We study a stochastic network that consists of a set of servers processing multiple classes of jobs. Each class of jobs requires a concurrent occupancy of several servers while being processed, and each server is shared among the job classes in a head-of-the-line processor-sharing mechanism. The allocation of the service capacities is a real-time control mechanism: in each network state, the control is the solution to an optimization problem that maximizes a general utility function. Whereas this resource control optimizes in a ``greedy'' fashion, with respect to each state, we establish its asymptotic optimality in terms of (a) deriving the fluid and diffusion limits of the network under this control, and (b) identifying a cost function that is minimized in the diffusion limit, along with a characterization of the so-called fixed point state of the network.
This paper studies a 2-class, 2-server parallel server system under the recently introduced extended heavy traffic condition, which states that the underlying 'static allocation' linear program (LP) is critical, but does not require that it has a unique solution. The main result is the construction of policies that asymptotically achieve a lower bound, proved in [1], on an expected discounted linear combination of diffusion-scaled queue lengths, and are therefore asymptotically optimal (AO). Each extreme point solution to the LP determines a control mode, i.e., a set of activities (class--serv…
This paper studies a multiclass queueing system with an associated risk- sensitive cost observed in heavy traffic at the moderate deviation scale, accounting for convex queue length penalties. The main result is the asymptotic optimality of a dynamic index policy known from the diffusion scale heavy traffic literature as the generalized cμ- rule.
We study transportation networks controlled by dynamical feedback tolls. We consider a multiscale transportation network model whereby the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter are influenced by the congestion status on the whole network as well as dynamic tolls set by the system operator. Our main result shows that a broad class of decentralized congestion-dependent tolls globally stabilise the transportation network around a Wardrop equilibrium. Moreover, using dynamic marginal cost tolls, stability of the transportation network ca…
We consider the ramp metering problem for a freeway stretch modeled by the Cell Transmission Model. Assuming perfect model knowledge and perfect traffic demand prediction, the ramp metering problem can be cast as a finite horizon optimal control problem with the objective of minimizing the Total Time Spent, i.e., the sum of the travel times of all drivers. For this reason, the application of Model Predictive Control (MPC) to the ramp metering problem has been proposed. However, practical tests on freeways show that MPC may not outperform simple, distributed feedback policies. Until now, a theo…
Dealing with meteorological uncertainty poses a major challenge in air traffic management (ATM). Convective weather (commonly referred to as storms or thunderstorms) in particular represents a significant safety hazard that is responsible for one quarter of weather-related ATM delays in the US. With commercial air traffic on the rise and the risk of potentially critical capacity bottlenecks looming, it is vital that future trajectory planning tools are able to account for meteorological uncertainty. We propose an approach to model the uncertainty inherent to forecasts of convective weather reg…
The Accuracy of Cell-based Dynamic Traffic Assignment: Impact of Signal Control on System Optimality
Faculty of Science Engineering and Technology, Swinburne University of Technology（斯威本科技大学科学与工程技学院）；Institute for Transport Studies, University of Leeds（利兹大学交通研究所）
The paper is mostly devoted to applications of a novel optimal control theory for perturbed sweeping/Moreau processes to two practical dynamical models. The first model addresses mobile robot dynamics with obstacles, and the second one concerns control and optimization of traffic flows. Describing these models as controlled sweeping processes with pointwise/hard control and state constraints and applying new necessary optimality conditions for such systems allow us to develop efficient procedures to solve naturally formulated optimal control problems for the models under consideration and comp…
We consider a class of optimal control problems for measure-valued nonlinear transport equations describing traffic flow problems on networks. The objective isto minimise/maximise macroscopic quantities, such as traffic volume or average speed,controlling few agents, for example smart traffic lights and automated cars. The measuretheoretic approach allows to study in a same setting local and nonlocal drivers interactionsand to consider the control variables as additional measures interacting with the driversdistribution. We also propose a gradient descent adjoint-based optimization method, ob-…
University of California, Berkeley（加州大学伯克利分校）；Hyundai Motor Group（现代汽车集团）
We present a hardware-in-the-loop (HIL) simulation setup for repeatable testing of Connected Automated Vehicles (CAVs) in dynamic, real-world scenarios. Our goal is to test control and planning algorithms and their distributed implementation on the vehicle hardware and, possibly, in the cloud. The HIL setup combines PreScan for perception sensors, road topography, and signalized intersections; Vissim for traffic micro-simulation; ETAS DESK-LABCAR/a dynamometer for vehicle and powertrain dynamics; and on-board electronic control units for CAV real time control. Models of traffic and signalized …
The paper concerns the study and applications of a new class of optimal control problems governed by a perturbed sweeping process of the hysteresis type with control functions acting in both play-and-stop operator and additive perturbations. Such control problems can be reduced to optimization of discontinuous and unbounded differential inclusions with pointwise state constraints, which are immensely challenging in control theory and prevent employing conventional variation techniques to derive necessary optimality conditions. We develop the method of discrete approximations married with appro…
The classic Dial-A-Ride Problem (DARP) aims at designing the minimum-cost routing that accommodates a set of user requests under constraints at an operations planning level, where users' preferences and revenue management are often overlooked. In this paper, we present a mechanism for accepting/rejecting user requests in a Demand Responsive Transportation (DRT) context based on the representative utilities of alternative transportation modes. We consider utility-maximizing users and propose a mixed-integer programming formulation for a Chance Constrained DARP (CC-DARP), that captures users' pr…
In this paper the necessary conditions of optimality in the form of maximum principle are derived for a very general class of variational problems. This class includes problems with any optimization criteria and constraints that can be constructed by combining some basic types (differential equation, integral equations, algebraic equation, differential equations with delays, etc). For each problem from this class the necessary optimality conditions are produced by constructing its Lagrange function $R$ and then by dividing its variables into three groups denoted as $u(t)$, $x(t)$ and $a$ corre…
The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a continuous optimization problem without integer variables by modeling traffic flow as sinusoidal. In this paper, we present a novel algorithm to solve this new formulation to near-global optimality on a large-scale. Specifically, we solve a convex relaxation of the nonconvex problem using a tree decomposition reduction, and use randomized rounding to recover a near…
We study the use of the System Optimum (SO) Dynamic Traffic Assignment (DTA) problem to design optimal traffic flow controls for freeway networks as modeled by the Cell Transmission Model, using variable speed limit, ramp metering, and routing. We consider two optimal control problems: the DTA problem, where turning ratios are part of the control inputs, and the Freeway Network Control (FNC), where turning ratios are instead assigned exogenous parameters. It is known that relaxation of the supply and demand constraints in the cell-based formulations of the DTA problem results in a linear progr…
This paper considers the optimization-based traffic allocation problem among multiple end points in connectionless networks. The network utility function is modeled as a non-concave function, since it is the best description of the quality of service perceived by users with inelastic applications, such as video and audio streaming. However, the resulting non-convex optimization problem, is challenging and requires new analysis and solution techniques. To overcome these challenges, we first propose a hierarchy of problems whose optimal value converges to the optimal value of the non-convex opti…
We propose a neural network approach to model general interaction dynamics and an adjoint based stochastic gradient descent algorithm to calibrate its parameters. The parameter calibration problem is considered as optimal control problem that is investigated from a theoretical and numerical point of view. We prove the existence of optimal controls, derive the corresponding first order optimality system and formulate a stochastic gradient descent algorithm to identify parameters for given data sets. To validate the approach we use real data sets from traffic and crowd dynamics to fit the parame…
With autonomous vehicles now sharing roads with human drivers, the era of mixed autonomy brings new challenges in dealing with congestion. One cause of congestion is when vehicle users choose their routes selfishly to minimize their personal travel delay rather than a global travel delay, and prior works address this phenomenon using tolling to influence routing choices, but do not address the setting of mixed autonomy. Tolls may be differentiated, meaning different users of a road experience different tolls, or they may be anonymous; the latter is desirable to allay concerns of fairness and p…
