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By Keys F.C.

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11 Chapter 17 serves as an introduction to mathematical finance. 6 Queueing and loss systems When multiple users contend for a resource simultaneously, congestion develops at the resource. Then, either users must be put into a queue of some sort or must be rejected from accessing the resource. Such rejected users are said to be lost. Examples of the queued case are (i) a queue of automobiles at a toll booth of a highway and (ii) data packets stored temporally enqueued in a buffer at a network router.

That the basis for the applicability of the results of the mathematical theory of probability to real ‘random phenomena’ must depend on some form of the frequency concept of 34 Pafnuty Lvovich Chebyshev (1821–1894) is known for his work in the fields of probability, statistics, and number theory. Among his students were Markov and Aleksandr Mikhailovich Lyapunov (1857–1918). 35 Henri Poincaré (1854–1912) was a French mathematician, theoretical physicist, and a philosopher of science. 36 Émile Borel (1871–1956) was a French mathematician and pioneered measure theory.

D. thesis advisor John B. D. , 1971) has greatly influenced the structure and contents of this book. The second author would like to acknowledge the support of the National Science Foundation under Grant No. 0916568 and to thank Professor Yariv Ephraim of George Mason University for valuable discussions on HMMs and related topics. The third author would like to thank Joseph Irgon, a graduate student of Princeton University, for valuable discussions on applications of clustering, HMMs, and Bayesian networks in bioinformatics.