Palm Probabilities and Stationary Queues [Paperback]

Tables of Contents.- 1. Stationary point processes and Palm probabilities.- 1. Stationary marked point processes.- 1.1. The canonical space of point processes on IR.- 1.2. Stationary point processes.- 1.3. Stationary marked point processes.- 1.4. Two properties of stationary point processes.- 2. Intensity.- 2.1. Intensity of a stationary point process.- 2.2. Intensity measure of a stationary marked point process.- 3. Palm probability.- 3.1. Mecke s definition.- 3.2. Invariance of the Palm probability.- 3.3. Campbell s formula.- 3.4. The exchange formula (or cycle formula) and Wald s equality.- 4. From Palm probability to stationary probability.- 4.1. The inversion formula.- 4.2. Feller s paradox.- 4.3. The mean value formulae.- 4.4. The inverse construction.- 5. Examples.- 5.1. Palm probability of a superposition of independent point processes.- 5.2. Palm probability associated with selected marks.- 5.3. Palm probability of selected transitions of a Markov chain.- 6. Local aspects of Palm probability.- 6.1. Korolyuk and Dobrushin s infinitesimal estimates.- 6.2. Conditioning at a point.- 7. Characterization of Poisson processes.- 7.1. Predictable ?-fields.- 7.2. Stochastic intensity and Radon-Nikodym derivatives.- 7.3. Palm view at Watanabe s characterization theorem.- 8. Ergodicity of point processes.- 8.1. Invariant events.- 8.2. Ergodicity under the stationary probability and its Palm probability.- 8.3. The cross ergodic theorem.- References for Part 1: Palm probabilities.- 2. Stationary queueuing systems.- 1. The G/G/1/? queue : construction of the customer stationary state.- 1.1. Loynes problem.- 1.2. Existence of a finite stationary load.- 1.3. Uniqueness of the stationary load.- 1.4. Construction points.- 1.5. Initial workload and long term behaviour.- 2. Formulae for the G/G/1/? queue.- 2.1. Construction of the time-stationary workload.- 2.2. Little s formulae: the FIFO case.- 2.3. Probability of emptiness.- 2.4. Takacs formulae.- 3. The G/G/s/? queulSC