2.1 Markov Processes and Markov Chains

2.1.1 Discrete Time Markov Chains

2.2 Birth Death Process

2.3 Kendall’s Notation for Queues

2.4 Little’s Result

2.5 Equilibrium Solutions for M/M/-/- Queues

2.5.1 PASTA - Poisson Arrivals See Time Averages

2.5.2 M/M/1 Queue

2.5.3 M/M/1 Queue with Discouraged Arrivals

2.5.4 M/M/m Queue (m servers, infinite number of waiting positions)

2.5.5 M/M/m/m Queue (m server loss system, no waiting)

2.5.6 M/M/1/K Queue (single server queue with K-1 waiting positions)

2.5.7 M/M/1/-/K Queue (single server, infinite number of waiting positions, finite customer population K)

2.5.8 M/M/-/-/K Queue (infinite servers, finite customer population)

2.6 Delay Analysis for FCFS M/M/1 and M/M/m Queues

2.6.1 Delay Analysis for a FCFS M/M/1 Queue

2.6.2 Delay Analysis for a FCFS M/M/m Queue

2.7 Departure Process from a M/M/m Queue

2.8 Time Reversibility Property of Irreducible, Aperiodic Markov Chains

2.9 The Method of Stages for Solving a M/-/1 FCFS Queue

2.10 Queues with Bulk (or Batch) Arrivals

2.10.1 The M^[X]/M/1 Queue

2.10.2 The M^[X]/M/s/s Queue

Problems