LEADER 04436nam 22007095 450 001 9910968883603321 005 20250725084857.0 010 $a1-4757-2426-8 024 7 $a10.1007/978-1-4757-2426-4 035 $a(CKB)2660000000022109 035 $a(SSID)ssj0000963070 035 $a(PQKBManifestationID)11517756 035 $a(PQKBTitleCode)TC0000963070 035 $a(PQKBWorkID)10976507 035 $a(PQKB)10943213 035 $a(DE-He213)978-1-4757-2426-4 035 $a(MiAaPQ)EBC3084802 035 $a(PPN)238031152 035 $a(EXLCZ)992660000000022109 100 $a20130421d1995 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aProbability, Stochastic Processes, and Queueing Theory $eThe Mathematics of Computer Performance Modeling /$fby Randolph Nelson 205 $a1st ed. 1995. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Springer,$d1995. 215 $a1 online resource (XXVIII, 584 p.) 300 $aBibliographic Level Mode of Issuance: Monograph 311 08$a0-387-94452-4 311 08$a1-4419-2846-4 327 $a1 Introduction -- I Probability -- 2 Randomness and Probability -- 3 Combinatorics -- 4 Random Variables and Distributions -- 5 Expectation and Fundamental Theorems -- II Stochastic Processes -- 6 The Poisson Process and Renewal Theory -- 7 The M/G/1 Queue -- 8 Markov Processes -- 9 Matrix Geometric Solutions -- 10 Queueing Networks -- 11 Epilogue and Special Topics -- A Types of Randomness -- A.1 Randomness: Physical Systems -- A.1.1 Intrinsic Probability -- A.2 Randomness: Deterministic Systems -- A.2.1 The Baker?s Transformation -- A.2.2 Dynamical Systems -- A.3 Deterministic Randomness** -- A.3.1 Isomorphism Between Systems -- A.3.2 Random Newtonian Systems -- A.4 Summary of Appendix A -- A.5 Problems for Appendix A -- B Combinatorial Equalities and Inequalities -- B.1 Noninteger Combinatorial Expressions -- B.2 Binomial Formula -- B.3 Stirling?s (de Moivre?s) Formula -- B.4 Bounds on Factorial Expressions -- B.5 Noninteger Factorials** -- C Tables of Laplace Transforms and Generating Functions -- C.0.1 Laplace Transforms -- C.1 Generating Functions -- D Limits and Order Relationships -- D.1 Limits -- D.2 Order Relationships -- E List of Common Summations -- References -- Index of Notation. 330 $aWe will occasionally footnote a portion of text with a "**,, to indicate Notes on the that this portion can be initially bypassed. The reasons for bypassing a Text portion of the text include: the subject is a special topic that will not be referenced later, the material can be skipped on first reading, or the level of mathematics is higher than the rest of the text. In cases where a topic is self-contained, we opt to collect the material into an appendix that can be read by students at their leisure. The material in the text cannot be fully assimilated until one makes it Notes on "their own" by applying the material to specific problems. Self-discovery Problems is the best teacher and although they are no substitute for an inquiring mind, problems that explore the subject from different viewpoints can often help the student to think about the material in a uniquely per­ sonal way. With this in mind, we have made problems an integral part of this work and have attempted to make them interesting as well as informative. 606 $aProbabilities 606 $aStatistics 606 $aDynamics 606 $aNonlinear theories 606 $aElectronic digital computers$xEvaluation 606 $aProbability Theory 606 $aStatistics 606 $aApplied Dynamical Systems 606 $aSystem Performance and Evaluation 615 0$aProbabilities. 615 0$aStatistics. 615 0$aDynamics. 615 0$aNonlinear theories. 615 0$aElectronic digital computers$xEvaluation. 615 14$aProbability Theory. 615 24$aStatistics. 615 24$aApplied Dynamical Systems. 615 24$aSystem Performance and Evaluation. 676 $a519.2 676 $a519.2 700 $aNelson$b Randolph$4aut$4http://id.loc.gov/vocabulary/relators/aut$0613970 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910968883603321 996 $aProbability, stochastic processes and queueing theory$91129060 997 $aUNINA