The Morning Commuting Problem with Variable Distribution of Traffic Demand in a Many-to-Many Road Corridor

The Morning Commuting Problem with Variable Distribution of Traffic Demand in a Many-to-Many Road Corridor


Ronghui Liu, Institute For Transport Studies, University Of Leeds, Ying Jin, The Martin Centre For Architectural And Urban Studies, University Of Cambridge


We make a significant extension to the bottleneck models, first for a ‘many-origin-to-one-destination’ corridor with exogenous road demand, then for ‘many-origin-to-many-destination’, and finally endogenous demand with a range of emerging commuter adaptations. The analysis is under a dynamic microsimulation framework.


Recent advances in engine technology have raised the prospect of turning cars into a significantly more sustainable as well as cost efficient means of travel, especially in suburban locations with defused residential and workplace locations. Meanwhile, road traffic has been subject to countervailing trends: on the one hand, densification and public realm measures (such as shared road space) have led to reallocation of road space away from car use; on the other hand, some commuters are enjoying better flexitime at work, improved opportunities to monitor traffic conditions prior to travel on the day, better facilities for cycling and walking, and possibilities to telecommute for some days of the week. These have created a new setting for modelling peak-time road traffic.

It is still reasonable to assume that for each major urban workplace destination, commuters will ideally want to arrive at the same destination within a narrow time band in the morning. Thus they all tend to arrive at the bottleneck part of the system at about the same time thereby causing congestion. Late arrival will incur a penalty, as will early arrivals if the extra time cannot be used productively. Consequently, each individual must decide how to minimise the sum of costs that includes travel, penalty for arriving early and for arriving late.

This morning commuter problem has traditionally been formulated as a bottleneck model which presents a framework for analysing the commuters’ departure-time choice when faced with congestion cost, and costs associated with early or late arrival at work. The well known bottleneck model was originally developed by Vickrey (1969) for commuting from a single origin to a single destination. The model attaches a cost to travel time (including free-flow and queuing time), a cost for arriving at work early and a cost for arriving late. It then models the commuters’ departure-time choice following a user equilibrium principle such that all commuters from the same origin experience the same total travel cost no matter when they leave home. The basic single bottleneck model has since been extended to consider elastic demand, heterogeneous commuters, and more recently to stochastic bottleneck capacity (see a comprehensive review in de Palma and Fosgerau, 2011). Most of the literature, however, is concerned with a single bottleneck. Arnott et al (1993) made the first attempt to make the bottleneck model spatial by examining two bottlenecks in series with two origins and a single destination. Lago and Daganzo (2007) extended the model of Arnott et al (1993) with an explicit model of spillovers.

This paper is concerned with a corridor connecting multiple residential origins to multiple workplace destinations. We first investigate a ‘many-origin-to-one-destination’ corridor, with an exogenous distribution of traffic demand by origin. We then extend it to a ‘many-origin-to-many-destination’ case. Finally, we extend the model by endogenising traffic demand distribution to represent mode switching and trip rescheduling (re-timing departure time or revert to telecommuting) that is triggered by traffic conditions on the day. The traffic analysis is carried out in a dynamic microsimulation framework with explicit representation of flow congestion at bottlenecks, heterogeneous commuters and stochastic capacity. The network characteristics are coded to reflect those of a real road corridor that covers urban, suburban and exurban conditions. The model will provide new insights into commuters’ travel adaptations and residential location choice, particularly the effects of variable travel demand distributions on commuting costs and network performance.

Arnott, R., A. de Palma, R. Lindsey. 1993. Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering. Transportation Sci. 27(2) 148–160.
De Palma, A. And Fosgerau, M. 2011. Dynamic traffic modeling. In de Palma, A., Lindsey, R., Quinet, E. & Vickeman, R. (eds). Handbook in Transport Economics, Cheltenham, UK: Edward Elgar, pp. 29–37.
Lago, A., Daganzo, C. F. 2007. Spillovers, merging traffic and the morning commute. Transportation Res. Part B 41(6) 670-683.
Vickrey, W. S. 1969. Congestion theory and transport investment. Amer. Economic Rev. 59(2) 251–261.


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