Exploring Computational Complexity Of Ride-Pooling Problems

Ride-pooling is computationally challenging. The number of feasible rides grows with the number of travelers and the degree (capacity of the vehicle to perform a pooled ride) and quickly explodes to the sizes making the problem not solvable analytically. In practice, heuristics are applied to limit the number of searches, e.g., maximal detour and delay, or (like we use in this study) attractive rides (for which detour and delay are at least compensated with the discount). Nevertheless, the challenge to solve the ride-pooling remains strongly sensitive to the problem settings. Here, we explore it in more detail and provide an experimental underpinning to this open research problem. We trace how the size of the search space and computation time needed to solve the ride-pooling problem grows with the increasing demand and greater discounts offered for pooling. We run over 100 practical experiments in Amsterdam with 10-minute batches of trip requests up to 3600 trips per hour and trace how challenging it is to propose the solution to the pooling problem with our ExMAS algorithm. We observed strong, non-linear trends and identified the limits beyond which the problem exploded and our algorithm failed to compute. Notably, we found that the demand level (number of trip requests) is less critical than the discount. The search space grows exponentially and quickly reaches huge levels. However, beyond some level, the greater size of the ride-pooling problem does not translate into greater efficiency of pooling. Which opens the opportunity for further search space reductions.Comment: 13 pages, 7 figures, Submitted to The Transportation Research Board (TRB), Annual Meeting (102nd

A low dimensional model for bike sharing demand forecasting

Big, transport-related datasets are nowadays publicly available, which makes data-driven mobility analysis possible. Trips with their origins, destinations and travel times are collected in publicly available big databases, which allows for a deeper and richer understanding of mobility patterns. This paper proposes a low dimensional approach to combine these data sources with weather data in order to forecast the daily demand for Bike Sharing Systems (BSS). The core of this approach lies in the proposed clustering technique, which reduces the dimension of the problem and, differently from other machine learning techniques, requires limited assumptions on the model or its parameters. The proposed clustering technique synthesizes mobility data quantitatively (number of trips) and spatially (mean trip origin and destination). This allows identifying recursive mobility patterns that - when combined with weather data - provide accurate predictions of the demand. The method is tested with real-world data from New York City. We synthesize more than four million trips into vectors of movement, which are then combined with weather data to forecast the daily demand at a city-level. Results show that, already with a one-parameters model, the proposed approach provides accurate predictions.Comment: 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other work

Knee joint injuries in football players: types of injuries, etiology, diagnostics and prevention

Introduction Football stands as the most widely embraced organized sport globally, boasting a staggering participation of over 200 million males and 21 million females officially registered under the auspices of the Fèdèration Internationale de Football Association (FIFA). Knee injuries are one of the most common health issues among soccer players at various levels of expertise. They arise from the intense nature of the game, which requires quick turns, running, jumping, kicking, and sudden changes in direction. These stresses can lead to strains and injuries in the structures of the knee joint, including ligaments, meniscus, tendons, and other soft tissues. This study gathers information about the most common types of knee injuries in soccer players, including situations in which these injuries occur, methods of diagnosis, treatment options, and strategies for injury prevention.  Aim The aim of this study is to gather and analyse the studies about knee injuries in soccer players at various levels of expertise. Materials and Methods Review and summary of research studies available in databases on Google Scholar and PubMed. Databases such as PubMed and Google Scholar were searched using the keywords: ‘soccer knee injuries’, ‘soccer injuries’, ‘ACL tear’, ‘MCL injury’, ‘meniscus injury’, ‘PCL and LCL tear’. Summary Soccer, as a high-contact sport, inherently carries a significant risk of various injuries, particularly to the knees. The prevalence of knee injuries, such as ACL, MCL, and meniscus tears, underscores the importance of effective prevention strategies. Proper warm-ups and specialized preventive exercises, such as those in the FIFA 11+ program, are crucial in reducing the incidence of these injuries. Injuries can severely impact a player's career, leading to long-term health consequences. Therefore, timely and accurate diagnosis, along with appropriate treatment, is essential for recovery and career longevity.&nbsp

Ride-pooling service assessment with rational, heterogeneous, non-deterministic travellers

Ride-pooling remains a promising emerging mode with a potential to contribute towards urban sustainability and emission reductions. Recent studies revealed complexity and diversity among travellers' ride-pooling aptitudes. So far, ride-poling analyses assumed homogeneity and/or determinism of ride-pooling travellers. This, as we demonstrate, leads to a false assessment of ride-pooling system performance. We experiment with an actual NYC demand from 2016 and classify travellers into four groups of various ride-pooling behaviours (value of time and penalty for sharing), as reported in the recent SP study. We replicate their random behaviour to obtain meaningful distributions. Unsurprisingly, results vary significantly from the deterministic benchmark: expected mileage savings were lower, while the utility gains for travellers were greater. Observing performance of heterogeneous travellers, we find that those with a low value of time are most beneficial travellers in the pooling system, while those with an average penalty for sharing benefit the most. Notably, despite the highly variable travellers' behaviour, the confidence intervals for the key performance indicators are reasonably narrow and system-wide performance remains predictable. Such findings shed a new light on the expected performance of large scale ride-pooling systems. We argue, that the policy recommendations shall be revised to accommodate behavioural heterogeneity

Simulation of rerouting phenomena in Dynamic Traffic Assignment with the Information Comply Model

We present the Information Comply Model (ICM) which extends the framework for macroscopic within-day DTA proposed by Gentile (2016) to represent the rerouting of drivers wrt a single traffic event. Rerouting is reproduced as a two-stage process: first, drivers become aware about the event and its consequences on traffic; second, drivers may decide to change path. At each arc, unaware drivers have a probability of being informed by multiple ATIS sources (radio, VMS, mobile apps), which depends not only on devise penetration rates, but also on users space and time coordinates wrt the position and interval of the event. At each node, aware drivers, who are somehow reluctant to change, may finally modify their path based on a random rerouting utility, which is composed of expected gains and avoided losses. ICM is thus capable of representing the evolution of rerouting phenomena in time and space when the information about a traffic event and its consequences on congestion spread among drivers and onto the network. This way, ICM extends the concept of dynamic user equilibrium to a case of imperfect information related to availability and awareness rather than to individual perception, as well as to a case of bounded rationality with prudent drivers. Besides the model architecture and specification, this paper provides a workable methodology which can be applied both off-line for transport planning and in real-time for traffic management on large size networks

Observing rerouting phenomena in dynamic traffic networks

This paper shows how rerouting phenomena can be observed from the available data and how to derive valuable input to estimate the rerouting models. By rerouting we mean changing the currently chosen path in road network after either receiving some information or observing consequences of an unexpected traffic event. Recently we have proposed Information Comply Model (ICM) to address the rerouting phenomena in Dynamic Traffic Assignment (DTA) [1]. In this paper we focus on estimation framework for the model and verify the assumptions on the rerouting behavior. The paper identifies two datasets where rerouting can be observed: (1) direct - path trajectories; (2) indirect - traffic flows over the cut-set of the network. Proposed method of formal analysis derives from the data the input to estimate the rerouting behavior, namely flow: information spreads (speed and range), drivers observe (how an atypical delay leads to rerouting), drivers decide (utility of rerouting used in discrete-choice model). Indirect estimation method from traffic flows is illustrated with a field-data from Warsaw bridges observed over several consecutive days including day of the event. Central findings are: a) about 20% of the affected traffic flow reroutes, b) rerouting flows are increasing in time, c) drivers show strategic capabilities, d) and maximize their utility while rerouting. Which were assumed while conceiving the ICM model

Real-time traffic forecasting with recent DTA methods

In this paper we revisit the real-time traffic forecasting problem. We review recently proposed Dynamic Traffic Assignment (DTA) methods and verify how they can improve the practice of traffic forecasting. In particular, we analyze: 1) the Gradient projection DTA model of Gentile (2016), 2) Day-to-day model by Watling and Cantarella (2016), 3) the Marginal Computation (MaC) method by Corthout et al. (2014), 4) dynamic origin-destination (O-D) demand estimation methods (Kostic and Gentile, 2015) and 5) the event rerouting model (Kucharski and Gentile, 2014). We discuss how these methods can be applied to improve short-term forecasting and, most importantly, if they are efficient and mature enough for practical, real-time implementations. We formulate the real-time DTA forecasting problem which searches for the solution using all of the above DTA methods. The main contribution of this paper can be seen as a review and synthesis of recently proposed DTA methods, summarized with conceptual real-time forecasting framework

Investigation of Instantaneous Effects of Real-time Crowding Information (RTCI) Availability upon Urban Public Transport System Performance: Results from a Simulation-based Case Study

The purpose of this study would be to analyse the implications of providing real-time crowding information (RTCI) on instantaneous (current) crowding levels of public transport (PT) services to travelers – and more specifically, to investigate the output RTCI impact for the on-going PT system performance, based on simulation works on a case study (city-level) network model. In recent years, an increasing emphasis has been put on development of various travel demand management tools and especially advanced traveler information systems (ATIS), which aim to overcome problems associated with ever growing passenger congestion in urban transport systems - and thus improve the overall travel experience, reliability and quality of service of the PT system. One of key ATIS developments has witnessed the widespread introduction of real-time information (RTI) systems [3], which provide passengers with information on current travel times of public transport services, waiting times at stops etc. Likewise, a further extension of these systems is highly feasible within the framework of modern-day ITS systems, as passenger flow data collected from various sources – APC and AFC systems, smart-card ticketing systems etc. – can be then utilized to inform travelers about the current passenger flows, i.e. real-time loading levels of public transport vehicles (the so-called RTCI system). However, this also indicates a substantial research gap as (to the best of our knowledge) there is still a fairly limited amount of relevant studies, with just individual sources having investigated the effects of RTCI provision in terms of simulation approach [2], [5] or survey analysis [6], [9]. Moreover, practical implementation of such systems in PT networks is yet (to this date) confined to limited-scale deployment, often on pilot (trial) basis. Consequently, little is known about the potential effectiveness of RTCI systems and their implications both on demand (passengers’) side or supply (operators’ side)

The shareability potential of ride-pooling under alternative spatial demand patterns

In In this study, we set out to explore how various spatial patterns of travel demand drive the effectiveness of ride-pooling services. To do so, we generate a broad range of synthetic, yet plausible demand patterns. We experiment with the number of attraction centres, the dispersion of destinations around these centres, and the trip length distribution. We apply a strategic ride-pooling algorithm across the generated demand patterns to identify shareability potential using a series of metrics related to ridepooling. Our findings indicate that, under a fixed demand level, vehicle-hour reduction due to ride-pooling can range between 18 and 59%. These results depend on the concentration of travel destinations around the centre and the trip length distribution. Ride-pooling becomes more efficient when trips are longer and destinations are more concentrated. A shift from a monocentric to a polycentric demand pattern is found to have a limited impact on the prospects of ride-pooling.Transport and Plannin

Investigation of Instantaneous Effects of Real-time Crowding Information (RTCI) Availability upon Urban Public Transport System Performance: Results from a Simulation-based Case Study

The purpose of this study would be to analyse the implications of providing real-time crowding information (RTCI) on instantaneous (current) crowding levels of public transport (PT) services to travelers – and more specifically, to investigate the output RTCI impact for the on-going PT system performance, based on simulation works on a case study (city-level) network model. In recent years, an increasing emphasis has been put on development of various travel demand management tools and especially advanced traveler information systems (ATIS), which aim to overcome problems associated with ever growing passenger congestion in urban transport systems - and thus improve the overall travel experience, reliability and quality of service of the PT system. One of key ATIS developments has witnessed the widespread introduction of real-time information (RTI) systems [3], which provide passengers with information on current travel times of public transport services, waiting times at stops etc. Likewise, a further extension of these systems is highly feasible within the framework of modern-day ITS systems, as passenger flow data collected from various sources – APC and AFC systems, smart-card ticketing systems etc. – can be then utilized to inform travelers about the current passenger flows, i.e. real-time loading levels of public transport vehicles (the so-called RTCI system). However, this also indicates a substantial research gap as (to the best of our knowledge) there is still a fairly limited amount of relevant studies, with just individual sources having investigated the effects of RTCI provision in terms of simulation approach [2], [5] or survey analysis [6], [9]. Moreover, practical implementation of such systems in PT networks is yet (to this date) confined to limited-scale deployment, often on pilot (trial) basis. Consequently, little is known about the potential effectiveness of RTCI systems and their implications both on demand (passengers’) side or supply (operators’ side).Transport and Plannin