Economic Analysis of In-vehicle Congestion Along a Transit Route: Emitted Versus Received Costs at the Level of the Trip Leg

Economic Analysis of In-vehicle Congestion Along a Transit Route: Emitted Versus Received Costs at the Level of the Trip Leg


Fabien Leurent, Université Paris Est, Laboratoire Ville Mobilité Transport, Marne-la-Vallée, France, Alexis Poulhès, Université Paris Est, Laboratoire Ville Mobilité Transport, Marne-la-Vallée, France


Crowding in transit vehicles induces congestion by comfort state sitting / standing. The paper provides specific definitions of marginal cost and user, together with an efficient computation scheme and application instances to metro lines in Paris.


This paper deals with in-vehicle congestion for transit passengers along a given route, at the level of a single service run or of a stationary period of operations.
In-vehicle congestion involves two traffic phenomena: first, the allocation of seats to passengers, since to be sitting is more comfortable than to be standing; second, the local density of passengers in a given position either sitting or standing. In urban mass transit, in-vehicle seats are allocated to passengers in a decentralized way: each passenger is a candidate to get a seat since, being rational, he prefers to get more comfort. It is assumed here, following Leurent (2006), that (i) from the standing state at a given stage, each candidate has an equal chance to get a seat, (ii) on-board candidates from upstream have prior access to available seats, as compared to people boarding at the next station. The associated model of passenger traffic along a route is called the “Line Model”.

Our objective here is (i) to evaluate congestion costs that stem from local passenger density, (ii) to attribute them by leg i.e. by pair of access and egress stations along the route. As prior access gives sitting priority, there is some asymmetry between legs; this requires identifying the legs. We are particularly interested into the marginal cost imposed by an additional passenger on a given leg onto the rest of passengers. Such a marginal cost is widely used in economic theory to derive an associated congestion toll – which is most often claimed to be applicable to every user. We shall depart from the traditional analysis and focus on the balance of congestion costs either imposed on or incurred by a particular passenger along his trip leg. To impose an overall balance of congestion emissions and receptions, average rather than marginal costs must be considered.

Our economic analysis is based on the Line Model, which delivers the leg matrix of travel cost incurred on average by individual leg trip-makers, on the basis of the seat capacity, the link local costs at sitting or standing respectively and the leg matrix of passenger flows. The Line Model involves two processes: first, Line Loading to assign leg flows to link loads and to model seat allocation, thereby producing sitting probabilities; second, the process of Line Costing to derive leg average costs from the local sitting probabilities and the link costs of sitting or standing.
Between the two processes, we insert the evaluation of congestion costs incurred by link and comfort state depending on the local load and the in-vehicle capacity of that state: thus the in-vehicle standing capacity is involved as well as the seat capacity. Furthermore, congestion cost is evaluated as the product of the link run time and a discomfort cost by unit time. The unitary discomfort cost increases with specific load and decreases with specific capacity.
By link, given the specific loads and capacities, we evaluate the overall local congestion cost and its value averaged by passenger. This is accumulated sequentially over each leg path in order to account for the congestion imposed by a particular leg user to all people. This is the congestion cost emitted by that user, to be compared to the congestion cost which he incurs – as evaluated in Line Costing.
The evaluation of cost emission by leg and of the imbalance of emitted versus incurred congestion cost at the leg level is performed in a novel process which we call Line Congestion. Its results can be used to perform comparison between legs, e.g. with respect to access station or to egress station.

The rest of the paper is in six parts.
Section 2 recalls the main features of the Line Model.
Section 3 provides Congestion functions at the link level and by discomfort state.
Section 4 is devoted to economic analysis and deals with issues of user attribution, equity between legs and congestion pricing.
Section 5 brings about evaluation formulas together with a computation scheme.
Section 6 addresses three instances of metro lines in the Paris area.
Lastly, Section 7 concludes with a discussion of the outreach and limitations of our technical-economic model.


Association for European Transport