When total parking supply in an urban downtown area is insufficient, morning commuters would choose their departure times not only to trade off bottleneck congestion and schedule delays, but also to secure a parking space. Recent studies found that an appropriate combination of reserved and unreserved parking spaces can spread the departures of those morning commuters and hence reduce their total travel cost. To further mitigate both traffic congestion and social cost from competition for parking, this study considers a parking reservation scheme with expiration times, where commuters with a parking reservation have to arrive at parking spaces for the reservation before a predetermined expiration time. We first show that if all parking reservations have the same expiration time, it is socially preferable to set the reservations to be non-expirable, i.e., without expiration time. However, if differentiated expiration times are properly designed, the total travel cost can be further reduced as compared with the reservation scheme without expiration time, since the peak will be further smoothed out. We explore socially desirable equilibrium flow patterns under the parking reservation scheme with differentiated expiration times. Finally, efficiencies of the reservation schemes are examined.

Expirable parking reservations for managing morning commute with parking space constraints

The bottleneck model introduced by Vickrey in 1969 has been recognized as a benchmark representation of the peak-period traffic congestion due to its ability to capture the essence of congestion dynamics in a simple and tractable way. This paper aims to provide a 50th anniversary review of the bottleneck model research since its inception. A bibliometric analysis approach is adopted for identifying the distribution of all journal publications, influential papers, top contributing authors, and leading topics in the past half century. The literature is classified according to recurring themes into travel behavior analysis, demand-side strategies, supply-side strategies, and joint strategies of demand and supply sides. For each theme, typical extended models developed to date are surveyed. Some potential directions for further studies are discussed.

Fifty years of the bottleneck model: A bibliometric review and future research directions

This study is the first in the literature to model the joint equilibrium of departure time and parking location choices when commuters travel with autonomous vehicles (AVs). With AVs, walking from parking spaces to the work location is not needed. Instead, AVs will drop off the commuters at the workplace and then drive themselves to the parking spaces. In this context, the equilibrium departure/arrival profile is different from the literature with non-autonomous vehicles (non-AVs). Besides modeling the commuting equilibrium, this study further develops the first-best time-dependent congestion tolling scheme to achieve the system optimum. Also, a location-dependent parking pricing scheme is developed to replace the tolling scheme. Furthermore, this study discusses the optimal parking supply to minimize the total system cost (including both the travel cost and the social cost of parking supply) under either user equilibrium or system optimum traffic flow pattern. It is found that the optimal planning of parking can be different from the non-AV situation, since the vehicles can drive themselves to parking spaces that are further away from the city center and walking of commuters is avoided. This paper sheds light on future parking supply planning and traffic management.

An equilibrium analysis of commuter parking in the era of autonomous vehicles

The purpose of this paper is to demonstrate that the scheduling of activities by consumers can be explicitly modeled in theoretically satisfactory and empirically productive way. Even in the case of urban work trips, probably one of the most tightly constrained of everyday activities, schedule shifting is found to be of quantitative importance for the understanding of urban transportation systems. Considerable effort will be required to assess fully the implications of this type of behavior for such important areas of transportation analysis as demand studies, value-of-time measurement, policy simulation, and cost-benefit analysis. Meanwhile, it seems likely that this approach can be applied productively to other goods subject to peak demands.

The scheduling of consumer activities: work trips

The timing of commuting trips made during morning and evening peaks has typically been investigated using Vickrey’s bottleneck model. However, in the conventional trip-based approach, the decisions that commuters make during the day about their activity schedules and time use are not explicitly considered. This study extends the bottleneck model to address the scheduling problem of commuters’ morning home-to-work and evening work-to-home journeys by using an activity-based approach. A day-long activity-travel scheduling model is proposed for the simultaneous determination of departure times for morning and evening commutes, together with allocations of time during the day among travel and activities undertaken at home or at the workplace. The proposed model maximizes the total net utility of the home-based tour, which is the difference between the benefits derived from participating in activities and the disutility incurred by travel between activity locations. The properties of the model solution are analytically explored and compared with the conventional bottleneck model for a special case with constant marginal-activity utility. For the case with linear marginal-activity utility, we develop a heuristic procedure to seek the equilibrium scheduling solution. We also explore the effects of marginal-work utility (or the employees’ average wage level) and of flexible work-hour schemes on the scheduling problem in relation to the morning and evening commuting tours.

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Bottleneck model revisited: An activity-based perspective

In this paper we investigate a bottleneck model in which the capacity of the bottleneck is assumed stochastic and follows a uniform distribution. The commuters' departure time choice is assumed to follow the user equilibrium principle according to mean trip cost. The analytical solution of the proposed model is derived. Both the analytical and numerical results show that the capacity variability would indeed change the commuters' travel behavior by increasing the mean trip cost and lengthening the peak period. We then design congestion pricing schemes within the framework of the new stochastic bottleneck model, for both a time-varying toll and a single-step coarse toll, and prove that the proposed piecewise time-varying toll can effectively cut down, and even eliminate, the queues behind the bottleneck. We also find that the single-step coarse toll could either advance or postpone the earliest departure time. Furthermore, the numerical results show that the proposed pricing schemes can indeed improve the efficiency of the stochastic bottleneck through decreasing the system's total travel cost.

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Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity

Morning commuters choose their departure times and travel modes based on a combinational evaluation of factors associated with the chances of running into bottleneck congestion, likely schedule delays, parking space availability as well as monetary costs of traveling and parking. This study investigates a morning commute problem with carpooling behavior under parking space constraint at destination. We consider such a scenario that as a competing mode of the transit line, the highway contains a carpool lane only used by carpoolers while all solo drivers are forced to use a general purpose (GP) lane. Unlike the standard bottleneck model, the rush-hour dynamic departure patterns with a binding parking supply vary with the relative proportion of the two lanes’ capacities. The possible departure pattern domain with different parking supply and lane capacity allocation is explored in terms of the relative extra carpool cost and distinguished between the bi-mode and multi-mode equilibria. It is found that compared with solo drivers, carpoolers have shorter rush hour in order to smooth the extra carpool cost. With the decrease of parking spots, the number of solo drivers cuts down gradually, whilst the number of carpoolers climbs up firstly and then declines in the multi-mode system. Under mild assumptions, the best system performance can be realized with the joint consideration of total travel cost and vehicle emission cost through optimizing the lane capacity allocation and the parking supply.

On the morning commute problem with carpooling behavior under parking space constraint

This paper investigates the impact of stochastic capacity at the downstream bottleneck after a merge and the impact of merging behavior on the morning commuters’ departure-time patterns. The classic bottleneck theory is extended to include a uniformly distributed capacity and the commuters’ equilibrium departure patterns are derived for two different merging rules. The results show that uncertainty in the bottleneck capacity increases the commuters’ mean trip cost and lengthens the peak period, and that the system total cost is lower under give-way merging than under a fixed-rate merging. Capacity paradoxes with dynamic user responses are found under both merging rules.

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Stochastic bottleneck capacity, merging traffic and morning commute

This paper proposes two tradable parking permit schemes for managing the morning commute with three alternative modes, i.e., transit, driving alone and carpool, under the parking space constraint at destination. The commuting equilibrium and system-optimal distributions of parking permits are further investigated in a many-to-one multi-modal network setting. It is found that the prices of parking permits, regardless of whether the trip is completed as a carpool or not, decrease with the parking supply, and the price for a solo driver to pay is larger than that a carpooler should pay. Furthermore, the tradable undifferentiated parking permit scheme with a uniform price is more efficient than the tradable differentiated parking permit scheme for solo-driving and carpool vehicles, but the former significantly changes the permit-holding order of solo drivers and carpoolers when the parking supply is relatively low.

Tradable permit schemes for managing morning commute with carpool under parking space constraint

This article proposes a tradable credit scheme for managing commuters’ travel choices. The scheme considers bottleneck congestion and modal split in a competitive highway–transit network with heterogeneous commuters who are distinguished by their valuation of travel time. The scheme charges all auto travelers who pass the bottleneck during a peak-time window in the form of mobility credits. Those who avoid the peak-time window, by either traveling outside the peak-time window or switching to the transit mode, may be rewarded credits. An artificial market is created so that the travelers may trade these credits with each other. We formulate the credit price and the rewarded and charged credits under tradable credit scheme. Our analyses indicate that the optimal tradable credit scheme can achieve nearly 40% efficiency gains depending on the level of commuters’ heterogeneity. In addition, this scheme distributes the benefits among all the commuters directly through the credit trading. Our results suggest tha...

https://journals.sagepub.com/doi/pdf/10.1177/1687814015612430

Ling-Ling Xiao

Papers

Congestion Behavior and Tolls in a Bottleneck Model with Stochastic Capacity

On the morning commute problem with carpooling behavior under parking space constraint

Stochastic bottleneck capacity, merging traffic and morning commute

Tradable permit schemes for managing morning commute with carpool under parking space constraint

Tradable credit scheme for rush hour travel choice with heterogeneous commuters