Queueing Theory with Applications to Packet Telecommunication

1. TERMINOLOGY AND EXAMPLES. 1.1 The Terminology of Queueing Systems. 1.2 Examples of Application to System Design. 1.3 Summary. 2. REVIEW OF RANDOM PROCESSES. 2.1 Statistical Experiments and Probability. 2.2 Random Variables. 2.3 Exponential Distribution. 2.4 Poisson Process. 2.5 Markov Chains. 3. ELEMENTARY CTMC-BASED QUEUEING MODELS. 3.1 M/M/1 Queueing System. 3.2 Dynamical Equations for General Birth-Death Process. 3.3 Time-Dependent Probabilities for Finite-State Systems. 3.4 Balance Equations Approach for Systems in Equilibrium. 3.5 Probability Generating Function Approach. 3.6 Supplementary Problems. 4. ADVANCED CTMC-BASED QUEUEING MODELS. 4.1 Networks. 4.2 Phase-Dependent Arrivals and Services. 4.3 Phase Type Distributions. 4.4 Supplementary Problems. 5. THE BASIC M/G/1 QUEUEING SYSTEM. 5.1 M/G/1 Transform Equations. 5.2 Ergodic Occupancy Distribution for M/G/1. 5.3 Expected Values Via Renewal Theory. 5.4 Supplementary Problems. 6. THE M/G/1 QUEUEING SYSTEM WITH PRIORITY. 6.1 M/G/1 Under LCFS-PR Discipline. 6.2 M/G/1 System Exceptional First Service. 6.3 M/G/1 under HOL Priority. 6.4 Ergodic Occupancy Probabilities for Priority Queues. 6.5 Expected Waiting Times under HOL Priority. 7. VECTOR MARKOV CHAINS ANALYSIS. 7.1 The M/G/1 and G/M/1 Paradigms. 7.2 G/M/1 Solution Methodology. 7.3 M/G/1 Solution Methodology. 7.4 Application to Statistical Multiplexing. 7.5 Generalized State Space Approach: Complex Boundaries. 7.6 Summary. 7.7 Supplementary Problems. 8. CLOSING REMARKS