I. Pedestrian and bicycle flow theory

The operations level describes the complex interactions between traffic participants of the same type (e.g. interactions between pedestrians), but also with participants of other types, either in a strictly regulated (e.g. a crossing), or a less regulated situation (e.g. shared space or other mixed flow situations).

Empirical facts of walking and cycling.
Data collection and analyses form the foundation for knowledge elicitation and theory and model development. Weidmann [1] presents a concise overview of empirical facts about pedestrian walking behaviour, concerning among other things factors influencing walking speeds, and the use of space by pedestrians. He shows that walking speeds are dependent on personal characteristics, properties of the infrastructure, environmental characteristics, etc. Speeds also depend on density, as is expressed by the so-called fundamental diagram. Many factors influence the shape of this diagram [1, 2]. In-depth empirical knowledge of the dynamic features of pedestrian flows is limited due to the complexity of collecting detailed field data. One of the few examples is described in [2], discussing the existence of stop-and-go waves and turbulent flows. Driven by the need for more detailed (i.e. microscopic) data, the applicant and his co-workers were the first to perform controlled walker experiments, revealing many new insights into the behaviour of individual pedestrians, their interaction with other pedestrians in their direct surroundings, and the collective pat-terns that emerge in different types of flow situations [3]. In [4] a range of new findings is presented that stem from analysing these microscopic data. Since then, a few large-scale experiments have been conducted, providing further evidence that pedestrian flows are characterised by fascinating self-organised structures [5], such as lane and diagonal stripe formation [6], herding, [7], the zipper effect [4], and the faster-is-slower effect [8]. Research providing behavioural explanations for these remark-able phenomena is still inconclusive [6].

Empirical research on bicycle flows is very limited: Navin [9] performed a series of experimental studies to determine the operating performance of a single bicycle, and the traditional traffic flow characteristics of a stream of bicycles and compare them to observed data. He concluded that under certain conditions, bicycle flow can be treated as vehicular flow, and concepts like capacity of bicycle paths, their level of service, etc., could be sensibly defined. Other work predominantly looks at traffic engineering concepts as levels of service, but provides little insight into cycle behaviour.

Gaps & Challenges
Despite some important research results, many research questions remain. For one, the validity of the data collected by controlled experiments remains a subject of debate. Moreover, most field studies have focussed on macroscopic (aggregate) features of pedestrian flow, rather than microscopic characteristics. But even at the macroscopic level, many challenges remain in unravelling the conditions under which phases self-organise or when phase transitions occur. We argue that this can only be achieved by combining state of the art data collection in the field, with controlled experiments, and with knowledge of the situational characteristics under which the data was collected.

Theory of walking and cycling
Goffman [10] describes how the environment of the pedestrian is ob-served through a mostly subconscious process called scanning in order to sidestep small obstructions on the flooring. Goffman also applies this notion to describe encounters with other pedestrians. Pedes-trians generally dislike walking too close to other pedestrians, yielding tension and irritation [11]. Wolff [12] describes the so-called step-and-slide movement, implying that interacting pedestrians often do not take a total detour or attempt to avoid physical contact at all cost. Sobel and Lillith [13] report that pedestrians are reluctant to unilaterally withdraw from an encounter until the last moment. At the same time, brushing sends signal to the ‘offender’ to co-operate. Not all encounters will result in a co-operative decision, as the amount of space granted by a pedestrian depends on cultural, social and demographic characteristics of the involved pedestrians [13]. Willis et al. [14] found similar results for one-to-many interactions. Note that for cycling, the research is very limited, and by and large focuses on crossing and interaction with other modes of transport.

Gaps & Challenges
Walking behaviour and the pedestrian flow operations it results in has been a fairly recent area of scientific research. Research efforts are found in the social science research domains, as well as in the more applied, quantative fields. The gap between these bodies of research is remarkable: while in the seventies and eighties, walking behaviour and the interactions between people has been studied from a behavioural viewpoint, quantitative researchers have taken a more mechanistic, quantitative approach, often inspired by approaches from physics. Closing this gap is crucial to advance this young field of research.

Mathematical modelling approaches and simulation
In the last few decades several types of microscopic and mesoscopic walker models have been developed. The first microscopic models were Cellular Automata [15-19], describing the movement of agents through a simulated environment using a discrete representation of both space and time. For bicycle flow, few applications of CA models are know as well, e.g. [20]. A second stream of microscopic models, the so-called Social Force models, was introduced by [21]. These models simulate movements based on deterministic force-based inter-actions and have a continuous representation of space. The interactions modelled might be physical or used to model interaction with elements or humans within the movement space (human interaction, light effects, attraction zones, etc.). Numerous adaptations have been proposed, among which, vision fields, collision bias and group formation forces. A third stream of models was proposed by the gaming industry [22-24].

Many of the microscopic approaches aimed at representing macroscopic features of the flow, including complex self-organised patterns described earlier, rather than representing or predicting the microscopic behaviour correctly. This severely reduces the predictive validity and thus the applicability. The applicant was the first amongst few researchers attempting to take the knowledge acquired in the social sciences, using it as a basis for a differential game based theory of walking behaviour; see [25]. The approach has lead the applicant and colleagues to develop NOMAD [26]. Their flexible modelling approach allows for different behavioural assumptions, while considering the physical and physiological constraints of pedestrians, or cyclists for that matter. The mathematical framework has since been used for modelling mixed flows [27].

Continuum (or macroscopic) models simulate the global movement effects during which pe-destrians are interpreted as particles of flow and partial differential equations are used to compute the solution [28-30]. Hughes [31] was the first to describe crowd movements by means of a continuous potential field approach, which is closely related to fluid dynamics. Note that [32] has used the princi-ple of least effort as a basis for a generic dynamic programming approach that – in combination with a conservation of pedestrian equation – yields a continuum model that allows for including factors like travel distance or time into the behaviour.

Recent work of the applicant has focussed on bridging the gap between microscopic and mac-roscopic approaches: in [33] a macroscopic model is put forward that bases macroscopic changes in speed and direction on the social-forces model. The resulting model to the best of our knowledge is the only continuum model that qualitatively predicts self-organisation phenomena and failing thereof in case of high traffic loads. Still, developing predictively valid continuum models remains a major challenge, while their application potential for many engineering applications (estimation, short-term prediction, etc.) is huge.

Gaps & Challenges
Next to the lack of empirical insights discussed earlier, theories explaining the phenomena we see at the microscopic and macroscopic levels are required. Predictively valid micro-scopic and macroscopic pedestrian flow models that are based on such a falsified behavioural theory are lacking. In particular, bicycle flow theory is still in its infancy, while only first steps in establishing theory and empirically underpinned models have been taken.

II. Activity scheduling, and route choice for slow modes (activity-travel behaviour)
Irrespective of the mode of travel, moving around in a network seldom is an objective in itself [34]: people walk, cycle or drive to a destination in order to perform some activity that satisfies some need. Looking only at travel related choices and not at the underling activities would not enable us to explain observed travel behaviour. Walking and cycling can play different roles in a trip: it may be the main mode of access or egress of a multi-modal trip, it may be the main transport mode for commuter trips, or for other types of trips (e.g. shopping, sightseeing); it may be the key transferring mode. Depending on the purpose of the ‘slow mode leg’, the needs that are to be satisfied as well as the boundary condi-tions in terms of origin and destination, time restrictions, etc., will vary strongly from trip to trip, and from person to person. These differences may be one of the reasons that the literature on activity and travel choice behaviour for the slow modes is rather unstructured. This is also due to different per-spectives from which behaviour has been addressed: studying walking or cycling from a health or safety perspective, urban form and city attractiveness for pedestrians and cyclist, and infrastructure planning, design and transport policy.

Determinants of choice behaviour. Factors that determine the way people make decision can be trip-related, personal, system or environment related [35, 36]. Trip-related factors such as purpose (com-muting, transferring, sightseeing, shopping, etc.) by and large determine time and location restrictions; need fulfilment and the related importance of activities. Examples are given by [34], showing the rela-tive importance of different route attributes (distance and travel time, directness, scenery, crowded-ness, etc.) for different trip purposes [34]. Personal factors, including those that are static (age, gender, income, education, personal security concerns) and those that are dynamic (knowledge, experience, habit formation, emotional state, fatigue, etc.) are also important determinants [37, 38]. The trip char-acteristics and personal characteristics – by and large – determine the impact of the attributes of the activities, activity locations, and of the routes. External conditions in turn affect the attributes of the activities, locations, and routes as well. Few scientific studies focus on the role of information provi-sion on the travel (and activity) behaviour of pedestrians [39]. Regarding cyclist route choice, a sub-stantial body of empirical research is available, often using relatively simple discrete choice models to identify the relative importance of the different route attributes. As an example, commuter cyclists choose their route by trading off safety with shortness and directness [40]; other studies show that pol-lution, exposure, grade, interaction with fast modes, intersection delay, and weather [41, 42] are also important factors; for a comprehensive overview, we refer to [43]. In looking at these different stud-ies, it is striking that the differences in the presented outcomes are quite large, possibly implying that there are large differences in preferences and perception dependent on context.

Gaps & Challenges: under the supervision of the applicant, Ton [37] used revealed preference data of passengers in a railway station to investigate their choice behaviour. Using a model-based approach, she shows how in a transferring context, travel-time, distance, orientation and stop location of the train have a significant influence on route choice. For activity location choice, the travel time, the total dis-tance, the detour level, and orientation are of significant influence. Ton’s [37] results provide first in-dications showing that traveller optimize their entire route when choosing the activity locations. The study shows the potential of using revealed data collected using BT/WiFi sensor networks in studying activity-travel choices. Many challenges however remain, also regarding the impact of information (collective, individual) on choices made [39].

Theory and modelling approaches. It is widely acknowledged that pedestrians and cyclists choose their route differently to drivers of private vehicles: for instance, the route choice decision of com-muter drivers is often modelled with one objective, to reduce their generalised travel cost. Commuter cyclists, on the other hand, usually have multiple objectives when choosing their route [44]. The dif-ferences go beyond the respective choice factors determining choices and are in fact much more fun-damental.
The theoretical framework of the applicant [45] describes the interactions between activity scheduling, location choice, and routing. He assumes that pedestrians optimise the expected utility of performing activities and travelling, within time and budgetary constraints. Ettema et al. [46] state that people are not able to find the best sequence from many possibilities because the effort for scheduling is too high. In their model the expected utility is weighted against the extra effort it takes to find a new sequence. These studies show that multiple theories are present about the formation of activity se-quences.
Random utility modelling appears to be the common way to model slow mode choice behav-iour. More advanced approaches, such as cumulative prospect theory or regret theory [47], may pro-vide more appropriate choice frameworks that more realistically represent choice behaviour in situa-tions where risk and risk perception is so very important. Furthermore, generic frameworks for the joint consideration of activity scheduling, location and route choice, which can be empirically under-pinned using appropriate data sources, are needed; approaches based on hypernetworks appear appro-priate to serve as a starting point for such a comprehensive modelling framework [48]. Next to more suitable modelling techniques, the way people build up knowledge about the network and determine choice sets, require explicit consideration.

Gaps & Challenges: looking at the different studies available, we conclude that a comprehensive framework of activity-travel behaviour of pedestrians and cyclists is lacking. This entails the choice mechanisms, but also to the impact of the different factors (trip-related, personal, external, etc.) and the interactions between these determinants. The empirical underpinning of such a theory is a key challenge, requiring the collection of rich datasets, and establishing appropriate model identification techniques. The relation with cognitive mapping (discussed in the next segment) is of great interest, since we believe that taking into account the knowledge level of a traveller is pivotal in achieving valid predictions of activity-travel choice behaviour. Finally, the impact of information provision and ICT services (either in individual or collective form) in activity-travel behaviour has not been embedded comprehensively in theory and modelling.

III. Knowledge gathering and representation
Travellers having to find their way through a city landscape need to have at least a basic idea of the network they are traversing: they either need to know at least one route from an origin to their intended destination, or they need to have a strategy to determine such a route, e.g. by means of exploration, information gathering, etc. Acquiring knowledge of the network, the routes, etc., either by direct in-formation acquisition (maps), interacting with the environment, exploring the environment, or directed travel, is a fundamental element in understanding travel behaviour. Nevertheless, the amount of re-search on spatial learning of urban environments and transport networks (cognitive mapping) and rep-resenting this knowledge (mental map) in transportation research is very limited [48, 49]. To the best of our knowledge, no dedicated studies have been performed for pedestrian or bike travel. Nonethe-less, important results for generic travel have been put forward that may form an important starting point for our proposed investigations.
In [49], a study is presented into how individuals’ spatial cognition and mental representation of urban networks develops over time and what impact landmarks have on spatial learning. The model takes perception [50] as an interface between the travellers and their spatial environment, and using cognition [51] as a way to describe how spatial information is represented in the brain. This spatial information is acquired using our senses, ICT, or via our social interactions. Literature typically distin-guishes between landmark knowledge, route knowledge, and survey knowledge [52]. Landmarks indi-cate location of other objects, and may be the goals of navigation, or mark the locations of changes of direction, or are used to maintain course [53]. Route knowledge pertains to sequences of landmarks and associated decisions and actions. Being able to construct routes pointing directly to unseen loca-tions, and to estimate distances are signs of survey knowledge. The dynamics of cognition are deter-mined by learning and memory decay. In [54] it is proposed that landmark knowledge is the first to be acquired, being the basis of other types of spatial knowledge, followed by route knowledge and sur-vey knowledge. According to the anchor point theory of [55, 56], the hierarchical ordering of loca-tions, paths and areas in a spatial environment is based on the relative significance of these locations to the individual. As interactions occur along paths between anchor points, there is a spread effect: neighbourhoods surrounding anchor points become known first, and continued interactions along paths increases spatial knowledge [34]. Trying to find new alternatives is a form of exploration behav-iour that results in expanding the traveller’s choice-sets. Landmarks appear crucial in spatial decision-making and can trigger cues indicating turning decisions, or reassuring cues confirming an individual in decisions already made. Singularity and saliency are key features of a landmark [57].
As an important first step to acquire a predictively valid theory of spatial learning, the model proposed in [58] presents calibration results of a mathematical cognitive learning model. In [59], the applicant and co-workers identify a model showing how travellers build up (survey) knowledge (i.e. route attributes) via experience and information. Note that in unfamiliar environments, individuals’ learning strategies are based on search and exploration according to heuristics [60].

Gaps & Challenges: thorough empirical underpinning and further development and specification of available theory are needed. Not only because of the importance of a strong empirical foundation, but also because of the largely unchartered role of spatial knowledge in activity-travel modelling. Fur-thermore, spatial learning modelling of the slow traveller has received little attention, while it likely to be fundamentally different from the fast modes. For instance, the meaning of salience will be differ-ent for a car driver and a pedestrian, for instance due to speed, perspective, etc. Information and communication technologies can serve as cognitive shortcuts and ICT, but will also affect the learning process (negatively) [61, 62] may have an impact on the proposed model system [49, 58]. The impact of ICT on the processes of knowledge acquisition and learning has not been dealt with in detail and has not been formalised in models. Given the popularity of apps like GoogleMaps, MapMyWalk, Cy-cleTrack, etc., this is an important gap our knowledge that needs attention.