Transport capacity constraints on the mass transit system: a systemic analysis

Figure 1 summarises the four subsystems and shows their main interactions. In the TCQSM, capacity factors are divided into Vehicle Characteristics, Right of Way Characteristics, Operating Characteristics, Passenger Traffic Characteristics, Street Traffic Characteristics and Methods of Headway Control (gap between two consecutive vehicles on a route) [1.3–18]. Our framework of analysis is more structured owing to the identification of sub-systems and their components; furthermore, it is abstract enough to cover public transit submodes in a generic way, whereas the manual divides public transport modes into bus, rail or ferry services. Lastly, it includes the economic dimension that pertains to passengers.

Passengers are the elementary moving entities of which traffic flows are made up: at any given moment, passenger trajectories add up locally and form trip flows at every point on the network. Passengers temporarily immobile in a waiting area form a local stock. Passengers temporarily contained within the vehicle also form a stock, either stationary or moving, depending on the status of the vehicle.

Individual passengers have their own specific characteristics: when standing, they occupy a certain portion of space and require a certain distance from other passengers. When moving on foot, they occupy a certain width and possess dynamic characteristics for horizontal or vertical movement, in particular pedestrian “cruise” speed. These characteristics give a passenger flow its macroscopic properties: compressibility, capacity for acceleration and deceleration that governs flow speed, spread of individual speeds and flow viscosity. The properties of pedestrian flows are currently an active field of research (e.g. Hoogendorn and Daamen [7]). For our purposes, it is enough that the static and dynamic characteristics of pedestrians determine the individual load (or occupation, consumption) that each of them requires on a capacity resource, whether a storage space or a transport element. Passenger trajectories generate the spatial and temporal structure of flows during an analysis period, in particular with respect to each network element and each origin-destination pair. This structure determines the load on the transport means, infrastructure section or vehicle or pedestrian element. In turn, this load determines the local state of congestion and influences quality of service. Finally, quality of service is experienced by the individual passenger, primarily in time spent, discomfort and reliability. These aspects constitute an important criterion in determining the passengers’ travel choices, in particular the choice of route and that of departure time.

Throughout a trip, a passenger uses certain elements of the network, forming a sequential composition. In his choice of path, he considers a set of alternative routes he might use, thus relating them in a kind of parallel composition. These possibilities for choice determine the local structure of trip flows within the network, and therefore have a feedback effect on local traffic loads and on quality of service.

So the economic choices made by passengers generate local traffic demand and therefore the demand for capacity on a local resource.

Vehicles are moving entities that can be simple or composite, through the assembly of “carriages” into a train. Their movement is the fundamental principle of public transport, replacing the movement of the individual traveller, who remains immobile (or almost immobile) within the vehicle.

Finally, the vehicle has one or more doors whose width and accessibility dictate the number of travellers able to move through them simultaneously and the time taken to do so: the positioning of the doors relative to the station platform determines the vehicle’s exchange capacity per unit of contact time.

The ultimate purpose of a station is to give passengers access to vehicles, for both boarding and alighting, for transfer to or from another service route or another mode of transport [2.5–41]. It must therefore allow storage space and internal circulation space for both passengers and transit vehicles.

Passenger flows require the provision of levels of equipment that match the intensity of the flows, from a simple post, a shelter or a single building, to a complex of buildings for a large station. The buildings contain areas and seats where people wait to board, possibly fare and information kiosks and passenger service areas, whether utilitarian (toilets, left luggage, restaurants) or more commercial (newsagents, cultural products, clothes, groceries etc.). Globally, stations contain areas allocated to different activities, some accessible to passengers, others reserved for personnel. Some activities are necessary for trip making, such as waiting on the platform or moving around the station. Others are useful or profitable in offering passengers opportunities and helping them make better use of their waiting time. As in a vehicle cabin, the layout of the space and control of the surroundings influence the traveller’s comfort. In addition, signage and static or dynamic information contribute to quality of service.

In a station, the concept of circulation capacity varies according to the type of space: waiting areas or corridors for passengers, platforms, lanes or tracks for vehicles. A waiting area can contain passengers in the same way as a vehicle, but in general with more possibilities for interchange with the outside, and conversely exposure to influences such as other movements of passengers or flows of pedestrians. The pedestrian elements under greatest stress are those with different directions and speeds of flow, and also spaces of vertical travel such as stairways and elevators, with particular stress on upwards movement.

Items of equipment involve constraints on capacity, in particular gates, barriers and fare desks. Just as a vehicle’s exchange capacity depends on its doors, some capacity constraints combine several parallel elements with similar functions, in particular corridors or stairways leading to platforms.

The elements set aside for vehicles are also subject to capacity constraints. Moreover, in certain stations, passengers access the mass transit system in an individual vehicle, with the concomitant constraints on parking capacity.

To sum up, a station is a collection of spaces and equipment whose individual characteristics place capacity constraints on passengers, mass transit vehicles and even individual vehicles. The configuration of these spaces determines capacities at a higher level, by providing possibilities for the transfer of moving bodies between neighbouring elements.

Finally, the arrival in the station of a large capacity vehicle can generate a flow of relatively high intensity for a short period: this kind of peak flow can saturate corridors and walkways, and result in transfers or spreads that cause temporary deterioration in certain capacities.

Let us analyze the Line subsystem into four components, respectively the vehicle travel infrastructure, route management, route organisation and run scheduling on a route.

The diagram in Fig. 1 not only shows the four subsystems in the form of blocks, but also their principal interactions, identified by arrows, which indicate:

These three complex interactions comprise the entirety of the interaction between the passenger and the service.

For a section of infrastructure in a given direction, occupancy demand consists of the vehicles to be carried, each corresponding to an elementary time length during which a given point-wise spot is occupied. Denoting by t _X the average elementary occupancy time per vehicle on a certain route (including a safety margin), and by X the number of such vehicles over a period H, the route demand is X.t _X . If a number say Y of other vehicles travels on the section, with an average occupancy time of t _Y per vehicle, then occupancy demand is . Other vehicles belong to other routes or other modes.

The capacity resource is an area of travel of a certain width allowing movement on f lanes of traffic in the direction concerned: the baseline capacity is K₀ = f.H for the period H. If flow in that section and direction conflicts with flows in other directions, let us say Z vehicles each requiring a time of t _Z on the average, then the initial flow capacity is reduced to . If the conflict between traffic flows occurs at a regulated junction, then where η is the proportion of the time in which the initial direction has priority on the junction.

The ratio between occupancy demand Ω and allocated capacity K determines the load rate, . Both Ω and K depend on local flows using the infrastructure and the local geometrical conditions: these are the specific conditions of this capacity phenomenon. The general consequence is that the average time taken to cover the section by a vehicle on the route increases with ρ, as do the associated risks of disruption, the energy consumption and the emissions. Whilst the ratio ρ remains well below 1, traffic remains fluid. But if ρ gets close to or temporarily exceeds 1, a queue forms and its size at the time a vehicle arrives determines how long that vehicle will wait (bottleneck model).

For a service route z, vehicle usage demand is the desired number of runs, N, multiplied by the service time, say an average of T _z for a round-trip: therefore Ω = N.T _z .

The vehicle time resource during the period H is K = n.H, where n is the number of vehicles. The capacity constraints on the fleet of vehicles allocated to the route is therefore , i.e. in terms of frequency, .

The composition of the round-trip determines the cycle time T _z , which is the segment running time plus the time spent in stations, together with operating margins for a reserve or recovery time for the vehicle driver.

With a fixed fleet, the constraint limits the frequency of service, which influences the number of passengers boarding and alighting at each station, and therefore dwelling time in the station.

This category includes three capacity constraints, respectively the number of seats, the total containment capacity of the vehicle and the number of passengers entering/leaving per unit of transfer time.

If the vehicles are of different sizes or have different loading conditions upstream, or if the headways between two consecutive vehicles are irregular, then the relation between demand and capacity varies over the period.

This group includes the capacities of the elements dedicated to pedestrian movement and to passenger storage.

This group comprises four types of constraint.

A share of the passengers may access public transport by individual mechanised modes, which employ a specific vehicle: private or shared car, taxi or two-wheels. In certain stations, access for such vehicles is provided by dedicated amenities, including park-and-ride areas where private vehicles can be stored.

In a station, therefore, the interface with individual vehicles involves elements of movement and elements of storage, each with its own specific operation, analogous with the handling of passengers within a station (apart from the fact that an unoccupied vehicle remains stationary).

Figure 2 summarises the capacity phenomena identified above and situates them within the framework shown in Fig. 1. Each phenomenon is situated in relation to the components of the system. For example, the second group, which relates to service frequency, depends on service time and fleet size. Another example for the fifth group: service frequency on a route influences the size of the stock of waiting passengers, and therefore the interaction between the stock and the capacity of the waiting area.

An area of space, such as a waiting area, constitutes a capacity resource for the elementary forms of occupancy required by entities such as passengers.

A period of time is a capacity resource for elementary periods of occupancy required by entities such as passengers or vehicles. In fact, duration relates to a physical resource: a passing point on an infrastructure or a mass transit vehicle.

To analyse a spatial resource such as a waiting area or section of infrastructure over a period of time, a valuable concept is that of space-time capacity, which is calculated by multiplying the spatial dimension of the resource by the duration of the period. This enables one to look at spatial resources that are larger than a single point in space. An elementary occupancy in space-time is calculated by multiplying the elementary spatial footprint by the length of occupancy of each point: i.e. L.t _X for a moving body travelling through a segment of length L and occupying each point in it for t _X ; or s _X .t _X for an entity of size s _X occupying a space in a waiting area for a period of t _X . Space-time analyses are useful in urban planning [4] and in transport [1, 2, 5, 6, 9].

All these occupancies are simple. Elementary occupancies are cumulative, and the resource is similarly calculated by adding together components in both time and space.

Figure 2 depicts the factors and consequences of capacity phenomena for the seven groups that were identified. The diagram enables one to track sequences between the phenomena and even cycles of dependency. For example, a vehicle’s dwelling time in a station depends on the flow of passengers boarding and alighting in that station; then, the dwelling time influences the vehicle’s cycle time, which influences route frequency; in turn, route frequency influences incoming and outgoing flows per vehicle.

The TCQS Manual [15] presents several combinations of factors respectively composing the capacity of a bus infrastructure [4.1–16], or the passenger capacity of a bus line [4.1–17], or railway capacities, in particular in the guise of flowcharts. This manual is very helpful in providing a more concrete understanding of the details of capacity constraints, with specific reference to the mode of transport concerned.

In addition, the Manual reveals complex sequences with subtle effects on capacity. Here are some instances:

A “congestion gear” is an interaction between several capacity phenomena such that they mutually affect each other, resulting in a reduction in capacity. In other words, a gear has devastating and potentially disastrous consequences. In running a system, they need to be avoided and prevented, or at the very least detected and their consequences managed.

A number of congestion gears can be identified, making up the following list—which is likely not complete:

In a public transport system, both users and operators are likely to react to traffic conditions. These reactions constitute complex feedback effects.

On the user side, quality of service determines the path choice. Every user perceives the quality of service under a given travel option, in particular with regard to time and discomfort, and chooses their option by trading off quality of service and price factors according to their own preferences, i.e. for personal rather than communal benefit. High levels of local congestion along a route will prompt users to transfer to another route, which distributes traffic between routes since route choices generate the trip flows. In principle, this should reduce congestion on the initial route. However, route diversions can actually trigger paradoxical effects: Braess [3] has shown that for certain network configurations and loads, detours by certain users can disadvantage others and adversely affect the global state of the system. For our purposes, it is enough that microeconomic behaviour by the user triggers interactions with local quality of service through the formation of traffic flows.

On the operator side, there are three groups of instruments: