Chapter 2. Basic Queueing Theory


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