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
