Time-dependent Road Network Design Frameworks with Land Use Consideration: Policy Implications

In the past, transport network design focused on the effect of designs on the transport system alone but not on the land use system, and ignored the land use-transport interaction over time. This may result in obtaining suboptimal designs. Additionally, the impacts of road network improvement policies on the land use system, especially the benefit of landowners cannot be evaluated without considering the interaction. With these considerations, this paper proposes optimization frameworks for road network design considering the land-use transport interaction over time. Unlike existing models, the optimization frameworks can determine the optimal designs automatically without trial-and-error once the objective(s) is/are clearly defined. Moreover, these frameworks allow the evaluation of the impacts of the optimal designs on the related parties including landowners, toll road operators, transit operators, and road users, and help network planners and profit-makers with decision-making by eliminating many alternative designs. A numerical study is set up to examine road network design’s effects on these related parties under three road network improvement schemes: exact cost recovery, build-operatetransfer, and cross-subsidization (using the increase in transit profit to subsidize road improvement projects). The results show that the changes in landowner profits are not the same after implementing any scheme. These unequal changes raise the issue of the landowner equity. If the government guarantees the occurrence of this equity without providing any subsidy, societal benefit can decrease and the road network can become more congested. This implies that the government has to consider tradeoffs between parties’ objectives carefully. Szeto, W. Y., Li, X. Q., O’Mahony, M. 3 INTRODUCTION Nowadays, many road network improvement projects are still ongoing, especially in some major cities in Asia and Europe. These projects are expensive. With respect to constrained government expenditure, especially for road network improvements, the government should carefully select cost-effective improvement projects to be implemented. Traditionally, the analysis involved belongs to the discipline of road network design. In the past, much research (e.g. 1-4) was performed on the static approach to the discipline. Yang and Bell (5) provides a comprehensive review on the static approach to this discipline. Recently, researchers consider the time dimension of transport network design. Three time scales are typically considered in the literature: seconds, days, and years. The smallest time scale (6) is used to capture the within-day dynamics such as queuing phenomena, the fluctuation of demand within a day, and the departure choice of travellers. The medium scale (7) is used to capture the route adjustment behaviour of travellers from day to day. The largest scale (8) is used to capture the changing demand, gradual network upgrades, and cost and benefit over a long period of time, to maintain a similar social equity level over years, and to determine the optimal infrastructure improvement timetable, and its associated financial arrangement and tolling scheme. All the previous efforts on transport network design, however, focus on the transport system alone and ignore the interaction between land use and transport over time. In reality, the transport system interacts with the land use system. When a new road is built or an existing road is widened, the travel costs between some zones decrease, and hence the accessibilities for those zones increase. Increases in the accessibilities lead to changes in population and employment distributions, and in turn a new travel demand pattern. The new travel demand pattern leads to a new traffic pattern and new congestion locations, which may require further improvements in the future. Ignoring the interaction may result in wrong allocations of budgets on (road) network improvements or starting the improvements at wrong locations or at a suboptimal time. In addition, the impact of road network improvement policies on the land use system, especially the benefit of landowners cannot be evaluated without considering the interaction. In this paper, we develop a general time-dependent road network design framework encapsulating the Lowry-type land use consideration so that the land use transport interaction can be dealt with when determining optimal designs. More importantly, unlike existing models, the optimal designs can be determined automatically through the optimization procedure without trial-and-error once the objective is clearly defined. In addition, the effects of road network improvement policies on the land use side such as subsidizing road network improvements using public fund or transit revenue, cost recovery, and build-operate–transfer (BOT) on the profits of landowners and their profit distribution as well as population and employment changes can be studied using the proposed framework. The time scale we consider in the framework is in years as in Szeto and Lo (8), since the pace of the adjustment process inside the land use system is slow compared with those occurring inside the transport system like the day-to-day route adjustment process or the second-to-second traffic dynamics. Nonetheless, a second smaller time dimension can be easily added to the proposed models to cope with the dynamics inside the transport system without conceptual difficulty and is left to future study. Since the largest time scale is used here, the inherent advantages of the model proposed by Szeto and Lo (8) can be Szeto, W. Y., Li, X. Q., O’Mahony, M. 4 found in this framework. The framework is formulated as a single-level single-objective optimisation program that can be solved by many existing optimization software. To incorporate the considerations of various parties involved in road network improvement projects, a multi-objective optimisation framework is then developed through the hybrid approach. A numerical study using a small network is also set up to clearly illustrate the frameworks, the effect of the implementation of road network improvement projects on the related parties, and the tradeoffs between various objectives of the related parties, although the models herein can be used to handle general networks and eliminate many alternative designs. Three improvement schemes are considered: exact cost recovery, build-operate–transfer (BOT), and to use the increase in transit profit to subsidize road improvement projects. The scenario under each scheme is formulated individually using the proposed frameworks, and the corresponding optimal design is obtained by employing the generalized reduced gradient method (9) to solve the models. The results show that the changes in landowner profits are not the same after implementing any one of three projects. This raises the issue of landowner equity in terms of changes in landowner profits. More importantly, the changes can be negative after the implementation. If we force the changes in landowner profits to be non-negative, societal benefit can be reduced and the road network can be more congested compared with the situation without enforcing non-negative changes in landowner profits. The rest of the paper is organized as follows: The next section describes the formulation of the single-objective framework. The numerical study comes after that followed by the framework extension, the concluding remarks, the acknowledgement, and the references. FORMULATIONS We consider a strongly connected multi-modal transportation network with multiple OriginDestination (OD) flows over the planning horizon [ ] 0,T . The planning horizon is divided into N equal design periods. The network is further divided into M subnetworks, one for each mode, to account for the unique travelling speed of each mode. The mode here can be an individual mode or a combined mode. With this consideration, we can formulate the proposed framework as a single-level, single-objective constrained optimisation program as follows: max ( ) y x , (1) subject to time-dependent Lowry-type constraints and modal-split/assignment constraints; road network design constraints; financial constraints, and; where ( ) y x is the objective function and x is the vector of decision variables including tolls and capacity enhancements. In the following, we discuss the framework. Time-dependent Lowry-type Constraints and Modal-split/assignment Constraints The time-dependent Lowry-type constraints are developed based on the Lowry-type land use model (10) and describe the interaction between employment and population over time according to the travel costs obtained from the transport model. The transport model is represented by the time-dependent modal-split assignment constraints that depict the modal choice and Wardropian Szeto, W. Y., Li, X. Q., O’Mahony, M. 5 (11) route choice behaviour in each design period based on the travel demand obtained from the Lowry model. Due to space limitation, the details of the time-dependent constraints are not provided here. They can be found in Li et al. (12). Note that one of the differences between the proposed single objective framework and the one in Li et al is that the latter is only consider time-dependent tolls while the former considers both time-dependent toll and capacity enhancement. Road Network Design Constraints They include link improvement constraints and toll constraints. Link improvement constraints are included to address the fact that a link (in road networks) cannot be built or expanded beyond an upper limit due to space limitation, and that the improvement must be non-negative. Toll constraints cater for scenarios that due to political reasons, the toll cannot be collected on certain links or set too high. These constraints can also be found in Li et al. (12). Financial Constraints They depict the relationship between the improvement costs, toll revenues, and subsidies. These constraints include cost and revenue functions and the cost recovery constraint. Cost and revenue functions The toll revenue Tτ , and the improvement and maintenance cost Kτ in period τ can be expressed in terms of the equilibrium link flow , m a v τ , the toll , m a τ ρ and the improvement , b y τ as follows: , , , m m a a m a T nv τ τ τ ρ τ = ∀ ∑∑ , (2) ( ) , , , b b b K h w τ τ τ τ = + ∀ ∑ , (3)