Probability theory is the field of mathematics that enables statistical inferences to be made. All equations used in statistical inferences must be based on mathematics (theorems and proofs) of probability theory. An example to illustrate this. Given a normal probability curve with a mean = 0 and variance of 1, 68% of the area under the curve is in the range of -1 to 1, as calculated from probability theory. Since it is proved by mathematics, we can state it as a fact. If we collect data, and the average of the data is zero, and the standard deviation is 1, then we can infer that we are 68% certain that the population mean lies between -1 to 1. Our conclusion is inferred based on our limited and imperfect sample and the assumption that our population is normally distributed.
Tomasz Rolski has written: 'Order relations in the set of probability distribution functions and their applications in queueing theory' -- subject(s): Distribution (Probability theory), Probabilities, Queuing theory
give some solved question paper
Statistics consists of Descriptive Statistics,Probability theory,Distribution theory,Quality Control, Design of Experiments, Reliability, Operations Research, Queuing theory, Inventory control,Measure theory, Sampling theory, Statistical inference, Analysis.
Aleksandr Alekseevich Borovkov has written: 'Ergodicity and stability of stochastic processes' -- subject(s): Ergodic theory, Stability, Stochastic processes 'Mathematical statistics' -- subject(s): Mathematical statistics 'Advances in Probability Theory' 'Probability theory' -- subject(s): Probabilities 'Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya' 'Asymptotic methods in queueing theory' -- subject(s): Queuing theory
Shaler Stidham has written: 'Optimal design for queuing systems' -- subject(s): Combinatorial optimization, Queuing theory
Zvi Rosberg has written: 'Queueing networks under the class of stationary service policies' -- subject(s): Queuing theory 'Queueing networks under the class of stationary service policies' -- subject(s): Queuing theory 'Queueing networks under the class of stationary service policies' -- subject(s): Queuing theory 'Queueing networks under the class of stationary service policies' -- subject(s): Network analysis (Planning), Queuing theory
What is the relationship between arrival rate and service rate in a queuing system? How does variability in arrival times impact system performance in queuing theory? What are the key differences between single-server and multi-server queuing systems? How can Little's Law be applied in the context of queuing analysis? What is the significance of queue discipline in managing waiting lines? How does the utilization factor affect the efficiency of a queuing system? What role does the length of the queue have in determining system performance? How can queuing theory be used to optimize staffing levels in service operations? What are the implications of finite queue capacity in real-world queuing systems? How can simulation modeling be used to analyze queuing systems in complex environments?
Wilma Louise Johnston has written: 'Queuing theory'
All the time. Statistic is based on the application of probability theory!
Statistics is based on probability theory so each and every development in statistics used probability theory.
Probability theory and distributive theory.
John N. Daigle has written: 'Queueing theory for telecommunications' -- subject(s): Computer networks, Queuing theory