Queueing Theory

P. P. Bocharov, C. D'Apice, A. V. Pechinkin

• Publisher: De Gruyter
• Year: 2011
• Print ISBN: 9783110622812
• eBook ISBN: 9783110936025
• Edition: 1
• Topic: Mathematics
• Subtopic: Mathematics General
• Index: Mathematics

No detailed description available for "Queueing Theory".

Table of contents

• Foreword
• Introduction
• 1 Probabilistic apparatus of the queueing theory
• 1.1 Characteristic transformations
• 1.2 Exponential and Poisson distributions
• 1.3 Renewal processes. Regenerative processes
• 1.4 Markov chains
• 1.5 Markov processes with discrete state set
• 1.6 Semi-Markov, linearwise, and piecewise-linear processes
• 1.7 Kronecker matrix product
• 2 Defining parameters of queueing systems
• 2.1 Input flow
• 2.2 System structure
• 2.3 Customer service times
• 2.4 Service discipline
• 2.5 Performance indices of a queueing system
• 2.6 Classification of queueing systems
• 2.7 Queueing networks
• 2.8 Properties of distributions for some types of recurrent input flows and service times
• 3 Elementary Markov models
• 3.1 M/M/l/∞ system
• 3.2 M/M/n/r system
• 3.3 M/M/l/∞ system with ‘impatient’ customers
• 3.4 System with a finite number of sources
• 3.5 M[X]/M/l/∞ system with batch arrivals
• 3.6 M/Em/l/∞ system
• 3.7 M/M/l/0 system with retrial queue
• 4 Markov systems: algorithmic methods of analysis
• 4.1 M/Hm/l/r and Hl/M/l/r systems
• 4.2 M2/M/n/r system with non-preemptive priority
• 4.3 M/PH/l/r and PH/M/l/r systems
• 4.4 M/PH/l/r system with server vacations and flow dependent on the queue state
• 4.5 PH/PH/l/r system
• 4.6 Markov systems described by generalised birth-and-death process
• 5 M/G/l/∞ system: investigation methods
• 5.1 Embedded Markov chain
• 5.2 Virtual waiting time
• 5.3 Residual service time
• 5.4 Elapsed waiting time
• 5.5 Use of renewal processes
• 6 Other simple non-Markov models
• 6.1 M/G/∞ system
• 6.2 G/G/∞ system
• 6.3 M/D/n/∞ system
• 6.4 G/M/l/∞ system
• 6.5 M/G/l/r system
• 6.6 M/G/n/0 system
• 7 MAP/G/l/r system
• 7.1 Embedded Markov chain: FCFS discipline
• 7.2 Supplementary variables: FCFS discipline
• 7.3 LCFS discipline
• 7.4 Matrix exponential moments
• 8 MAP/G/l/∞ system
• 8.1 Embedded Markov chain
• 8.2 Virtual waiting time
• 8.3 Supplementary variables: FCFS discipline
• 8.4 LCFS discipline
• 9 MAP/G/l/r system: generalisation
• 9.1 BMAP/SM/l/r system
• 9.2 MAP/G2/l/r system with preemptive priority
• 9.3 MAP/G2/l/r system with non-preemptive priority
• 9.4 MAP/G/l/r retrial system
• 9.5 MAP/G/l/∞ system withforeground-background processor sharing discipline
• 9.6 MAP/G/l/r system with LCFS discipline and bounded total volume of customers
• 9.7 G/MSP/l/r system
• 10 Queueing networks
• 10.1 Network classes
• 10.2 Open exponential networks
• 10.3 Closed exponential networks
• Bibliography
• Index