arXiv subjects

Vee-Liem Saw

Publications and source records attributed to Vee-Liem Saw.

At least 19 recordsLinked to original sources

arXiv2022

Inferring origin-destination distribution of agent transfer in a complex network using deep gated recurrent units

Predicting the origin-destination (OD) probability distribution of agent transfer is an important problem for managing complex systems. However, prediction accuracy of associated statistical estimators suffer from underdetermination. While specific techniques have been proposed to overcome this deficiency, there still lacks a general approach. Here, we propose a deep neural network framework with gated recurrent units (DNNGRU) to address this gap. Our DNNGRU is \emph{network-free}, as it is trained by supervised learning with time-series data on the volume of agents passing through edges. We use it to investigate how network topologies affect OD prediction accuracy, where performance enhancement is observed to depend on the degree of overlap between paths taken by different ODs. By comparing against methods that give exact results, we demonstrate the near-optimal performance of our DNNGRU, which we found to consistently outperform existing methods and alternative neural network architectures, under diverse data generation scenarios.

physics.soc-ph↗

arXiv2022

Can bus bunching reduce waiting time?

Bus bunching is ostensibly regarded as a detrimental phenomenon in bus systems. We study a bus loop with two bus stops, one regular and one spike bus stop, where bunched buses can outperform staggered buses. The spike bus stop models a bus stop connected to a train or metro service, where passengers arrive in groups at periodic intervals (spikes). We introduce the configuration of synchronised bunched buses, where bunched buses wait for the spike in demand. For a wide range of parameters, synchronised bunched buses outperform perfectly staggered buses in terms of minimising the waiting time of commuters. We present an analytical formulation of the average waiting time in the case of bunched buses, synchronised bunched buses and perfectly staggered buses with the consideration of different passenger demand, number of buses, and bus capacity. We demonstrate the validity of our analytical results through an agent-based simulation of the bus loop system.

physics.soc-ph↗

arXiv2021

Bunching Dynamics of Buses in a Loop

Bus bunching is a curse of transportation systems such as buses in a loop. Here we present an analytical method to find the number of revolutions before two buses bunch in an idealised system, as a function of the initial distance and the crowdedness of the bus stops. We can also characterise the average waiting time for passengers as the buses bunch. The results give a better understanding of the phenomenon of bus bunching and design recommendations for bus loops.

cond-mat.stat-mech↗

arXiv2021

Chaotic semi-express buses in a loop

Urban mobility involves many interacting components: buses, cars, commuters, pedestrians, trains etc., making it a very complex system to study. Even a bus system responsible for delivering commuters from their origins to their destinations in a loop service already exhibits very complicated dynamics. Here, we investigate the dynamics of a simplified version of such a bus loop system consisting of two buses serving three bus stops. Specifically, we consider a configuration of one bus operating as a normal bus which picks up passengers from bus stops $A$ and $B$, and then delivers them to bus stop $C$, whilst the second bus acts as an express bus which picks up passengers only from bus stop $B$ and then delivers them to bus stop $C$. The two buses are like asymmetric agents coupled to bus stop $B$ as they interact via picking up passengers from this common bus stop. Intriguingly, this \emph{semi-express} bus configuration is more efficient and has a lower average waiting time for buses, compared to a configuration of two normal buses or a configuration of two express buses. We reckon the efficiency arises from the chaotic dynamics exhibited in the semi-express system, where the tendency towards anti-bunching is greater than that towards bunching, in contradistinction to the regular bunching behavior of two normal buses or the independent periodic behaviour of two non-interacting express buses.

physics.soc-ph↗

arXiv2021

Optimal assignment of buses to bus stops in a loop by reinforcement learning

Bus systems involve complex bus-bus and bus-passengers interactions. We study the problem of assigning buses to bus stops to minimise the average waiting time of passengers, W. An analytical theory for two specific cases of interactions is formulated: normal situation where all buses board passengers from every bus stop, versus novel express buses where disjoint subsets of non-interacting buses serve disjoint subsets of bus stops. Our formulation allows exact calculation of W for general loops in the two cases examined. Compared with regular buses, we present scenarios where express buses show improvement in W. Useful insights are obtained from our theory: 1) there is a minimum number of buses needed, 2) splitting a crowded bus stop into two less crowded ones always increases W for regular buses, 3) changing the destination of passengers and location of bus stops do not influence W. In the second part, we introduce a reinforcement-learning platform that overcomes limitations of our analytical method to search for better allocations of buses to bus stops that minimise W. Compared with the previous cases, any possible interaction between buses is allowed, unlocking novel emergent strategies. We apply this tool to a simple toy model and three empirically-motivated bus loops, based on data collected from the Nanyang Technological University shuttle bus system. In the simplified model, we observe an unexpected strategy emerging that could not be analysed with our mathematical formulation and displays chaotic behaviour. The possible configurations in the three empirically-motivated scenarios are approximately 10^11, 10^11 and 10^20, so a brute-force approach is impossible. Our algorithm reduces W by 12% to 32% compared with regular buses and 12% to 29% compared with express buses. This tool has practical applications because it works independently of the specific characteristics of a bus loop.

physics.soc-ph↗

arXiv2020

No-boarding buses: Synchronisation for efficiency

We investigate a no-boarding policy in a system of $N$ buses serving $M$ bus stops in a loop, which is an entrainment mechanism to keep buses synchronised in a reasonably staggered configuration. Buses always allow alighting, but would disallow boarding if certain criteria are met. For an analytically tractable theory, buses move with the same natural speed (applicable to programmable self-driving buses), where the average waiting time experienced by passengers waiting at the bus stop for a bus to arrive can be calculated. The analytical results show that a no-boarding policy can dramatically reduce the average waiting time, as compared to the usual situation without the no-boarding policy. Subsequently, we carry out simulations to verify these theoretical analyses, also extending the simulations to typical human-driven buses with different natural speeds based on real data. Finally, a simple general adaptive algorithm is implemented to dynamically determine when to implement no-boarding in a simulation for a real university shuttle bus service.

physics.soc-ph↗

arXiv2020

Analysis and simulation of intervention strategies against bus bunching by means of an empirical agent-based model

In this paper, we propose an Empirically-based Monte Carlo Bus-network (EMB) model as a test bed to simulate intervention strategies to overcome the inefficiencies of bus bunching. The EMB model is an agent-based model which utilizes the positional and temporal data of the buses obtained from the Global Positioning System (GPS) to constitute: (1) a set of empirical velocity distributions of the buses, and (2) a set of exponential distributions of inter-arrival time of passengers at the bus stops. Monte Carlo sampling is then performed on these two derived probability distributions to yield the stochastic dynamics of both the buses' motion and passengers' arrival. Our EMB model is generic and can be applied to any real-world bus network system. In particular, we have validated the model against the Nanyang Technological University's Shuttle Bus System by demonstrating its accuracy in capturing the bunching dynamics of the shuttle buses. Furthermore, we have analyzed the efficacy of three intervention strategies: holding, no-boarding, and centralized-pulsing, against bus bunching by incorporating the rule-set of these strategies into the model. Under the scenario where the buses have the same velocity, we found that all three strategies improve both the waiting and travelling time of the commuters. However, when the buses have different velocities, only the centralized-pulsing scheme consistently outperform the control scenario where the buses periodically bunch together.

physics.soc-ph↗

arXiv2019

Peeling property and asymptotic symmetries with a cosmological constant

This paper establishes two things in an asymptotically (anti-)de Sitter spacetime, by direct computations in the physical spacetime (i.e. with no involvement of spacetime compactification): (1) The peeling property of the Weyl spinor is guaranteed. In the case where there are Maxwell fields present, the peeling properties of both Weyl and Maxwell spinors similarly hold, if the leading order term of the spin coefficient $ρ$ when expanded as inverse powers of $r$ (where $r$ is the usual spherical radial coordinate, and $r\rightarrow\infty$ is null infinity, $\mathcal{I}$) has coefficient $-1$. (2) In the absence of gravitational radiation (a conformally flat $\mathcal{I}$), the group of asymptotic symmetries is trivial, with no room for supertranslations.

gr-qc↗

arXiv2019

Stability of anti-bunched buses and local unidirectional Kuramoto oscillators

Inspired by our recent work that relates bus bunching as a phenomenon of synchronisation of phase oscillators, we construct a model of Kuramoto oscillators that follows an analogous interaction mechanism of local unidirectional coupling. In the bus loop system, we can introduce a no-boarding policy as a form of kicking force to achieve a stable staggered (anti-bunched) state. For Kuramoto oscillators, it turns out that such stable anti-bunched states can exist (without any additional kicking force) if the number of oscillators are at least five. This correspondence between the bus loop system and the local unidirectional Kuramoto oscillators leads to the insight on how the bus loop system can remain staggered.

nlin.AO↗

arXiv2019

Intelligent buses in a loop service: Emergence of no-boarding and holding strategies

We study how $N$ intelligent buses serving a loop of $M$ bus stops learn a \emph{no-boarding strategy} and a \emph{holding strategy} by reinforcement learning. The high level no-boarding and holding strategies emerge from the low level actions of \emph{stay} or \emph{leave} when a bus is at a bus stop and everyone who wishes to alight has done so. A reward that encourages the buses to strive towards a staggered phase difference amongst them whilst picking up people allows the reinforcement learning process to converge to an optimal Q-table within a reasonable amount of simulation time. It is remarkable that this emergent behaviour of intelligent buses turns out to minimise the average waiting time of commuters, in various setups where buses have identical natural frequency, or different natural frequencies during busy as well as lull periods. Cooperative actions are also observed, e.g. the buses learn to \emph{unbunch}.

physics.soc-ph↗

arXiv2019

No-boarding buses: Agents allowed to cooperate or defect

We study a bus system with a no-boarding policy, where a "slow" bus may disallow passengers from boarding if it meets some criteria. When the no-boarding policy is activated, people waiting to board at the bus stop are given the choices of \emph{cooperating} or \emph{defecting}. The people's heterogeneous behaviours are modelled by inductive reasoning and bounded rationality, inspired by the El Farol problem and the minority game. In defecting the no-boarding policy, instead of the minority group being the winning group, we investigate several scenarios where defectors win if the number of defectors does not exceed the maximum number of allowed defectors but lose otherwise. Contrary to the classical minority game which has $N$ agents repeatedly playing amongst themselves, many real-world situations like boarding a bus involves only a subset of agents who "play each round", with \emph{different subsets playing at different rounds}. We find for such realistic situations, there is no phase transition with no herding behaviour when the usual control paramater $2^m/N$ is small. The absence of the herding behaviour assures feasible and sustainable implementation of the no-boarding policy with allowance for defections, without leading to bus bunching.

physics.soc-ph↗

arXiv2019

Bus bunching as a synchronisation phenomenon

Bus bunching is a perennial phenomenon that not only diminishes the efficiency of a bus system, but also prevents transit authorities from keeping buses on schedule. We present a physical theory of buses serving a loop of bus stops as a ring of coupled self-oscillators, analogous to the Kuramoto model. Sustained bunching is a repercussion of the process of phase synchronisation whereby the phases of the oscillators are locked to each other. This emerges when demand exceeds a critical threshold. Buses also bunch at low demand, albeit temporarily, due to frequency detuning arising from different human drivers' distinct natural speeds. We calculate the critical transition when \emph{complete phase locking} (full synchronisation) occurs for the bus system, and posit the critical transition to \emph{completely no phase locking} (zero synchronisation). The intermediate regime is the phase where clusters of partially phase locked buses exist. Intriguingly, these theoretical results are in close correspondence to real buses in a university's shuttle bus system.

physics.soc-ph↗

arXiv2018

Bondi mass with a cosmological constant

The mass loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant $Λ\in\R$ was recently worked out, using the Newman-Penrose-Unti approach. In that same article, an expression for the Bondi mass of the isolated system, $M_Λ$, for the $Λ>0$ case was proposed. The stipulated mass $M_Λ$ would ensure that in the absence of any incoming gravitational radiation from elsewhere, the emitted gravitational waves must carry away a positive-definite energy. That suggested quantity however, introduced a $Λ$-correction term to the Bondi mass $M_B$ (where $M_B$ is the usual Bondi mass for asymptotically flat spacetimes) which would involve not just information on the state of the system at that moment, but ostensibly also its past history. In this paper, we derive the identical mass-loss equation using an integral formula on a hypersurface formulated by Frauendiener based on the Nester-Witten identity, and argue that one may adopt a generalisation of the Bondi mass with $Λ\in\R$ \emph{without any correction}, viz. $M_Λ=M_B$ for any $Λ\in\R$. Furthermore with $M_Λ=M_B$, we show that for \emph{purely quadrupole gravitational waves} given off by the isolated system (i.e. when the "Bondi news" $σ^o$ comprises only the $l=2$ components of the "spherical harmonics with spin-weight 2"), the energy carried away is \emph{manifestly positive-definite} for the $Λ>0$ case. For a general $σ^o$ having higher multipole moments, this perspicuous property in the $Λ>0$ case still holds if those $l>2$ contributions are weak --- more precisely, if they satisfy any of the inequalities given in this paper.

gr-qc↗

arXiv2017

Mass loss due to gravitational waves with $Λ>0$

The theoretical basis for the energy carried away by gravitational waves that an isolated gravitating system emits was first formulated by Hermann Bondi during the 1960s. Recent findings from looking at distant supernovae revealed that the rate of expansion of our universe is accelerating, which may be well-explained by sticking in a positive cosmological constant into the Einstein field equations for general relativity. By solving the Newman-Penrose equations (which are equivalent to the Einstein field equations), we generalise this notion of Bondi mass-energy and thereby provide a firm theoretical description of how an isolated gravitating system loses energy as it radiates gravitational waves, in a universe that expands at an accelerated rate. This is in line with the observational front of LIGO's first announcement in February 2016 that gravitational waves from the merger of a binary black hole system have been detected.

gr-qc↗

arXiv2017

Asymptotically simple spacetimes and mass loss due to gravitational waves

The cosmological constant $Λ$ used to be a freedom in Einstein's theory of general relativity, where one had a proclivity to set it to zero purely for convenience. The signs of $Λ$ or $Λ$ being zero would describe universes with different properties. For instance, the conformal structure of spacetime directly depends on $Λ$: null infinity $\mathcal{I}$ is a spacelike, null, or timelike hypersurface, if $Λ>0$, $Λ=0$, or $Λ<0$, respectively. Recent observations of distant supernovae have taught us that our universe expands at an accelerated rate, and this can be accounted for by choosing $Λ>0$ in Einstein's theory of general relativity. A quantity that depends on the conformal structure of spacetime, especially on the nature of $\mathcal{I}$, is the Bondi mass which in turn dictates the mass loss of an isolated gravitating system due to energy carried away by gravitational waves. This problem of extending the Bondi mass to a universe with $Λ>0$ has spawned intense research activity over the past several years. Some aspects include a closer inspection on the conformal properties, working with linearisation, attempts using a Hamiltonian formulation based on "linearised" asymptotic symmetries, as well as obtaining the general asymptotic solutions of de Sitter-like spacetimes. We consolidate on the progress thus far from the various approaches that have been undertaken, as well as discuss the current open problems and possible directions in this area.

gr-qc↗

arXiv2017

Behaviour of asymptotically electro-$Λ$ spacetimes

We present the asymptotic solutions for spacetimes with non-zero cosmological constant $Λ$ coupled to Maxwell fields, using the Newman-Penrose formalism. This extends a recent work that dealt with the vacuum Einstein (Newman-Penrose) equations with $Λ\neq0$. The results are given in two different null tetrads: the Newman-Unti and Szabados-Tod null tetrads, where the peeling property is exhibited in the former but not the latter. Using these asymptotic solutions, we discuss the mass-loss of an isolated electro-gravitating system with cosmological constant. In a universe with $Λ>0$, the physics of electromagnetic (EM) radiation is relatively straightforward compared to those of gravitational radiation: 1) It is clear that outgoing EM radiation results in a decrease to the Bondi mass of the isolated system. 2) It is also perspicuous that if any incoming EM radiation from elsewhere is present, those beyond the isolated system's cosmological horizon would eventually arrive at the spacelike $\mathcal{I}$ and increase the Bondi mass of the isolated system. Hence, the (outgoing and incoming) EM radiation fields do not couple with $Λ$ in the Bondi mass-loss formula in an unusual manner, unlike the gravitational counterpart where outgoing gravitational radiation induces non-conformal flatness of $\mathcal{I}$. These asymptotic solutions to the Einstein-Maxwell-de Sitter equations presented here may be used to extend a raft of existing results based on Newman-Unti's asymptotic solutions to the Einstein-Maxwell equations where $Λ=0$, to now incorporate the cosmological constant $Λ$.

gr-qc↗

arXiv2016

Mass-loss of an isolated gravitating system due to energy carried away by gravitational waves with a cosmological constant

We derive the asymptotic solutions for vacuum spacetimes with non-zero cosmological constant $Λ$, using the Newman-Penrose formalism. Our approach is based exclusively on the physical spacetime, i.e. we do not explicitly deal with conformal rescaling nor the conformal spacetime. By investigating the Schwarzschild-de Sitter spacetime in spherical coordinates, we subsequently stipulate the fall-offs of the null tetrad and spin coefficients for asymptotically de Sitter spacetimes such that the terms which would give rise to the Bondi mass-loss due to energy carried by gravitational radiation (i.e. involving $σ^o$) must be non-zero. After solving the vacuum Newman-Penrose equations asymptotically, we propose a generalisation to the Bondi mass involving $Λ$ and obtain a positive-definite mass-loss formula by integrating the Bianchi identity involving $D'Ψ_2$ over a compact 2-surface on $\mathcal{I}$. Whilst our original intention was to study asymptotically de Sitter spacetimes, the use of spherical coordinates implies that this readily applies for $Λ<0$, and yields exactly the known asymptotically flat spacetimes when $Λ=0$. In other words, our asymptotic vacuum solutions with $Λ\neq0$ reduce smoothly to those where $Λ=0$, in spite of the distinct characters of $\mathcal{I}$ being spacelike, timelike and null for de Sitter, anti-de Sitter and Minkowski, respectively. Unlike for $Λ=0$ where no incoming radiation corresponds to setting $Ψ^o_0=0$ on some initial null hypersurface, for $Λ\neq0$, no incoming radiation requires $Ψ^o_0=0$ everywhere.

gr-qc↗

arXiv2015

Constructing vacuum spacetimes by generating manifolds of revolution around a curve

We develop a general perturbative analysis on vacuum spacetimes which can be constructed by generating manifolds of revolution around a curve, and apply it to the Schwarzschild metric. The following different perturbations are carried out separately: 1) Non-rotating 2-spheres are added along a plane curve slightly deviated from the ``Schwarzschild line''; 2) General non-rotating topological 2-spheres are added along the ``Schwarzschild line'' 3) Slow-rotating 2-spheres are added along the ``Schwarzschild line''. For (1), we obtain the first order vacuum solution and show that no higher order solution exists. This linearised vacuum solution turns out however to be just a gauge transformation of the Schwarzschild metric. For (2), we solve the general linearised vacuum equations under several special cases. In particular, there exist linearised vacuum solutions with signature-changing metrics that contain closed timelike curves (though these do not correspond to adding topological 2-spheres). For (3), we find that the first order vacuum solution is equivalent to the slowly rotating Kerr metric. This is hence a much simpler and geometrically insightful derivation as compared to the gravitomagnetic one, where this rotating-shells construction is a direct manifestation of the frame-dragging phenomenon. We also show that the full Kerr however, cannot be obtained via adding rotating ellipsoids.

gr-qc↗