Random Walks in the Quarter Plane

Part I. The General Theory

1. Probabilistic Background
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

2. Foundations of the Analytic Approach
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

3. Analytic Continuation of the Unknown Functions in the Genus 1 Case
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

4. The Case of a Finite Group
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

5. Solution in the Case of an Arbitrary Group
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

6. The Genus 0 Case
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

7. Criterion for the Finiteness of the Group in the Genus 0 Case
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

8. Miscellanea
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

Part II. Applications to Queueing Systems and Analytic Combinatorics

9. A Two-Coupled Processor Model
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

10. Joining the Shorter of Two Queues: Reduction to a Generalized BVP
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

11. Counting Lattice Walks in the Quarter Plane
Guy Fayolle, Roudolf Iasnogorodski, Vadim Malyshev

Keywords: Mathematics, Probability Theory and Stochastic Processes, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences, Probability and Statistics in Computer Science, Difference and Functional Equations