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Recently, a lane-based optimization method was developed for the design of isolated signal-controlled junctions. The lane markings are relaxed as binary-type control variables and are integrated into the design framework, in which the lane markings and signal settings can be optimized simultaneously to maximize the overall junction performance. To take into account the time-varying effects of traffic demand, the lane-based optimization method has been enhanced to cater for multi-period demand patterns. To eliminate ambiguity, only a single set of lane markings (also referred to as the permitted movements) can be established on the ground for operation throughout all of the design periods, which implies that during various design periods road users that approach a junction will be guided by the same set of lane markings. In accordance with the specific traffic conditions in different design periods, road users can make their own choice of traffic lane for turning, provided that they do not violate the permitted movement patterns. In the present formulation, the actual lane utilization patterns are referred to as the effective movements. A set of linear constraints is developed to relate all of the lane-based control variables and to prescribe the feasible solution region. The optimization for the usual objective function is formulated as a mathematical program. Standard and heuristic solution methods are derived, and numerical examples are also given for demonstration.

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This paper describes the development of a computer model and algorithms for finding the time‐dependent minimum path between two stations in a multi‐route, multi‐mode transit system running to fixed schedules. Selection of the minimum path can be based either on journey time or on weighted time. A worked example using a simple transit network is given to illustrate how the model works. The model has several applications in transport planning: it can be used for generating route schedule information to guide transit users, for assisting in route schedule coordination, and for analyzing transit system accessibility.