Parking equilibrium along the street

Natalia Kotelnikova,Fabien Leurent

doi:10.1007/s12544-016-0211-y

Abstract

The paper studies the progressive occupancy of parking capacity along the street by candidate users, under the user equilibrium paradigm. The situation depicted typically applies to a parking peak period. In our model, the parking supply is made up of capacitated lots situated along a spatial axis, while the demand is disaggregated continuously in both destination place and preferred time of arrival. Each user selects a parking lot and time from among options on the basis of their trade-offs between walking, driving, parking price and schedule delay. Efficient algorithms are developed and an application instance is dealt with in detail. The dynamical equilibrium pattern exhibits parking lots “efficiency regions” in the plane of destination places and preferred arrival times. These efficiency regions are dynamic market areas with strong yet simple structural characteristics, making it easy to assign each parking user to his preferred option and to derive the lot saturation times. The latter are identified as the key state variables for the parking system, since they induce the lot efficiency regions. The equilibrium state is characterized as the solution to a fixed-point problem with respect to the saturation times. Our model improves upon previous parking models in economic theory, by adopting a higher resolution in space and time on both supply and demand side. The higher resolution is enabled by focusing on the street level, thus restricting the outreach of the model. Further research may be directed to extend the model to a network of streets, on the side of traffic assignment, and to study parking management policies, on the side of parking economics.

Highlights

Context Making a trip by means of an individual vehicle— say a private car—requires a parking space at the trip’s end or near it
A parking user can adapt to the saturation of a parking lot either (i) by diverting to another lot that is still available— probably at the expense of more walking, driving or higher tariffs, (ii) by scheduling the time of his trip in order to park his car before the lot gets saturated—at the expense of schedule delay at his destination, or (iii) by some trade-off between diversion in space and trip scheduling
It is shown that the problem of deterministic, dynamic user equilibrium of parking traffic amounts to a fixed point problem with respect to the lot saturation times

Summary

Introduction

Context Making a trip by means of an individual vehicle— say a private car—requires a parking space at the trip’s end or near it. Every car user that holds a garage inside or near their houses has the opportunity to use it whenever he needs it. The rest of car users rely on public parking either on street or off street. A parking user can adapt to the saturation of a parking lot either (i) by diverting to another lot that is still available— probably at the expense of more walking, driving or higher tariffs, (ii) by scheduling the time of his trip in order to park his car before the lot gets saturated—at the expense of schedule delay at his destination, or (iii) by some trade-off between diversion in space and trip scheduling. User costs resulting from parking congestion impede car trips making the management of parking supply an important lever in urban transportation policies

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Conclusion