An Elementary Introduction to Queueing Systems

Ch. 1. Modeling of queueing systems. 1.1. Mathematical modeling. 1.2. The Poisson input process. 1.3. Superposition of independent Poisson processes. 1.4. Decomposition of a Poisson process. 1.5. The exponential interarrival time distribution. 1.6. The Markov property or memoryless property. 1.7. Relationship between the Poisson distribution and the exponential distribution. 1.8. The service time distribution. 1.9. The residual service time distribution. 1.10. The birth and death process. 1.11. The outside observer's distribution and the arriving customer's distribution -- ch. 2. Queueing systems with losses. 2.1. Introduction. 2.2. The Erlang loss system. 2.3. The Erlang loss formula -- ch. 3. Queueing systems allowing waiting. 3.1. Introduction. 3.2. The Erlang delay system. 3.3. The distribution function of the waiting time. 3.4. Little's formula -- ch. 4. The Engset loss and delay systems. 4.1. Introduction. 4.2. The Engset loss system. 4.3. The arriving customer's distribution for the Engset loss system. 4.4. The offered load and carried load in the Engset loss system. 4.5. The Engset delay system. 4.6. The waiting time distribution function for the Engset delay system. 4.7. The mean waiting time in the Engset delay system. 4.8. The offered load and carried load in the Engset delay system -- ch. 5. Queueing systems with a single server. 5.1. Introduction. 5.2. The M/M/1 queue. 5.3. The M/G/1 queue and the Pollaczek-Khinchin formula for the mean waiting time. 5.4. The M/G/1 queue with vacations. 5.5. The M/G/1 queue with priority discipline. 5.6. The GI/M/1 queue