Switching Processes in Queueing Models

Name: Switching Processes in Queueing Models
Brand: Wiley-ISTE
Price: 160.99 EUR
Availability: OnlineOnly

Vladimir Anisimov(Author)

Wiley-ISTE (Publisher)

Published on 11. January 2010

352 pages

E-Book

PDF with Adobe-DRM

System requirements

978-0-470-39395-6 (ISBN)

€160.99incl. 7% vat

System requirements

for PDF with Adobe-DRM

E-Book Single Licence

Available for download

Description

More details

Other editions

Person

Content

Intro
Switching Processes in Queueing Models
Contents
Preface
Definitions
Chapter 1. Switching Stochastic Models
1.1. Random processes with discrete component
1.1.1. Markov and semi-Markov processes
1.1.2. Processes with independent increments and Markov switching
1.1.3. Processes with independent increments and semi-Markov switching
1.2. Switching processes
1.2.1. Definition of switching processes
1.2.2. Recurrent processes of semi-Markov type (simple case)
1.2.3. RPSM with Markov switching
1.2.4. General case of RPSM
1.2.5. Processes with Markov or semi-Markov switching
1.3. Switching stochastic models
1.3.1. Sums of random variables
1.3.2. Random movements
1.3.3. Dynamic systems in a random environment
1.3.4. Stochastic differential equations in a random environment
1.3.5. Branching processes
1.3.6. State-dependent flows
1.3.7. Two-level Markov systems with feedback
1.4. Bibliography
Chapter 2. Switching Queueing Models
2.1. Introduction
2.2. Queueing systems
2.2.1. Markov queueing models
2.2.1.1. A state-dependent system MQ/MQ/1/8
2.2.1.2. Queueing system MM,Q/MM,Q/1/m
2.2.1.3. System MQ,B/MQ,B/1/8
2.2.2. Non-Markov systems
2.2.2.1. Semi-Markov system SM/MSM,Q/1
2.2.2.2. System MSM,Q/MSM,Q/1/8
2.2.2.3. System MSM,Q/MSM,Q/1/V
2.2.3. Models with dependent arrival flows
2.2.4. Polling systems
2.2.5. Retrial queueing systems
2.3. Queueing networks
2.3.1. Markov state-dependent networks
2.3.1.1. Markov network (MQ/MQ/m/8)r
2.3.1.2. Markov networks (MQ,B/MQ,B/m/8)r with batches
2.3.2. Non-Markov networks
2.3.2.1. State-dependent semi-Markov networks
2.3.2.2. Semi-Markov networks with random batches
2.3.2.3. Networks with state-dependent input
2.4. Bibliography
Chapter 3. Processes of Sums of Weakly-dependent Variables
3.1. Limit theorems for processes of sums of conditionally independent random variables
3.2. Limit theorems for sums with Markov switching
3.2.1. Flows of rare events
3.2.1.1. Discrete time
3.2.1.2. Continuous time
3.3. Quasi-ergodic Markov processes
3.4. Limit theorems for non-homogenous Markov processes
3.4.1. Convergence to Gaussian processes
3.4.2. Convergence to processes with independent increments
3.5. Bibliography
Chapter 4. Averaging Principle and Diffusion Approximation for Switching Processes
4.1. Introduction
4.2. Averaging principle for switching recurrent sequences
4.3. Averaging principle and diffusion approximation for RPSMs
4.4. Averaging principle and diffusion approximation for recurrent processes of semi-Markov type (Markov case)
4.4.1. Averaging principle and diffusion approximation for SMP
4.5. Averaging principle for RPSM with feedback
4.6. Averaging principle and diffusion approximation for switching processes
4.6.1. Averaging principle and diffusion approximation for processes with semi-Markov switching
4.7. Bibliography
Chapter 5. Averaging and Diffusion Approximation in Overloaded Switching Queueing Systems and Networks
5.1. Introduction
5.2. Markov queueing models
5.2.1. System MQ,B/MQ,B/1/8
5.2.2. System MQ/MQ/1/8
5.2.3. Analysis of the waiting time
5.2.4. An output process
5.2.5. Time-dependent system MQ,t/MQ,t/1/8
5.2.6. Asystem with impatient calls
5.3. Non-Markov queueing models
5.3.1. System GI/MQ/1/8
5.3.2. Semi-Markov system SM/MSM,Q/1/8
5.3.3. System MSM,Q/MSM,Q/1/8
5.3.4. System SMQ/MSM,Q/1/8
5.3.5. System GQ/MQ/1/8
5.3.6. Asystemwith unreliable servers
5.3.7. Polling systems
5.4. Retrial queueing systems
5.4.1. Retrial system MQ/G/1/w.r
5.4.2. System M/G/1/w.r
5.4.3. Retrial system M/M/m/w.r
5.5. Queueing networks
5.5.1. State-dependent Markov network (MQ/MQ/1/8)r
5.5.2. Markov state-dependent networks with batches
5.6. Non-Markov queueing networks
5.6.1. A network (MSM,Q/MSM,Q/1/8)r with semi-Markov switching
5.6.2. State-dependent network with recurrent input
5.7. Bibliography
Chapter 6. Systems in Low Traffic Conditions
6.1. Introduction
6.2. Analysis of the first exit time from the subset of states
6.2.1. Definition of S-set
6.2.2. An asymptotic behavior of the first exit time
6.2.3. State space forming a monotone structure
6.2.4. Exit time as the time of first jump of the process of sums with Markov switching
6.3. Markov queueing systems with fast service
6.3.1. M/M/s/m systems
6.3.1.1. System MM/M/l/m in a Markov environment
6.3.2. Semi-Markov queueing systems with fast service
6.4. Single-server retrial queueing model
6.4.1. Case 1: fast service
6.4.1.1. State-dependent case
6.4.2. Case 2: fast service and large retrial rate
6.4.3. State-dependent model in a Markov environment
6.5. Multiserver retrial queueing models
6.6. Bibliography
Chapter 7. Flows of Rare Events in Low and Heavy Traffic Conditions
7.1. Introduction
7.2. Flows of rare events in systems with mixing
7.3. Asymptotically connected sets (Vn-S-sets)
7.3.1. Homogenous case
7.3.2. Non-homogenous case
7.4. Heavy traffic conditions
7.5. Flows of rare events in queueing models
7.5.1. Light traffic analysis in models with finite capacity
7.5.2. Heavy traffic analysis
7.6. Bibliography
Chapter 8. Asymptotic Aggregation of State Space
8.1. Introduction
8.2. Aggregation of finite Markov processes (stationary behavior)
8.2.1. Discrete time
8.2.2. Hierarchic asymptotic aggregation
8.2.3. Continuous time
8.3. Convergence of switching processes
8.4. Aggregation of states in Markov models
8.4.1. Convergence of the aggregated process to a Markov process (finite state space)
8.4.2. Convergence of the aggregated process with a general state space
8.4.3. Accumulating processes in aggregation scheme
8.4.4. MP aggregation in continuous time
8.5. Asymptotic behavior of the first exit time from the subset of states (non-homogenous in time case)
8.6. Aggregation of states of non-homogenous Markov processes
8.7. Averaging principle for RPSM in the asymptotically aggregated Markov environment
8.7.1. Switching MP with a finite state space
8.7.2. Switching MP with a general state space
8.7.3. Averaging principle for accumulating processes in the asymptotically aggregated semi-Markov environment
8.8. Diffusion approximation for RPSM in the asymptotically aggregated Markov environment
8.9. Aggregation of states in Markov queueing models
8.9.1. System MQ/MQ/r/8 with unreliable servers in heavy traffic
8.9.2. System MM,Q/MM,Q/1/8 in heavy traffic
8.10. Aggregation of states in semi-Markov queueing models
8.10.1. System SM/MSM,Q/1/8
8.10.2. System MSM,Q/MSM,Q/1/8
8.11. Analysis of ows of lost calls
8.12. Bibliography
Chapter 9. Aggregation in Markov Models with Fast Markov Switching
9.1. Introduction
9.2. Markov models with fast Markov switching
9.2.1. Markov processes with Markov switching
9.2.2. Markov queueing systems with Markov type switching
9.2.3. Averaging in the fast Markov type environment
9.2.4. Approximation of a stationary distribution
9.3. Proofs of theorems
9.3.1. Proof of Theorem 9.1
9.3.2. Proof of Theorem 9.2
9.3.3. Proof of Theorem 9.3
9.4. Queueing systems with fast Markov type switching
9.4.1. System MM,Q/MM,Q/1/N
9.4.1.1. Averaging of states of the environment
9.4.1.2. The approximation of a stationary distribution
9.4.2. Batch system BMM,Q/BMM,Q/1/N
9.4.3. System M/M/s/m with unreliable servers
9.4.4. Priority model MQ/MQ/m/s,N
9.5. Non-homogenous in time queueing models
9.5.1. System MM,Q,t/MM,Q,t/s/m with fast switching - averaging of states
9.5.2. System MM,Q/MM,Q/s/m with fast switching - aggregation of states
9.6. Numerical examples
9.7. Bibliography
Chapter 10. Aggregation in Markov Models with Fast Semi-Markov Switching
10.1. Markov processes with fast semi-Markov switches
10.1.1. Averaging of a semi-Markov environment
10.1.2. Asymptotic aggregation of a semi-Markov environment
10.1.3. Approximation of a stationary distribution
10.2. Averaging and aggregation in Markov queueing systems with semi- Markov switching
10.2.1. Averaging of states of the environment
10.2.2. Asymptotic aggregation of states of the environment
10.2.3. The approximation of a stationary distribution
10.3. Bibliography
Chapter 11. Other Applications of Switching Processes
11.1. Self-organization in multicomponent interacting Markov systems
11.2. Averaging principle and diffusion approximation for dynamic systems with stochastic perturbations
11.2.1. Recurrent perturbations
11.2.2. Semi-Markov perturbations
11.3. Random movements
11.3.1. Ergodic case
11.3.2. Case of the asymptotic aggregation of state space
11.4. Bibliography
Chapter 12. Simulation Examples
12.1. Simulation of recurrent sequences
12.2. Simulation of recurrent point processes
12.3. Simulation of RPSM
12.4. Simulation of state-dependent queueing models
12.5. Simulation of the exit time from a subset of states of a Markov chain
12.6. Aggregation of states in Markov models
Index

System requirements

Save as PDF Copy link into clipboard

Schweitzer Fachinformationen

Switching Processes in Queueing Models

Description

More details

Other editions

Additional editions

Person

Content

System requirements