Critical Review of Time-Dependent Shortest Path Algorithms: A Multimodal Trip Planner Perspective

Abstract

A multimodal trip planner that produces optimal journeys involving both public transport and private vehicle legs has to solve a number of shortest path problems, both on the road network and the public transport network. The algorithms that are used to solve these shortest path problems have been researched since the late 1950s. However, in order to provide accurate journey plans that can be trusted by the user, the variability of travel times caused by traffic congestion must be taken into consideration. This requires the use of more sophisticated time-dependent shortest path algorithms, which have only been researched in depth over the last two decades, from the mid-1990s. This paper will review and compare nine algorithms that have been proposed in the literature, discussing the advantages and disadvantages of each algorithm on the basis of five important criteria that must be considered when choosing one or more of them to implement in a multimodal trip planner.     

Safe design of personal rapid transit systems

The safety of personal rapid transit systems involves careful attention to all features of the design such as the use of a hierarchy of fault-tolerant redundant control systems, bi-stable fail-safe switching, back-up power supplies, vehicle and passenger protection, and attention to the interaction of people with the system. Safety, together with reliability and adequate capacity, must be achieved while making the system economically attractive, hence techniques to achieve these goals at minimum life-cycle cost are primary in PRT design. Building on theory of safe, reliable, environmentally acceptable, and cost-effective design of PRT systems developed during the 1970′s, in 1981 the author and his colleagues initiated design of a new PRT system, now called Taxi 2000. The paper describes the relevant features of Taxi 2000 and principles of safe design incorporated into it.     

What transportation modeling needs from a GIS: a conceptual framework

Both the geographic information system (GIS) and transportation modeling environments have seen continually developing analytic concepts and techniques. However, these developments have seldom resulted in the integration of GISs and transportation models. This paper explores the potential inherent in merging of these environments through a systematic investigation of the fundamental basis of integration. To do this, the traditional four step transportation modeling process is extended to include input and output steps. We then define functional components for GIS data handling — data management, manipulation, and analysis. The steps of modeling are matched against the list of GIS data handling functions within a matrix‐based framework. GIS functions that enhance a land‐use based urban transportation modeling process are then categorized. Conclusions are drawn and directions for future developments are discussed.     

Longitudinal control of a vehicle

Generally applicable formulae for the gain constants in a proportional plus integral controller required for stable control of the speed of any vehicle in terms of natural frequency, damping ratio, vehicle mass, and thruster time constant are derived. An example, based on a simulation of the controller and vehicle, is given. The theory shows that only speed and position feedback are needed. Acceleration feedback is unnecessary.     

The shape of MaaS: The potential for MaaS Lite

Mobility as a Service (MaaS) is about improving mobility for people. Since Gothenburg piloted the first multi-modal Mobility as a Service (MaaS) scheme from 2012, there have been many further attempts at introducing connected and bundled services globally, invariably provided as a mobile app and a single, simple ticketing interface. As in any emerging paradigm, the varying flavour, or ‘shapes’ of MaaS that are piloted reflect the search for a sustainable business model and connectivity between transport operators at varying levels that includes risk reallocation and data sharing. The varying levels of success of MaaS and Mobility on Demand (MOD) lead the authors to propose MaaS Lite, which reflects an incremental approach to MaaS based on a simpler organisational arrangement that does not depend upon the introduction of a Mobility Operator as a new player. MaaS Lite also recognises that most trips are not complex at all, often based on one or two connected mechanised modes that meets highly local needs, including FMLM service connectivity.Overall, MaaS is not a ‘one size fits all’ solution for all regions but the benefits of the highly targeted MaaS Lite could realise early public benefits as a first step in the development of a multi-phased ‘services road map’ that evolves towards the implementation of multi-modal, region-wide operationally integrated MaaS. Case studies in Hong Kong and Brisbane demonstrate the merits of MaaS Lite in these two contrasting environments having different regulatory regimes, population densities and levels of private car ownership.     

A Dynamical Analysis of a Towed Two-Wheel Trailer1

The towed trailer method for skid resistance measurements is a practical one for characterizing the friction characteristics of highway pavements, and has been standardized by the ASTM 11). Numerous papers have been published about the improvement of equipment and field-testing techniques but little has been done toward a theoretical explanation.

This paper presents a mathematical model of the trailer which includes roll, pitch, and vertical motion. The skid resistance calculated by using this model gives an excellent check on the standard ASTM skid number formula. The response time and damping effect after locking one test wheel can be clearly seen in this model. Possible effects of the dimensions of trailer, stiffness of suspension system, tire pressure, etc. to skid resistance can also be examined.     

Synchronous or clear-path control in personal rapid transit systems

This note derives an equation for the ratio of the maximum possible station flow to average line flow in a personal rapid transit or dual-mode system using fully synchronous control. It is shown that such a system is impractical except in very small networks.     

Optimization of transit-system characteristics

The transit industry is facing declining ridership and increasing costs with with no apparent end in sight. This paper takes the view that totally new solutions are needed. The approach is to examine the equation for total cost of a transit system per passenger-mile to determine how to configure a new system to minimize this quantity. Term-by-term analysis leads to derivation of a consistent set of optimum characteristics. Guideway costs are minimized by distributing the load in very small capsules. The fleet cost is minimized by increasing the average speed without increasing the cruising speed by use of off-line stations, which in turn minimize energy use by permitting nonstop trips. Maintenance costs are minimized by designing a very light-weight, automated vehicle with very few moving parts. While this general configuration has been known for several decades, it has not been generally recognized that it can be derived by minimization of system costs, and that cost minimization is obtained simultaneously with service maximization. While a great deal of controversy surrounded this concept a decade ago, advances in technology make it fully practical now.     

Turbulence in coastal fronts near the mouths of Block Island and Long Island Sounds

Measurements of turbulence were performed in four frontal locations near the mouths of Block Island Sound (BIS) and Long Island Sound (LIS). These measurements extend from the offshore front associated with BIS and Mid-Atlantic Bight Shelf water, to the onshore fronts near the Montauk Point (MK) headland, and the Connecticut River plume front. The latter feature is closely associated with the major fresh water input to LIS. Turbulent kinetic energy (TKE) dissipation rate, ε, was obtained using shear probes mounted on an autonomous underwater vehicle. Offshore, the BIS estuarine outflow front showed, during spring season and ebb tide, maximum TKE dissipation rate, ε, estimates of order 10^− 5 W/kg, with background values of order 10^− 6 to 10^− 9 W/kg. Edwards et al. [Edwards, C.A., Fake, T.A., and Bogden, P.S., 2004a. Spring–summer frontogenesis at the mouth of Block Island Sound: 1. A numerical investigation into tidal and buoyancy-forced motion. Journal of Geophysical Research 109 (C12021), doi:10.1029/2003JC002132.] model this front as the boundary of a tidally driven, baroclinically adjusted BIS flow around the MK headland eddy. At the entrance to BIS, near MK, two additional fronts are observed, one of which was over sand waves. For the headland site front east of MK, without sand waves, during ebb tide, ε estimates of 10^− 5 to 10^− 6 W/kg were observed. The model shows that this front is at the northern end of an anti-cyclonic headland eddy, and within a region of strong tidal mixing. For the headland site front further northeast over sand waves, maximum ε estimates were of order 10^− 4 W/kg within a background of order 10^− 7–10^− 6 W/kg. From the model, this front is at the northeastern edge of the anti-cyclonic headland eddy and within the tidal mixing zone. For the Connecticut River plume front, a surface trapped plume, during ebb tide, maximum ε estimates of 10^− 5 W/kg were obtained, within a background of 10^− 6 to 10^− 8 W/kg. Of all four fronts, the river plume front has the largest finescale mean-square shear, S² ~ 0.15 s^− 2. All of the frontal locations had local values of the buoyancy Reynolds number indicating strong isotropic turbulence at the dissipation scales. Local values of the Froude number indicated shear instability in all of the fronts.