A differential game formulation of a controlled network
type: Item
instance of: scholarly article
title: A differential game formulation of a controlled network
zbMATH Open document ID: 1188.90069
author: Hui-Ming Pai
published in: Queueing Systems
publication date: 2010-04-28T00:00:00Z
review text: Consider a multiclass queueing network system with fixed routing. Let service control be one player; service rate, the other. This paper studies the resulting differential game. The main result of the paper is a simple representation of the value function; the proof however is hard. The paper computes a useful example.
Mathematics Subject Classification ID: 90B22
Mathematics Subject Classification ID: 90B35
Mathematics Subject Classification ID: 49N70
zbMATH DE Number: 5702562
zbMATH Keywords: differential game
zbMATH Keywords: controlled network
zbMATH Keywords: fixed routing
zbMATH Keywords: Isaacs equations
zbMATH Keywords: Hamiltonians
zbMATH Keywords: value function
zbMATH Keywords: service control
zbMATH Keywords: service rate
MaRDI profile type: Publication
full work available at URL: s11134-009-9161-6
OpenAlex ID: W2091591567
cites work: Simple Necessary and Sufficient Conditions for the Stability of Constrained Processes
cites work: Positive systems. Proceedings of the second multidisciplinary international symposium on positive systems: Theory and applications (POSTA 06), Grenoble, France, August 30 -- September 1, 2006
cites work: On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limit models
cites work: A Fluid Heuristic for Minimizing Makespan in Job Shops
cites work: Boundary-influenced robust controls: two network examples
cites work: Explicit Solution to a Robust Queueing Control Problem
cites work: On lipschitz continuity of the solution mapping to the skorokhod problem, with applications
cites work: Convex duality and the Skorokhod problem. I
cites work: Robust properties of risk-sensitive control
cites work: The existence of value in differential games of pursuit and evasion
cites work: Q4032143
cites work: State-space formulae for all stabilizing controllers that satisfy an \(H_{\infty}\)-norm bound and relations to risk sensitivity
cites work: A uniqueness result for the Isaacs equation corresponding to nonlinear \(H_\infty\) control
cites work: Transience of multiclass queueing networks via fluid limit models
cites work: Sequencing and routing in multiclass queueing networks. I: Feedback regulation
cites work: Sequencing and Routing in Multiclass Queueing Networks Part II: Workload Relaxations
cites work: Q4235027
cites work: $\mathcal{H}_\infty $ Control of Nonlinear Systems: Differential Games and Viscosity Solutions
cites work: Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks
cites work: Q4842994
DOI: 10.1007/S11134-009-9161-6
Recommended article: Construction of Dynamically Stable Solutions in Differential Network Games
Recommended article: Q3170047
Recommended article: Network models of discrete optimal control and dynamic games with p players
Recommended article: Discrete control and algorithms for solving antagonistic dynamic games on networks
Recommended article: Q4678075
Recommended article: The core of cooperative differential games on networks
Recommended article: Analysis and Control of Networked Game Dynamics via A Microscopic Deterministic Approach
Recommended article: Q5393259
Recommended article: Differential Network Games with Infinite Duration
description: scientific article; zbMATH DE number 5702562