From Markov Jump Processes to Spatial Queues (Hardcover, 2003)

I A Closer Look into Theory.- 1. Markov Jump Processes.- 1. Definition and Construction.- 2. Kolmogorov Differential Equations.- 3. The Homogeneous Case and an Approximation.- 4. Quasi-Commutability of Generators.- 5. Periodic Markov Jump Processes.- 5.1 Transient distributions.- 5.2 Asymptotic distributions.- 2. Markov-Additive Jump Processes.- 1. Definition and Transition Probabilities.- 2. Elementary Properties.- 3. MAJPs on a Real Vector Space.- 4. Discrete Markovian Arrival Processes.- 5. Laws of Large Numbers.- II Classical Queues.- 3. Examples of Markovian Arrival Processes.- 1. Batch Markovian Arrival Processes.- 1.1 The homogeneous case.- 1.2 The general case.- 2. Fluid Markovian Arrival Processes.- 2.1 The homogeneous case.- 2.2 The general case.- 4. The Periodic BMAP/PH/C Queue.- 1. Transition Probabilities.- 2. Stability and Asymptotic Distributions.- 5. The BMAP/G/? Queue.- 1. The Homogeneous Case.- 2. Asymptotic Stability.- 3. The General Case.- 4. An Approximation.- 5. Bounds for the BMAP/G/c/c Loss System.- 6. Model Fitting For Homogeneous BMAPs.- 1. An EM algorithm for MAPs and BMAPs.- 1.1 Complete sample case for MAPs.- 1.2 EM for MAPs.- 1.3 EM for BMAPs.- 2. A simpler estimation procedure.- 2.1 Estimating the Matrix D0.- 2.2 Phases at Arrival Instants.- 2.3 Estimating the Matrices Dn for n ? 1.- 3. Numerical results.- III Spatial Queues.- 7. Spatial Markovian Arrival Processes.- 1. Stochastic Point Fields.- 1.1 Definition and construction.- 1.2 Examples.- 2. Definition and Construction of SMAPs.- 3. The homogeneous case.- 4. The general case.- 5. Examples.- 8. The SMAP/MT/C/C Queue.- 1. Transition Probabilities.- 2. Asymptotic Distributions.- 3. A Loss Formula.- 9. Spatial Queues with Infinitely Many Servers.- 1. Homogeneous Arrival Rates without User Movements.- 1.1 One-dimensional marginal distributions.- 1.2 Joint distribution in finitely many subsets.- 1.3 Asymptotic Stability.- 2. General Arrival Rates without User Movements.- 2.1 Transient Distribution.- 2.2 An Approximation.- 3. General Arrival Rates with User Movements.- 4. Application: Planning a Mobile Communication Network.- 10. Model Fitting for a Class of SMAPs.- 1. Arrival Rates.- 2. Phases at Arrival Instants.- 3. Generator Matrix.- References.