Road Space Allocation in a Congested Transportation Network

with Bus and Toll Lanes

Dongwook Kim, Graduate Student

Department of Civil & Environmental Engineering

University of Maryland

College Park, MD 20742, USA

Tel: 301-405-3160

Fax: 301-405-2585

Email:

Paul Schonfeld, Professor

Department of Civil & Environmental Engineering

University of Maryland

College Park, MD 20742, USA

Tel: 301-405-1954

Fax: 301-405-2585

Email:

Submitted for the 11th World Conference on Transport Research

June, 2007


Abstract

In extending the network design problem, we explore the road space allocation problem in a congested road network, particularly by considering two special-purpose lane types: toll and bus lanes. To address efficiency and equity issues resulting from road space allocation, the problem is formulated as a bi-level programming problem with an upper-level problem that optimizes roadway allocation and a lower-level problem that evaluates the travelers’ mode and route choice behavior. A multiclass, multimodal network equilibrium model is developed. A heuristic algorithm based on the simulated annealing algorithm is described and used to solve a small problem.

Key words: Road space allocation, Network design problem, Multimodal network design, Simulated annealing, Equity


Introduction

The transportation network design problem (NDP) identifies design components to be added or improved, and determines their optimal size or operating strategy under budget constraints. For a road network, most NDP-related studies focus on link addition or link capacity expansion alternatives. To broaden the range of alternatives considered, this study extends the NDP to also determine the most efficient utilization of existing roadways, considering the conversion of existing general-purpose lanes into special-purpose lanes.

Since the 1970’s, special-purpose lanes on roadways have offered attractive roadway improvement options to transportation planners, especially in conjunction with efficient roadway use concepts such as road pricing and public transit service and traffic safety enhancements. Thus, such dedicated special-purpose lanes have been developed and operated with two types of special lanes: 1) exclusive lanes for certain vehicle classes, and 2) toll lanes such as the high occupancy toll (HOT) lanes and express toll lanes. Existing studies regarding such special lanes can be extensively found in feasibility studies for a specific lane type, with emphasis on operational and economical aspects. However, special-purpose lanes must be planned by considering complex issues arising from those lanes within total transportation network, because those lanes involve the allocation of limited road space and financial resources. Schonfeld (1977) considered the optimal road space allocation concept to choose among a wide of range of alternatives for highway and public transportation modes. Xu (1993) tested the optimal road space allocation for transportation modes in a simple network, which considered mixed traffic, bus lanes, and bicycle lanes. Barker and Polzin (2004) investigated synergistic strategies by integrating an HOT lane and Bus Rapid Transit with a simple spreadsheet simulation model.

As an extension of the NDP, this study models the road space allocation problem (RSAP) in a congested road network, especially by considering simultaneously two types of special-purpose lanes: (1) toll lanes and (2) bus lanes. Specifically, toll lanes may include express toll lanes or HOT lanes, and bus lanes may be general exclusive bus lanes or bus rapid transit (BRT) lanes. Although toll lanes including HOT lanes have been implemented successfully for efficient value-pricing of roadways, they have posed some serious equity issues, since they serve only users able to pay. The RSAP considering toll lanes and bus lanes allows us to resolve more comprehensively both equity and efficiency issues, since tradeoffs among various lane types are not limited to single roads. The conversion of existing general-purpose lanes into special-purpose lanes may significantly change travel patterns in an existing network.

In order to address such complex issues, the RSAP is formulated as a bi-level programming problem with discrete decision variables for optimizing lane configuration of road links. The upper-level problem finds the optimal set of alternatives associated with a roadway allocation configuration satisfying certain constraints, while the lower-level problem analyzes travelers’ mode and route choice behavior in response to the roadway allocation change. A multimodal network equilibrium model with multiple user classes was developed and applied to the lower-level problem. For solving the RSAP, a heuristic algorithm is developed, in which the simulated annealing algorithm is incorporated. A numerical example is also presented to illustrate the proposed model and algorithm.

Methodology and Basic Concepts

Design attributes and design alternatives

The objective of the road space allocation problem (RSAP) is to determine the optimal lane assignment, considering special-purpose lanes within the available road space. In a road network with nodes and links, such lane assignment involves two types of link attributes: 1) the number of lanes of links (l) and 2) its lane exclusiveness (h). For convenience, we call them the design attributes. The second design attribute h, which can be represented as a binary number indicating lane exclusiveness for a link, is necessary for our demand estimation procedure, especially for a bus network.

A road space allocation alternative may just redesign the lane configuration within existing roadway width, or it may add a special-purpose lane after widening the existing link width, if that is possible. Hence, the RSAP can be modeled to consider roadway width expansion as well as lane assignment. As an example of road space allocation to allow a special-purpose lane for a candidate roadway, we may 1) convert a general-purpose lane into a special-purpose lane, 2) widen the existing link with a special-purpose lane, or 3) just widen without a special-purpose lane.

Decision variables and bi-level programming problem

The RSAP can be formulated as a discrete network design problem (DNDP) with discrete decision variables of the design attributes of each candidate link, {l, h}, or of design alternative set, Y. We use the design alternative sets as decision variables instead of design attributes. Each design alternative set includes design attributes of corresponding links. That is, if Y is a design alternative set over a network, for a link a, .

Alternatives for a link are mutually exclusive and, among links, interdependent. If given N candidate links, the number of alternatives for i link is , the number of the elements of finite alternative set Y, can be calculated, including the do-nothing alternative, as:

(1)

Accordingly, the RSAP finds the optimal alternative sets of candidate links for road space allocation among the finite alternative sets. We formulate the RSAP as a discrete bi-level programming problem with an upper-level problem and a lower-level problem. The upper-level problem finds the optimal design alternative set for corresponding candidate links such that the objective function of the upper-level problem is minimized under constraints. The lower-level problem evaluates the network that changed by the roadway allocation alternatives in terms of total travel cost over the entire network by obtaining traffic flows.

Multimodal network design problem/equilibrium

Since there may exist a special-purpose lane for a specific transportation mode in a road network, a multimodal network approach is necessary for the RSAP. The RSAP is treated as a multimodal network design problem (MNDP) and formulated as a bimodal network design problem for bus and auto modes. Note that bus routes are pre-specified and the RSAP is not a bus route network optimization problem.

The MNDP also involves the multimodal network equilibrium model as the demand side problem. Various models to deal with the multimodal cases in travel demand forecasting have been developed for the past decades. This study utilizes the combined mode split and assignment equilibrium problem developed by Florian (1977) and by Abdulaal and Leblanc (1979). We use the combined mode choice/assignment method without an explicit mode split function. The mode choice is treated as a route choice based on generalized costs.

Multiple user class, multi-criteria network equilibrium and equity issue

Similarly to new construction for new modes or capacity expansion for existing modes, the reallocation of some road space leads travelers to change their travel behavior, especially in mode and route choice. Unlike the latter cases, however, the reallocation of the road space may reduce the service capacity. A certain lane assignment option may be more favorable to a certain traveler group with common individual characteristics, since the option may increase the capacity for a certain mode or certain users, while it may reduce the capacity for the other modes or users. In order to address such natural and critical issues expected in the RSAP, this study incorporates three existing modeling concepts into the RSAP.

The first concept is the multi-user class model for demand analysis. The multi-class network equilibrium problem is an important and natural extension of the classical network equilibrium problem (Marcotte and Wynter, 2004), since the travelers’ preferences and value of time affecting travel demand differ by income-based user class. Hence this study uses a multi-class network equilibrium problem in the RSAP. Different values of time and travel cost preference by user class are used in this network equilibrium model.

Secondly, the multi-criteria route-mode choice approach is used in the RSAP. Nagurney (2000, 2002) developed the multi-criteria network equilibrium model in which each class of traveler perceives his travel disutility associated with a route as a weighting of two criteria, travel time and travel cost. We apply the multi-criteria approach in the combined mode and route choice equilibrium model, similarly to Dial’s model (1979). In the multimodal network for the RSAP, travelers’ mode and route diversion change their monetary cost as well as travel time. The weighting factors among those travel impedances should differ by each user class.

Finally, an equity issue among user classes is incorporated into the RSAP. The reallocation of the road space for a certain transportation mode inevitably changes the service levels of the transportation facilities used by travelers. Hence the conversion of existing general-purpose lanes into special-purpose lanes, especially for toll lane may raise an equity issue among traveler classes. Small (1992) and Litman (1997) considered equity issues in road pricing and revenue distribution, while Yang Zhang (2002) analyzed spatial and social equity issues in their toll design problem. For the equity issue in the RSAP, we do not consider revenue distribution, and deal with the issue with a different equity measure. The RSAP is formulated as a discrete NDP, taking into account the equity among user classes whose income levels differ.


Development of the Road Space Allocation Problem Model

Multimodal (bimodal) network representation and assumptions

Let G = (N, A) be a transportation network defined by a set N of nodes and a set A of links. Figure 1 represents a road network with 6 nodes and 10 links, which can be considered as a typical traffic corridor from node 1 to node 6. Let the doubled line (link ) be an expressway on which a special-purpose lane such as a toll lane would be installed as an alternative, and the other links be arterials. The broken lines and represent bus routes running along links - and -, respectively.

For a network applicable to the RSAP, as shown in Figure 2, the special-purpose lane that will be operated on the link can be represented as links 13 and 25 by using a dummy node 10 for codifying it. Assuming exclusive bus lanes on arterial links, for the purpose of bus route representation in a multimodal network, the following considerations are necessary: 1) simultaneous representation of both bus links shared with auto and exclusive bus link, 2) representation of common bus routes on a link, 3) waiting at bus stops, and 4) transfer among bus routes and among modes. Accordingly, the bus network is represented as shown in Figure 2 with separate bus links, loading/unloading links, and transfer links.

Link grouping

We classify all the links in the multimodal network into several link groups. The purposes of link grouping are 1) to analyze the multiclass, multimodal network equilibrium problem for the RSAP, and 2) to yield design attributes (i.e. the number of lanes and lane exclusiveness) appropriate to link characteristics. Six link groups are considered as follows:

-  Link group 1: auto links (arterials/expressways), design attribute: number of lanes

-  Link group 2: auto links with bus routes, design attribute: number of lanes and lane exclusiveness

-  Link group 3: toll links, design attribute: number of lanes

-  Link group 4: bus links, design attribute: number of lanes and lane exclusiveness

-  Link group 5: bus passenger loading links (for boarding or transfer among bus routes/modes)

-  Link group 6: bus unloading links

Auto links with bus routes (link group 2) are separately grouped from ones without bus routes (link group 1), because an auto link on which bus routes exist (link group 2) has the design attribute of lane exclusiveness in addition to the number of lanes, and its link cost function differs from that of link group 1, due to interaction between auto and bus. Among the groups, only link groups 1~4 have design attributes. The design attributes of each link are determined by design alternatives.

Link cost function by link group

Each link group has its own link cost function type. For the multi-criteria mode and route choice approach, the generalized cost on each link a is defined as a weighted sum of travel time cost and other monetary travel costs. Since the value of time would differ by income level of users and since lower-income users are more sensitive to out-of-pocket cost, the weighting factors differ by user class, and hence lower-income users usually have higher weighting factors for monetary cost. The generalized cost of user class k on a link a, , is represented as:

(2)

Monetary travel cost () includes all the payments incurred by travelers such as vehicle operating cost, toll, and transit fare. Vehicle operating costs include all the costs generated from driving a vehicle such as fuel, oil, tire, and other maintenance costs.