## Elements of Queueing Theory: Palm Martingale Calculus and Stochastic RecurrencesQueueing theory is a fascinating subject in Applied Probability for two con tradictory reasons: it sometimes requires the most sophisticated tools of stochastic processes, and it often leads to simple and explicit answers. More over its interest has been steadily growing since the pioneering work of Erlang in 1917 on the blocking of telephone calls, to the more recent applications on the design of broadband communication networks and on the performance evaluation of computer architectures. All this led to a huge literature, articles and books, at various levels of mathematical rigor. Concerning the mathematical approach, most of the explicit results have been obtained when specific assumptions (Markov, re newal) are made. The aim of the present book is in no way to give a systematic account of the formulas of queueing theory and their applications, but rather to give a general framework in which these results are best understood and most easily derived. What knowledge of this vast literature is needed to read the book? As the title of the book suggests, we believe that it can be read without prior knowledge of queueing theory at all, although the unifying nature of the proposed framework will of course be more meaningful to readers who already studied the classical Markovian approach. |

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### Contents

II | 1 |

III | 2 |

V | 3 |

VI | 6 |

VII | 11 |

VIII | 12 |

IX | 13 |

X | 14 |

LXVII | 131 |

LXVIII | 133 |

LXIX | 135 |

LXX | 138 |

LXXI | 140 |

LXXII | 141 |

LXXIII | 145 |

LXXIV | 147 |

XII | 16 |

XIII | 17 |

XIV | 20 |

XV | 21 |

XVI | 23 |

XVII | 24 |

XVIII | 25 |

XIX | 27 |

XX | 28 |

XXI | 32 |

XXII | 33 |

XXIII | 35 |

XXIV | 38 |

XXV | 39 |

XXVI | 42 |

XXVII | 44 |

XXIX | 45 |

XXX | 46 |

XXXI | 50 |

XXXII | 52 |

XXXIV | 53 |

XXXV | 55 |

XXXVI | 58 |

XXXVII | 60 |

XXXVIII | 61 |

XXXIX | 64 |

XL | 65 |

XLI | 69 |

XLII | 73 |

XLIII | 75 |

XLIV | 76 |

XLV | 78 |

XLVI | 80 |

XLVII | 83 |

XLVIII | 84 |

XLIX | 87 |

L | 89 |

LII | 91 |

LIV | 92 |

LV | 94 |

LVI | 98 |

LVIII | 100 |

LIX | 104 |

LX | 107 |

LXI | 109 |

LXII | 114 |

LXIII | 121 |

LXIV | 123 |

LXV | 124 |

LXVI | 128 |

LXXV | 151 |

LXXVI | 153 |

LXXVII | 154 |

LXXVIII | 158 |

LXXIX | 161 |

LXXX | 165 |

LXXXI | 171 |

LXXXII | 179 |

LXXXIII | 181 |

LXXXIV | 182 |

LXXXV | 185 |

LXXXVI | 193 |

LXXXVII | 195 |

LXXXVIII | 197 |

LXXXIX | 201 |

XC | 205 |

XCI | 211 |

XCII | 213 |

XCIII | 218 |

XCIV | 221 |

XCV | 228 |

XCVI | 231 |

XCVII | 236 |

XCVIII | 237 |

C | 238 |

CI | 244 |

CII | 248 |

CIII | 257 |

CIV | 259 |

CV | 261 |

CVI | 264 |

CVII | 266 |

CVIII | 272 |

CX | 274 |

CXI | 277 |

CXII | 278 |

CXIII | 279 |

CXIV | 281 |

CXV | 282 |

CXVI | 285 |

CXVII | 288 |

CXVIII | 292 |

CXIX | 294 |

CXXI | 300 |

CXXII | 304 |

CXXIII | 308 |

CXXIV | 314 |

317 | |

329 | |

### Other editions - View all

Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences Francois Baccelli,Pierre Bremaud No preview available - 2010 |

Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences Francois Baccelli,Pierre Bremaud No preview available - 2014 |

### Common terms and phrases

addition admits applied arrival associated Assume assumptions average bounded called Chapter compatible Consider constant construction continuous convergence coupling defined definition denote discipline distribution equal equation equivalent ergodic Example Exercise exists fact FIFO Figure finite flow formula function given gives holds implies independent initial condition input instance integrable intensity Lemma limit Loynes mapping Markov mean measure monotone non-decreasing non-negative Observe obtain Palm probability particular point process Poisson positive present priority probability probability space proof Property prove queue queueing system random variables relation Remark resp respectively result satisfies sequence server Show solution stability station stationary stationary point process stochastic stochastic process stochastic recurrence Suppose taking theorem theory unique values vector waiting workload process