scholarly journals Computation of Dynamic Equilibria in Series-Parallel Networks

2021 ◽  
Author(s):  
Marcus Kaiser
Keyword(s):  
Dynamic Equilibrium ◽  
Recursive Algorithm ◽  
Constructive Proof ◽  
Queuing Model ◽  
Parallel Networks ◽  
In Series ◽  
Small Flow ◽  
Flow Propagation ◽  
Flows Over Time ◽  
Dynamic Equilibria

We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a dynamic equilibrium, every infinitesimally small flow particle reaches the sink as early as possible given the pattern of the rest of the flow. Although this model has been examined for many decades, progress has been relatively recent. In particular, the derivatives of dynamic equilibria have been characterized as thin flows with resetting, which allows for more structural results. Our two main results are based on the formulation of thin flows with resetting as a linear complementarity problem and its analysis. We present a constructive proof of existence for dynamic equilibria if the inflow rate is right-monotone. The complexity of computing thin flows with resetting, which occurs as a subproblem in this method, is still open. We settle it for the class of two-terminal, series-parallel networks by giving a recursive algorithm that solves the problem for all flow values simultaneously in polynomial time.

scholarly journals On the Price of Anarchy for Flows over Time

2021 ◽  
Author(s):  
José Correa ◽  
Andrés Cristi ◽  
Tim Oosterwijk
Keyword(s):  
Network Flows ◽  
Dynamic Equilibrium ◽  
Price Of Anarchy ◽  
Dynamic Network ◽  
Queuing Model ◽  
Worst Case ◽  
Theoretical Understanding ◽  
Dynamic Network Flows ◽  
Flows Over Time ◽  
Over Time

Dynamic network flows, or network flows over time, constitute an important model for real-world situations in which steady states are unusual, such as urban traffic and the internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper, we study dynamic equilibria in the deterministic fluid queuing model in single-source, single-sink networks—arguably the most basic model for flows over time. In the last decade, we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the price of anarchy, measured as the worst-case ratio between the minimum time required to route a given amount of flow from the source to the sink and the time a dynamic equilibrium takes to perform the same task. Our main result states that, if we could reduce the inflow of the network in a dynamic equilibrium, then the price of anarchy is bounded by a factor, parameterized by the longest path length that converges to [Formula: see text], and this is tight. This significantly extends a result by Bhaskar et al. (SODA 2011). Furthermore, our methods allow us to determine that the price of anarchy in parallel-link and parallel-path networks is exactly 4/3. Finally, we argue that, if a certain, very natural, monotonicity conjecture holds, the price of anarchy in the general case is exactly [Formula: see text].

scholarly journals Dynamic Equilibria in Statistical and Nonlinear Physics of Uniform Stress Rotating Space Elevators (USRSE)

2019 ◽  
Vol 11 (6) ◽  
pp. 56
Author(s):  
Leonardo Golubovic ◽  
Steven Knudsen
Keyword(s):  
Carbon Nanotubes ◽  
Materials Science ◽  
Dynamic Equilibrium ◽  
Outer Space ◽  
Point Of View ◽  
Uniform Stress ◽  
The Earth ◽  
Equilibrium Configurations ◽  
Space Elevators ◽  
Dynamic Equilibria

The discovery of ultra-strong materials such as carbon nanotubes and diamond nano-thread structures has recently motivated an enhanced interest for the physics of Space Elevators connecting the Earth with outer space. A new concept has recently emerged in space elevator physics: Rotating Space Elevators (RSE) [Golubović, L. & Knudsen, S. (2009). Classical and statistical mechanics of celestial scale spinning strings: Rotating space elevators. Europhysics Letters 86(3), 34001.]. Objects sliding along rotating RSE string (sliding climbers) do not require internal engines or propulsion to be transported from the Earth's surface into outer space. Here we address the physics of a special RSE family, Uniform Stress Rotating Space Elevators (USRSE), characterized by constant tensile stress along the string. From the point of view of materials science, this condition provides the best control of string’s global integrity. We introduce an advanced analytic approach to obtain the dynamic equilibrium configurations of USRSE strings. We use our results to discuss the applications of USRSE for spacecraft launching.

Maximizing the Mean Number of Communicating Vertex Pairs in Series-Parallel Networks

1986 ◽  
Vol 35 (3) ◽  
pp. 247-251 ◽  
Author(s):  
Brent N. Clark ◽  
Eric M. Neufeld ◽  
Charles J. Colbourn
Keyword(s):  
Parallel Networks ◽  
In Series ◽  
The Mean

Tolerance Analysis of Dynamic Equilibria in Multibody Systems Having Prescribed Rotational Motion

2007 ◽  
Author(s):  
Dong Hwan Choi ◽  
Hong Hee Yoo ◽  
Jonathan A. Wickert
Keyword(s):  
Monte Carlo ◽  
Rotational Motion ◽  
Multibody Systems ◽  
Dynamic Equilibrium ◽  
Tolerance Analysis ◽  
Computational Method ◽  
Speed Governor ◽  
Gyroscope Sensor ◽  
Power Generation Systems ◽  
Dynamic Equilibria

A general formulation for the tolerance analysis of dynamic equilibria in multibody systems having prescribed rotational motion is developed. In a state of dynamic equilibrium, a subset of generalized coordinates assume constant values, while the remaining coordinates vary and respond in time. Applications in which multibody systems exhibit dynamic equilibria include robots, spacecraft, propulsion and power generation systems, and some sensor devices. In the derived approach, manufacturing tolerances are mathematically modeled by probabilistic and statistical variables, through an analytical approach and through Monte Carlo simulation. An efficient computational method based upon direct differentiation is developed to calculate the first order sensitivity of the equilibria with respect to the design and manufacturing variables. To verify the accuracy and effectiveness of the present method, the present analytical method and the companion Monte Carlo approach are applied in examples to a rotating pendulum, a mechanical speed governor, and a model of a rate gyroscope sensor.

The Recognition of Double Euler Trails in Series-Parallel Networks

1998 ◽  
Vol 28 (2) ◽  
pp. 216-257 ◽  
Author(s):  
Tung-Yang Ho ◽  
Ting-Yi Sung ◽  
Lih-Hsing Hsu ◽  
Chang-Hsiung Tsai ◽  
Jeng-Yan Hwang
Keyword(s):  
Parallel Networks ◽  
In Series

DISCRETE TIME DYNAMIC GAMES WITH CONTINUUM OF PLAYERS II: SEMI-DECOMPOSABLE GAMES

2003 ◽  
Vol 05 (01) ◽  
pp. 27-40 ◽  
Author(s):  
AGNIESZKA WISZNIEWSKA-MATYSZKIEL
Keyword(s):  
Financial Markets ◽  
Dynamic Games ◽  
Dynamic Equilibrium ◽  
Stock Exchanges ◽  
Time Dynamic ◽  
Response Sets ◽  
Best Response ◽  
Continuum Of Players ◽  
Discrete Time Dynamic Games ◽  
Dynamic Equilibria

In this paper we consider dynamic games with continuum of players which can constitute a framework to model large financial markets. They are called semi-decomposable games. In semi-decomposable games the system changes in response to a (possibly distorted) aggregate of players' decisions and the payoff is a sum of discounted semi-instantaneous payoffs. The purpose of this paper is to present some simple properties and applications of these games. The main result is an equivalence between dynamic equilibria and families of static equilibria in the corresponding static perfect-foresight games, as well as between dynamic and static best response sets. The existence of a dynamic equilibrium is also proven. These results are counterintuitive since they differ from results that can be obtained in games with a finite number of players. The theoretical results are illustrated with examples describing large financial markets: markets for futures and stock exchanges.

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