Written by a prominent Russian mathematician, this concise monograph examines aspects of queuing theory as an application of probability. The three-part treatment begins with a study of the stream of incoming demands (or `calls,` in the author's terminology). Subsequent sections explore systems with losses and systems allowing delay. Prerequisites include a familiarity with the theory of probability and mathematical analysis. A. Y. Khinchin made significant contributions to probability theory, statistical physics, and several other fields. His elegant, groundbreaking work will prove of substantial interest to advanced undergraduates, graduate students, and professionals in the fields of statistics, probability, and operations research.
Frequently asked questions
How do I cancel my subscription?
Simply head over to the account section in settings and click on āCancel Subscriptionā - itās as simple as that. After you cancel, your membership will stay active for the remainder of the time youāve paid for. Learn more here.
Can/how do I download books?
At the moment all of our mobile-responsive ePub books are available to download via the app. Most of our PDFs are also available to download and we're working on making the final remaining ones downloadable now. Learn more here.
What is the difference between the pricing plans?
Both plans give you full access to the library and all of Perlegoās features. The only differences are the price and subscription period: With the annual plan youāll save around 30% compared to 12 months on the monthly plan.
What is Perlego?
We are an online textbook subscription service, where you can get access to an entire online library for less than the price of a single book per month. With over 1 million books across 1000+ topics, weāve got you covered! Learn more here.
Do you support text-to-speech?
Look out for the read-aloud symbol on your next book to see if you can listen to it. The read-aloud tool reads text aloud for you, highlighting the text as it is being read. You can pause it, speed it up and slow it down. Learn more here.
Is Mathematical Methods in the Theory of Queuing an online PDF/ePUB?
Yes, you can access Mathematical Methods in the Theory of Queuing by A. Y. Khinchin, D. M. Andrews, M. H. Quenouille in PDF and/or ePUB format, as well as other popular books in Mathematics & Probability & Statistics. We have over one million books available in our catalogue for you to explore.
The general theory of streams (of uniform events) might reasonably begin with abstract definitions of the main components of such streams. However, any such general approach will be postponed till Chapter 2 where it will be dealt with to the extent necessary. Meanwhile, we prefer to introduce the reader into the field of concrete investigations of streams of the simplest type in order to achieve from the start a clear picture of the basic ways of thought, of the mathematical models in the theory of mass service, and of the form of this science as a mathematical discipline. When these concrete explanations have been sufficiently mastered, the study of a more abstract general theory should not seem difficult.
We also add that the simple type of stream to be studied in this chapter has, in course of time, shown itself to be almost the only one useful in application; only in comparatively recent years has the necessity been clearly shown for the study of streams of a more general type. Meanwhile, even nowadays the great majority of applications of the theory of mass service (in particular in telephone applications) arise from the assumption that an incoming stream of demands (calls) belongs to this simple type. Explanations, particularly technical ones, of the theory of the simple stream have in the past few decades developed to the extent that even elementary courses in the theory of probability nowadays usually include a special chapter devoted to this theory.
1 Definition and statement of the problem
We will call a stream of uniform events āsimpleā if it possesses the following three characteristics ā
(1) Stationariness. For any t > 0 and integer k
0, the probability that during the period of time (a, a + t) there will occur k events is the same for every a
0 (and so depends only on t and k); hereafter we shall indicate this probability by Ļ k(t). Throughout the book we shall deal only with streams in which, during a finite period of time with probability 1, there occur only a finite number of events. Thus, for any t, we shall always have
The stationariness of a stream expresses the invariability of i...
