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**An introduction to probability models.
6th ed.**
*(English)*
Zbl 0914.60005

Boston, MA: Academic Press. 656 p. (1997).

This is the sixth edition of the monograph, for a review of the fifth edition (1993) see Zbl 0781.60001, for the fourth edition (1989) see Zbl 0676.60002.

Although the organization of the chapters remained unchanged compared to the fifth edition, the new edition includes additional material in all chapters. Notably, Section 2.6.1 presents a simple derivation of the joint distribution of the sample mean and variance of a normal data sample. Section 3.6.4 presents \(k\)-record values and Ignatov’s theorem. In Section 4.5.3, an analysis, based on random walk theory, of a probabilistic algorithm for the satisfiability problem is given. Section 4.6 deals with the mean times a Markov chain spends in transient states. Markov chain Monte Carlo methods are introduced in Section 4.9. Section 7.9 presents new results concerning the distribution of time until a certain pattern occurs, when a sequence of independent and identically distributed random variables is observed. Section 9.6.1 illustrates a method for determining an upper bound for the expected life of a parallel system of not necessarily independent components. In Section 11.6.4 the simulation technique of importance sampling and the usefulness of tilted distributions in this context is introduced. Among the new examples are those relating to: random walks on circles, matching rounds problem, the best prize problem, a probabilistic characterization of \(e\) and Ignatov’s theorem. In the new edition, a large number of new exercises has been added. For more than 100 of the now approximately 570 exercises a solution is provided.

The edition retains the character of the previous ones: it is an elementary introduction to probability theory and stochastic processes with lots of exercises, examples and applications in the fields such as engineering, management science, physical and social sciences, and operations research.

Although the organization of the chapters remained unchanged compared to the fifth edition, the new edition includes additional material in all chapters. Notably, Section 2.6.1 presents a simple derivation of the joint distribution of the sample mean and variance of a normal data sample. Section 3.6.4 presents \(k\)-record values and Ignatov’s theorem. In Section 4.5.3, an analysis, based on random walk theory, of a probabilistic algorithm for the satisfiability problem is given. Section 4.6 deals with the mean times a Markov chain spends in transient states. Markov chain Monte Carlo methods are introduced in Section 4.9. Section 7.9 presents new results concerning the distribution of time until a certain pattern occurs, when a sequence of independent and identically distributed random variables is observed. Section 9.6.1 illustrates a method for determining an upper bound for the expected life of a parallel system of not necessarily independent components. In Section 11.6.4 the simulation technique of importance sampling and the usefulness of tilted distributions in this context is introduced. Among the new examples are those relating to: random walks on circles, matching rounds problem, the best prize problem, a probabilistic characterization of \(e\) and Ignatov’s theorem. In the new edition, a large number of new exercises has been added. For more than 100 of the now approximately 570 exercises a solution is provided.

The edition retains the character of the previous ones: it is an elementary introduction to probability theory and stochastic processes with lots of exercises, examples and applications in the fields such as engineering, management science, physical and social sciences, and operations research.

Reviewer: A.Brandt (Berlin)

### MSC:

60-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory |