An error bound for a continuous time approximation of a time-sharing queue

1995 ◽  
Vol 11 (1) ◽  
pp. 163-169
Author(s):  
G. Falin
Keyword(s):  
Error Bound ◽  
Continuous Time ◽  
Time Sharing ◽  
Time Approximation

Continuous-time allocation indices and their discrete-time approximation

1986 ◽  
Vol 18 (03) ◽  
pp. 724-746
Author(s):  
W. J. R. Eplett
Keyword(s):  
Markov Processes ◽  
Discrete Time ◽  
Time Allocation ◽  
Optimal Policy ◽  
Continuous Time ◽  
Bandit Problems ◽  
Time Approximation ◽  
Discrete Time Approximation ◽  
Strong Markov

The theory of allocation indices for defining the optimal policy in multi-armed bandit problems developed by Gittins is presented in the continuous-time case where the projects (or ‘arms’) are strong Markov processes. Complications peculiar to the continuous-time case are discussed. This motivates investigation of whether approximation of the continuous-time problems by discrete-time versions provides a valid technique with convergent allocation indices and optimal expected rewards. Conditions are presented under which the convergence holds.

Sensitivity analysis for Markov reward structures until entrance times

2000 ◽  
Vol 37 (1) ◽  
pp. 45-63 ◽  
Author(s):  
N. M. van Dijk ◽  
H. Korezlioglu
Keyword(s):  
Sensitivity Analysis ◽  
Markov Chain ◽  
Error Bound ◽  
Continuous Time ◽  
Infinitesimal Generator ◽  
Continuous Time Markov Chain ◽  
Entrance Time ◽  
Reward Function ◽  
Switched Network ◽  
Markov Reward

This work presents an estimate of the error on a cumulative reward function until the entrance time of a continuous-time Markov chain into a set, when the infinitesimal generator of this chain is perturbed. The derivation of an error bound constitutes the first part of the paper while the second part deals with an application where the time until saturation is considered for a circuit switched network which starts from an empty state and which is also subject to possible failures.

Optimal Control of Time-Delayed Linear Systems With the Method of Continuous Time Approximation

2008 ◽  
Author(s):  
Jian-Qiao Sun ◽  
Bo Song
Keyword(s):  
Optimal Control ◽  
Output Feedback ◽  
Continuous Time ◽  
Output Feedback Control ◽  
Optimal Controls ◽  
Feedback Controls ◽  
Time Approximation ◽  
Dimensional State Space ◽  
Delayed System ◽  
Space Formulation

This paper presents optimal control studies of delayed dynamical systems with the help of a method of continuous time approximation (CTA). The CTA method proposes a continuous time approximation of the delayed portion of the response leading to a high and finite dimensional state space formulation of the time-delayed system. Optimal controls of the system such as LQR and output feedback controls are readily designed with the existing design tools. In the paper, we present an output feedback control by means of the mapping approach studied previously. In order to accomplish the objective of control design, we also examine various discretization schemes of the CTA method in frequency domain.

Discrete-time approximationsfor continuous-time Markoviancontrol systems

1984 ◽  
Vol 16 (1) ◽  
pp. 15-16
Author(s):  
A. Hordijk ◽  
F. A. Van Der Duyn Schouten
Keyword(s):  
Decision Theory ◽  
Discrete Time ◽  
Continuous Time ◽  
Time System ◽  
Time Approximation ◽  
Discrete Time Systems ◽  
Discrete Time Approximation ◽  
And Control ◽  
Time Systems ◽  
Continuous Time System

The method of discrete-time approximation is widespread in control and decision theory. However, little attention has been paid to the conditions on parameters and control under which the discrete-time systems come close to the continuous-time system.

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