| Point Processes | |
| General Definitions | |
| Poisson Processes | |
| Poisson Point Processes on the Real Line | |
| Renewal Point Processes | |
| The GI/GI/1 FIFO Queue and Random Walks | |
| General results on the GI/GI/1 FIFO Queue | |
| Wiener-Hopf Factorization | |
| Applications to the GI/GI/1 Queue | |
| The GI/M/1 and M/GI/1 Queues | |
| The H/G/1 Queue | |
| A Probabilistic Proof | |
| Limit Theorems for the GI/GI/1 Queue | |
| Introduction | |
| The Biased Random Walk | |
| The Tail Distribution of W | |
| The Maximum of a Busy Period | |
| The GI/GI/1 Queue near Saturation | |
| The Random Walk Conditioned to Hit Level a | |
| Stochastic Networks and Reversibility | |
| Introduction | |
| Reversibility of Markov Processes | |
| Local Balance Equations | |
| Queueing Networks with Product Form | |
| The M/M/1 Queue | |
| Introduction | |
| Exponential Martingales | |
| Hitting Times: Downward | |
| Convergence to Equilibrium | |
| Hitting Times: Upward | |
| Rare Events | |
| Fluid Limits | |
| Large Deviations | |
| Appendix | |
| The M/M/infinity Queue | |
| Introduction | |
| Positive Martingales | |
| Hitting Times: Downward | |
| Hitting Times: Upward | |
| Fluid Limits | |
| A Functional Central Limit Theorem | |
| The M/M/N/N Queue | |
| Appendix | |
| Queues with Poisson Arrivals | |
| FIFO Queue | |
| Infinite Server Queue | |
| LIFO Queue with Preemptive Service | |
| Processor-Sharing Queue | |
| The Insensitivity Property | |
| The Distribution Seen by Customers | |
| Recurrence and Transience of Markov Chains | |
| Recurrence of Markov Chains | |
| Ergodicity | |
| Transience | |
| Ergodicity of Markov Processes | |
| Some Applications | |
| The Classical Version of Lyapunov's Theorem | |
| Rescaled Markov Processes and Fluid Limits | |
| Introduction | |
| Rescaled Markov Processes | |
| The Fluid Limits of a Class of Markov Processes | |
| Fluid Limits and Skorohod Problems | |
| Fluid Limits and Ergodicity Properties | |
| Fluid Limits and Local Equilibrium | |
| Bibliographical Notes | |
| Ergodic Theory: Basic Results | |
| Discrete Dynamical Systems | |
| Ergodic Theorems | |
| Continuous Time Dynamical Systems | |
| Markovian Endomorphisms | |
| Stationary Point Processes | |
| Introduction | |
| The Palm Space of the Arrival Process | |
| Construction of a Stationary Point Process | |
| Relations Between the Palm Space and Its Extension | |
| Joint Distribution of the Points Around t=0 | |
| Some Properties of Stationary Point Processes | |
| Appendix | |
| The G/G/1 FIFO Queue | |
| The Waiting Time | |
| Virtual Waiting Time | |
| The Number of Customers | |
| The Associated Stationary Point Processes | |
| The Unstable G/G/1 Queue | |
| A Queue with Two Servers, the G/G/2 Queue | |
| Martingales | |
| Discrete Time Parameter Martingales | |
| Continuous Time Martingales | |
| The Stochastic Integral for a Poisson Process | |
| Stochastic Differential Equations with Jumps | |
| Markovian Jump Processes: B.1 Q-Matrices | |
| global Balance Equations | |
| The Associated Martingales | |
| Convergence in Distribution: C.1 The Total Variation Norm on Probability Distributions | |
| Convergence of Stochastic Processes | |
| An Introduction to Skorohod Problems: D.1 Dimension 1 | |
| Multi-Dimensional Skorohod Problems | |
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