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The dynamic pricing problem of a freeway corridor with high-occupancy toll (HOT) lanes was formulated and solved based on a point queue abstraction of the traffic system [Yin and Lou, 2009]. However, existing pricing strategies cannot guarantee that the closed-loop system converges to the optimal state, in which the HOT lanes' capacity is fully utilized but there is no queue on the HOT lanes, and a well-behaved estimation and control method is quite challenging and still elusive. This paper attempts to fill the gap by making three fundamental contributions: (i) to present a simpler formulation of the point queue model based on the new concept of residual capacity, (ii) to propose a simple feedback control theoretic approach to estimate the average value of time and calculate the dynamic price, and (iii) to analytically and numerically prove that the closed-loop system is stable and guaranteed to converge to the optimal state, in either Gaussian or exponential manners., Comment: 34 pages, 16 figures

A stable dynamic pricing scheme is essential to guarantee the desired performance of high-occupancy-toll (HOT) lanes, where single-occupancy vehicles (SOVs) can pay a price to use the HOT lanes. But existing methods apply to either only one type of lane-choice models with unknown parameters or different types of lane-choice models but with known parameters. In this study we present a new dynamic pricing scheme that is stable and applies to different types of lane-choice models with unknown parameters. There are two operational objectives for operating HOT lanes: (i) to maintain the free-flow condition to guarantee the travel time reliability; and (ii) to maximize the HOT lanes' throughput to minimize the system's total delay. The traffic dynamics on both HOT and general purpose (GP) lanes are described by point queue models, where the queueing times are determined by the demands and capacities. We consider three types of lane-choice models: the multinomial logit model when SOVs share the same value of time, the vehicle-based user equilibrium model when SOVs' values of time are heterogeneous and follow a distribution, and a general lane-choice model. We demonstrate that the second objective is approximately equivalent to the social welfare optimization principle for the logit model. Observing that the dynamic price and the excess queueing time on the GP lanes are linearly correlated in all the lane-choice models, we propose a feedback control method to determine the dynamic prices based on two integral controllers. We further present a method to estimate the parameters of a lane-choice model once its type is known. Analytically we prove that the equilibrium state of the closed-loop system with constant demand patterns is ideal, since the two objectives are achieved in it, and that it is asymptotically stable. With numerical examples we verify the effectiveness of the solution method., Comment: 24 pages, 10 figures

Two-dimensional (2D) van der Waals (vdW) magnets are crucial for ultra-compact spintronics. However, so far, no vdW crystal has exhibited tunable above-room-temperature intrinsic ferromagnetism in the 2D ultrathin regime. Here, we report the tunable above-room-temperature intrinsic ferromagnetism in ultrathin vdW crystal Fe$_{3+x}$GaTe$_2$ ($x$ = 0 and 0.3). By increasing the Fe content, the Curie temperature (TC) and room-temperature saturation magnetization of bulk Fe$_{3+x}$GaTe$_2$ crystals are enhanced from 354 to 376 K and 43.9 to 50.4 emu/g, respectively. Remarkably, the robust anomalous Hall effect in 3-nm Fe$_{3.3}$GaTe$_2$ indicate a record-high TC of 340 K and a large room-temperature perpendicular magnetic anisotropy energy of 6.6 * 10^5 J/m$^3$, superior to other ultrathin vdW ferromagnets. First-principles calculations reveal the asymmetric density of states and an additional large spin exchange interaction in ultrathin Fe$_{3+x}$GaTe$_2$ responsible for robust intrinsic ferromagnetism and higher Tc. This work opens a window for above-room-temperature ultrathin 2D magnets in vdW-integrated spintronics.

Developing novel high-temperature van der Waals ferromagnetic semiconductor materials and investigating their interface coupling effects with two-dimensional topological semimetals are pivotal for advancing next-generation spintronic and quantum devices. However, most van der Waals ferromagnetic semiconductors exhibit ferromagnetism only at low temperatures, limiting the proximity research on their interfaces with topological semimetals. Here, we report an intrinsic, van der Waals layered room-temperature ferromagnetic semiconductor crystal, FeCr0.5Ga1.5Se4 (FCGS), with a Curie temperature as high as 370 K, setting a new record for van der Waals ferromagnetic semiconductors. The saturation magnetization at low temperature (2 K) and room temperature (300 K) reaches 8.2 emu/g and 2.7 emu/g, respectively. Furthermore, FCGS possesses a bandgap of approximately 1.2 eV, which is comparable to the widely used commercial silicon. The FCGS/graphene heterostructure exhibits an impeccably smooth and gapless interface, thereby inducing a robust magnetic proximity coupling effect between FCGS and graphene. After the proximity coupling, graphene undergoes a charge carrier transition from electrons to holes, accompanied by a transition from non-magnetic to ferromagnetic transport behavior with robust anomalous Hall effect. Notably, the anomalous Hall effect remains robust even temperatures up to 400 K.

Agent-based models have been extensively used to simulate the behavior of travelers in transportation systems because they allow for realistic and versatile modeling of interactions. However, traditional agent-based models suffer from high computational costs and rely on tracking physical locations, raising privacy concerns. This paper proposes an efficient formulation for the agent-based bathtub model (AB2M) in the relative space, where each agent's trajectory is represented by a time series of the remaining distance to its destination. The AB2M can be understood as a microscopic model that tracks individual trips' initiation, progression, and completion and is an exact numerical solution of the bathtub model for generic (time-dependent) trip distance distributions. The model can be solved for a deterministic set of trips with a given demand pattern (defined by the start time of each trip and its distance), or it can be used to run Monte Carlo simulations to capture the average behavior and variation stochastic demand patterns, described by probabilistic distributions of trip distances and departure times. To enhance the computational efficiency, we introduce a priority queue formulation, eliminating the need to update trip positions at each time step and allowing us to run large-scale scenarios with millions of individual trips in seconds. We systematically explore the scaling properties and discuss the introduction of biases and numerical errors. The systematic exploration of scaling properties of the modeling of individual agents in the relative space with the AB2M further enhances its applicability to large-scale transportation systems and opens up opportunities for studying travel time reliability, scheduling, and mode choices.

Room-temperature electrically-tuned coercivity and nonvolatile multi-states magnetization switching is crucial for next-generation low-power 2D spintronics. However, most methods have limited ability to adjust the coercivity of ferromagnetic systems, and room-temperature electrically-driven magnetization switching shows high critical current density and high power dissipation. Here, highly-tunable coercivity and highly-efficient nonvolatile multi-states magnetization switching are achieved at room temperature in single-material based devices by 2D van der Waals itinerant ferromagnet Fe$_3$GaTe$_2$. The coercivity can be readily tuned up to ~98.06% at 300 K by a tiny in-plane electric field that is 2-5 orders of magnitude smaller than that of other ferromagnetic systems. Moreover, the critical current density and power dissipation for room-temperature magnetization switching in 2D Fe$_3$GaTe$_2$ are down to ~1.7E5 A cm$^{-2}$ and ~4E12 W m$^{-3}$, respectively. Such switching power dissipation is 2-6 orders of magnitude lower than that of other 2D ferromagnetic systems. Meanwhile, multi-states magnetization switching are presented by continuously controlling the current, which can dramatically enhance the information storage capacity and develop new computing methodology. This work opens the avenue for room-temperature electrical control of ferromagnetism and potential applications for vdW-integrated 2D spintronics.

Magnetic tunnel junctions (MTJs) based on all-two dimensional (2D) van der Waals heterostructures with sharp and clean interfaces in atomic scale are essential for the application of next-generation spintronics. However, the lack of room-temperature intrinsic ferromagnetic crystals with perpendicular magnetic anisotropy has greatly hindered the development of vertical MTJs. The discovery of room-temperature intrinsic ferromagnetic 2D crystal Fe3GaTe2 has solved the problem and greatly facilitated the realization of practical spintronic devices. Here, we demonstrate a room-temperature MTJ based on Fe3GaTe2/WS2/Fe3GaTe2 heterostructure. The tunnelling magnetoresistance (TMR) ratio is up to 213% with high spin polarization of 72% at 10 K, the highest ever reported in Fe3GaTe2-based MTJs up to now. The tunnelling spin-valve signal robustly exists at room temperature (300 K) with bias current down to 10 nA. Moreover, the spin polarization can be modulated by bias current and the TMR shows a sign reversal at large bias current. Our work sheds light on the potential application for low-energy consumption all-2D vdW spintronics and offers alternative routes for the electronic control of spintronic devices.