Queueing Theory and Scheduling

4.

Advanced Queueing Models

4.1.

Non-Markovian Single-Server Queues

4.1.1.

The M/G/1 Queue

4.1.1.1.

Model Assumptions

4.1.1.2.

Embedded Markov Chain

4.1.1.3.

Pollaczek-Khinchine Formula

4.1.1.4.

Residual Service Time

4.1.1.5.

Waiting Time Analysis

4.1.1.6.

Busy Period Analysis

4.1.1.7.

Transform Methods

4.1.2.

The G/M/1 Queue

4.1.2.1.

Model Assumptions

4.1.2.2.

Embedded Markov Chain

4.1.2.3.

Solution Techniques

4.1.2.4.

Performance Analysis

4.1.3.

The G/G/1 Queue

4.1.3.1.

Model Assumptions

4.1.3.2.

Lindley's Equation

4.1.3.3.

Approximation Methods

4.1.3.4.

Kingman's Formula

4.1.3.5.

Heavy Traffic Approximations

4.2.

Priority Queueing Systems

4.2.1.

Priority Disciplines

4.2.1.1.

Non-preemptive Priority

4.2.1.2.

Preemptive-Resume Priority

4.2.1.3.

Preemptive-Repeat Priority

4.2.2.

M/G/1 Priority Queues

4.2.2.1.

Non-preemptive Analysis

4.2.2.2.

Preemptive Analysis

4.2.2.3.

Waiting Time Distributions

4.2.3.

Multi-class Priority Systems

4.2.4.

Dynamic Priority Systems

4.3.

Queueing Systems with Special Features

4.3.1.

Queues with Impatient Customers

4.3.1.1.

4.3.1.2.

4.3.1.3.

4.3.2.

Queues with Server Vacations

4.3.2.1.

Single Vacation Models

4.3.2.2.

Multiple Vacation Models

4.3.2.3.

Vacation Policies

4.3.3.

Queues with Breakdowns

4.3.3.1.

Server Reliability

4.3.3.2.

Repair Time Analysis

4.3.4.

Batch Service Queues

4.3.4.1.

Fixed Batch Size

4.3.4.2.

Variable Batch Size

4.3.4.3.

Threshold Policies

4.4.

Multi-Server Non-Markovian Queues

4.4.1.

4.4.2.

4.4.3.

Approximation Methods

4.4.4.

Performance Analysis

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3. Basic Markovian Queueing Models

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5. Queueing Networks