Optimal control of arrivals to multiserver queues in a random environment

1984 ◽  
Vol 21 (3) ◽  
pp. 602-615 ◽  
Author(s):  
Werner E. Helm ◽  
Karl-Heinz Waldmann
Keyword(s):  
Optimal Control ◽  
Random Environment ◽  
Cost Structure ◽  
Control Limit ◽  
Inductive Approach ◽  
Multiserver Queues ◽  
Special Cases ◽  
Actual Environment

We study the problem of optimal customer admission to multiserver queues. These queues are assumed to live in an extraneous environment which changes in a semi-Markovian way. Arrivals, service mechanism and random reward/cost structure may all depend on these surroundings. Included as special cases are SM/M/c queues, in particular G/M/c queues, in a random environment. By a direct inductive approach we establish optimality of a generalized control-limit rule depending on the actual environment. Particular emphasis is laid on different applications that show the versatility of the proposed setup.

Optimal control of arrivals to multiserver queues in a random environment

1984 ◽  
Vol 21 (03) ◽  
pp. 602-615 ◽  
Author(s):  
Werner E. Helm ◽  
Karl-Heinz Waldmann
Keyword(s):  
Optimal Control ◽  
Random Environment ◽  
Cost Structure ◽  
Control Limit ◽  
Inductive Approach ◽  
Multiserver Queues ◽  
Special Cases ◽  
Actual Environment

We study the problem of optimal customer admission to multiserver queues. These queues are assumed to live in an extraneous environment which changes in a semi-Markovian way. Arrivals, service mechanism and random reward/cost structure may all depend on these surroundings. Included as special cases are SM/M/c queues, in particular G/M/c queues, in a random environment. By a direct inductive approach we establish optimality of a generalized control-limit rule depending on the actual environment. Particular emphasis is laid on different applications that show the versatility of the proposed setup.

GENERAL MODEL OF DYNAMICS OF HUMAN AND HUMANOID MOTION: FEASIBILITY, POTENTIALS AND VERIFICATION

2006 ◽  
Vol 03 (01) ◽  
pp. 21-47 ◽  
Author(s):  
VELJKO POTKONJAK ◽  
MIOMIR VUKOBRATOVIĆ ◽  
KALMAN BABKOVIĆ ◽  
BRANISLAV BOROVAC
Keyword(s):  
General Problem ◽  
General Model ◽  
Real Motion ◽  
Inductive Approach ◽  
Special Cases ◽  
Bipedal Gait ◽  
Simulated Motion ◽  
Single Support Phase ◽  
The Impact ◽  
Support Phase

This paper elaborates a generalized approach to the modeling of human and humanoid motion. Instead of the usual inductive approach that starts from the analysis of different situations of real motion (like bipedal gait and running; playing tennis, soccer, or volleyball; gymnastics on the floor or using some gymnastic apparatus) and tries to make a generalization, the deductive approach considered begins by formulating a completely general problem and deriving different real situations as special cases. The paper first explains the general methodology. The concept and the software realization are verified by comparing the results with the ones obtained by using "classical" software for one particular well-known problem: biped walk. The applicability and potentials of the proposed method are demonstrated by simulation using a selected example. The simulated motion includes a landing on one foot (after a jump), the impact, a dynamically balanced single-support phase, and overturning (falling down) when the balance is lost. It is shown that the same methodology and the same software can cover all these phases.

scholarly journals Gradient Optimal Control of the Bilinear Reaction–Diffusion Equation

2021 ◽  
Author(s):  
El Hassan Zerrik ◽  
Abderrahman Ait Aadi
Keyword(s):  
Optimal Control ◽  
Diffusion Equation ◽  
Minimization Problem ◽  
Reaction Diffusion ◽  
Numerical Approach ◽  
Time Dependent ◽  
Reaction Diffusion Equation ◽  
Energy Term ◽  
Bounded Controls ◽  
Special Cases

In this chapter, we study a problem of gradient optimal control for a bilinear reaction–diffusion equation evolving in a spatial domain Ω⊂Rn using distributed and bounded controls. Then, we minimize a functional constituted of the deviation between the desired gradient and the reached one and the energy term. We prove the existence of an optimal control solution of the minimization problem. Then this control is characterized as solution to an optimality system. Moreover, we discuss two special cases of controls: the ones are time dependent, and the others are space dependent. A numerical approach is given and successfully illustrated by simulations.

The optimal admission policy to a multiserver queue with finite horizon

1972 ◽  
Vol 9 (01) ◽  
pp. 103-116
Author(s):  
H. Emmons
Keyword(s):  
Optimal Policy ◽  
Finite Time ◽  
Queue Length ◽  
Queueing System ◽  
Cost Structure ◽  
Finite Horizon ◽  
Control Limit ◽  
Admission Policy ◽  
Inverse Control

An M/M/s queueing system with a simple cost structure is considered, under the assumption that the system will close in a finite time after which any remaining customers will require extra overtime service costs. We determine the optimal policy for admitting customers to the queue, as a function of the time, t, to closing and the current queue length, i. It is shown to have the form: admit if and only if f 1(t) ≦ i ≦ f 2(t). The bounds f 1(t) and f 2(t) are specified, and it is shown under what conditions f 1(t) = 0 (a control limit rule) or f 2(t) = ∞ (an inverse control limit rule).

Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis Using a Phase Methodology

2021 ◽  
Author(s):  
Akram Khaleghei ◽  
Michael Jong Kim
Keyword(s):  
Optimal Control ◽  
Control Policy ◽  
Computational Approach ◽  
Control Limit ◽  
New Approach ◽  
Problem Class ◽  
Optimal Value ◽  
Markov Decision ◽  
Decision Epoch ◽  
Partially Observable

In “Optimal Control of Partially Observable Semi-Markovian Failing Systems: An Analysis using a Phase Methodology,” Khaleghei and Kim study a maintenance control problem a as partially observable semi-Markov decision process (POSMDP), a problem class that is typically computationally intractable and not amenable to structural analysis. The authors develop a new approach based on a phase methodology where the idea is to view the intractable POSMDP as the limiting problem of a sequence of tractable POMDPs. They show that the optimal control policy can be represented as a control limit policy which monitors the estimated conditional reliability at each decision epoch, and, by exploiting this structure, an efficient computational approach to solve for the optimal control limit and corresponding optimal value is developed.

scholarly journals Linear Feedback of Mean-Field Stochastic Linear Quadratic Optimal Control Problems on Time Scales

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Yingjun Zhu ◽  
Guangyan Jia
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Mean Field ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Coupled Riccati Equations ◽  
Special Cases ◽  
Quadratic Optimal Control ◽  
Linear State

This paper addresses a version of the linear quadratic control problem for mean-field stochastic differential equations with deterministic coefficients on time scales, which includes the discrete time and continuous time as special cases. Two coupled Riccati equations on time scales are given and the optimal control can be expressed as a linear state feedback. Furthermore, we give a numerical example.

Optimal R&D programs in a random environment

1990 ◽  
Vol 27 (2) ◽  
pp. 343-350 ◽  
Author(s):  
M. J. M. Posner ◽  
D. Zuckerman
Keyword(s):  
Random Environment ◽  
Optimal Stopping ◽  
Development Time ◽  
Research Effort ◽  
Stopping Time ◽  
Control Limit ◽  
Decision Variable ◽  
Classical Approach ◽  
Termination Time ◽  
D Model

Our study examines a stochastic R&D model with flexible termination time and without rivalry. Specifically, we assume a stochastic relationship between expenditures rate and the project's status. Furthermore, the termination time of the project is incorporated into the R&D model as a decision variable by allowing the controller to ‘sell' the obtained technology from the project at any point of time. The proposed framework extends the classical approach in the R&D literature.The main purpose of our study is to determine the optimal stopping time of the project and to characterize qualitatively the firm's expenditure strategy. We show that under certain realistic conditions, the optimal stopping strategy is a control limit policy. Furthermore, the research effort increases monotonically over the development time of the project.

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