scholarly journals Optimal Congestion Pricing with Day-to-Day Evolutionary Flow Dynamics: A Mean–Variance Optimization Approach

2021 ◽  
Vol 13 (9) ◽  
pp. 4931
Author(s):  
Qixiu Cheng ◽  
Jun Chen ◽  
Honggang Zhang ◽  
Zhiyuan Liu
Keyword(s):  
Steady State ◽  
Congestion Pricing ◽  
Flow Dynamics ◽  
Optimization Approach ◽  
Planning Period ◽  
Whale Optimization ◽  
Dynamic Congestion Pricing ◽  
Node Network ◽  
The Mean ◽  
Mean Variance

This paper investigates the optimal congestion pricing problem that considers day-to-day evolutionary flow dynamics. Under the circumstance that traffic flows evolve from day to day and the system might be in a non-equilibrium state during a certain period of days after implementing (or adjusting) a congestion toll scheme, it is questionable to use an equilibrium-based index under steady state as the objective to measure the performance of a congestion toll scheme. To this end, this paper proposes a mean–variance-based congestion pricing scheme, which is a robust optimization model, to consider the evolution process of traffic flow dynamics in the optimal toll design problem. More specifically, in the mean–variance-based toll scheme, travelers aim to minimize the variance of expected total travel costs (ETTCs) on different days to reduce risk in daily travels, while the average ETTC over the whole planning period is restricted to being no larger than a predetermined target value set by the authorities. A metaheuristic approach based on the whale optimization algorithm is designed to solve the proposed mean–variance-based day-to-day dynamic congestion pricing problem. Finally, a numerical experiment is conducted to validate the effectiveness of the proposed model and solution algorithm. Results show that the used 9-node network can reach a steady state within 18 days after implementing the mean–variance-based congestion pricing, and the optimal toll scheme can be also obtained with this toll strategy.

Exploring the mean-variance portfolio optimization approach for planning wind repowering actions in Spain

2017 ◽  
Vol 106 ◽  
pp. 335-342 ◽  
Author(s):  
F.J. Santos-Alamillos ◽  
N.S. Thomaidis ◽  
J. Usaola-García ◽  
J.A. Ruiz-Arias ◽  
D. Pozo-Vázquez
Keyword(s):  
Portfolio Optimization ◽  
Optimization Approach ◽  
The Mean ◽  
Mean Variance Portfolio ◽  
Mean Variance

scholarly journals Modeling the Excess Velocity of Low-Viscous Taylor Droplets in Square Microchannels

Fluids ◽  
2019 ◽  
Vol 4 (3) ◽  
pp. 162 ◽  
Author(s):  
Thorben Helmers ◽  
Philip Kemper ◽  
Jorg Thöming ◽  
Ulrich Mießner
Keyword(s):  
High Speed ◽  
Process Intensification ◽  
Continuous Phase ◽  
Channel Cross Section ◽  
Optimization Approach ◽  
Mean Flow ◽  
Bypass Flow ◽  
Wall Film ◽  
Proposed Model ◽  
The Mean

Microscopic multiphase flows have gained broad interest due to their capability to transfer processes into new operational windows and achieving significant process intensification. However, the hydrodynamic behavior of Taylor droplets is not yet entirely understood. In this work, we introduce a model to determine the excess velocity of Taylor droplets in square microchannels. This velocity difference between the droplet and the total superficial velocity of the flow has a direct influence on the droplet residence time and is linked to the pressure drop. Since the droplet does not occupy the entire channel cross-section, it enables the continuous phase to bypass the droplet through the corners. A consideration of the continuity equation generally relates the excess velocity to the mean flow velocity. We base the quantification of the bypass flow on a correlation for the droplet cap deformation from its static shape. The cap deformation reveals the forces of the flowing liquids exerted onto the interface and allows estimating the local driving pressure gradient for the bypass flow. The characterizing parameters are identified as the bypass length, the wall film thickness, the viscosity ratio between both phases and the C a number. The proposed model is adapted with a stochastic, metaheuristic optimization approach based on genetic algorithms. In addition, our model was successfully verified with high-speed camera measurements and published empirical data.

SET-VALUED PERFORMANCE APPROXIMATIONS FOR THE QUEUE GIVEN PARTIAL INFORMATION

2020 ◽  
pp. 1-23
Author(s):  
Yan Chen ◽  
Ward Whitt
Keyword(s):  
Steady State ◽  
Decay Rate ◽  
Waiting Time ◽  
Partial Information ◽  
Upper And Lower Bounds ◽  
Interarrival Time ◽  
Limited Information ◽  
Wide Range ◽  
The Mean ◽  
Third Moment

In order to understand queueing performance given only partial information about the model, we propose determining intervals of likely values of performance measures given that limited information. We illustrate this approach for the mean steady-state waiting time in the $GI/GI/K$ queue. We start by specifying the first two moments of the interarrival-time and service-time distributions, and then consider additional information about these underlying distributions, in particular, a third moment and a Laplace transform value. As a theoretical basis, we apply extremal models yielding tight upper and lower bounds on the asymptotic decay rate of the steady-state waiting-time tail probability. We illustrate by constructing the theoretically justified intervals of values for the decay rate and the associated heuristically determined interval of values for the mean waiting times. Without extra information, the extremal models involve two-point distributions, which yield a wide range for the mean. Adding constraints on the third moment and a transform value produces three-point extremal distributions, which significantly reduce the range, producing practical levels of accuracy.

scholarly journals Multi-Machine Repairable System with One Unreliable Server and Variable Repair Rate

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1299
Author(s):  
Shengli Lv
Keyword(s):  
Steady State ◽  
Transient State ◽  
Repairable System ◽  
Repair Rate ◽  
Numerical Illustration ◽  
Transform Method ◽  
Unreliable Server ◽  
Busy Time ◽  
The Mean ◽  
Mean Time

This paper analyzed the multi-machine repairable system with one unreliable server and one repairman. The machines may break at any time. One server oversees servicing the machine breakdown. The server may fail at any time with different failure rates in idle time and busy time. One repairman is responsible for repairing the server failure; the repair rate is variable to adapt to whether the machines are all functioning normally or not. All the time distributions are exponential. Using the quasi-birth-death(QBD) process theory, the steady-state availability of the machines, the steady-state availability of the server, and other steady-state indices of the system are given. The transient-state indices of the system, including the reliability of the machines and the reliability of the server, are obtained by solving the transient-state probabilistic differential equations. The Laplace–Stieltjes transform method is used to ascertain the mean time to the first breakdown of the system and the mean time to the first failure of the server. The case analysis and numerical illustration are presented to visualize the effects of the system parameters on various performance indices.

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