# A model for stochastic hybrid systems with application to communication networks

@article{Hespanha2005AMF, title={A model for stochastic hybrid systems with application to communication networks}, author={Jo{\~a}o Pedro Hespanha}, journal={Nonlinear Analysis-theory Methods \& Applications}, year={2005}, volume={62}, pages={1353-1383} }

## 154 Citations

### Modelling and analysis of stochastic hybrid systems

- Mathematics
- 2006

The author describes a model for stochastic hybrid systems (SHSs) where transitions between discrete modes are triggered by stochastic events. The rate at which these transitions occur is allowed to…

### Modeling and Analysis of Stochastic Hybrid Systems

- Computer Science
- 2007

The author describes a model for Stochastic Hybrid Systems (SHSs) where transitions between discrete modes are triggered by stochastic events. The rate at which these transitions occur is allowed to…

### Stochastic Hybrid Systems with Renewal Transitions: Moment Analysis with Application to Networked Control Systems with Delays

- Mathematics, Computer ScienceSIAM J. Control. Optim.
- 2013

An approach based on a set of Volterra equations to compute any statistical moment of the state of the SHS and a method to compute the Lyapunov exponents of a given degree, i.e., the exponential rate of decrease or increase at which statistical moments converge to zero or to infinity, respectively are proposed.

### Modeling Communication Networks with Hybrid Systems : Extended Version

- Computer Science

A general hybrid systems framework to model the flow of traffic in communication networks, faithfully capturing the dynamics of transient phenomena and yet providing significant flexibility in modeling various congestion control mechanisms, different queuing policies, multicast transmission, etc.

### A Stochastic Hybrid Systems framework for analysis of Markov reward models

- Computer ScienceReliab. Eng. Syst. Saf.
- 2014

### A Stochastic Hybrid Systems Framework for Analyzing Markov Reward Models

- Computer Science
- 2012

The proposed SHS-based framework unifies the analysis of a variety of previously studied reward models and illustrates the application of the framework to performability analysis via analytical and numerical examples.

### Stochastic Hybrid Systems with renewal transitions

- MathematicsProceedings of the 2010 American Control Conference
- 2010

We consider Stochastic Hybrid Systems (SHSs) for which the lengths of times that the system stays in each mode are independent random variables with given distributions. We propose an analysis…

### Modeling Data Communication Networks Using Hybrid Systems

- Computer Science
- 2006

A general hybrid systems framework to model the flow of traffic in communication networks, faithfully capturing the dynamics of transient phenomena and yet providing significant flexibility in modeling various congestion control mechanisms, different queuing policies, multicast transmission, etc.

### Moment dynamics for a class of time-triggered stochastic hybrid systems

- Mathematics, Computer Science
- 2016

This work identifies a subclass of linear time-triggered SHS, where the first and second-order moments depend only on the mean time interval between events and invariant of their higher-order statistics.

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