A new transit operating strategy is presented in which service vehicles operate in pairs with the lead vehicle providing an all-stop local service and the following vehicle being allowed to skip some stops as an express service. The underlying scheduling problem is formulated as a nonlinear integer programming problem with the objective of minimizing the total costs for both operators and passengers. A sensitivity analysis using a real-life example is performed to identify the conditions under which the proposed operating strategy is most advantageous.

Real-Time Optimization Model for Dynamic Scheduling of Transit Operations

Urban transit demand exhibits peaks in time and space, which can be efficiently served by means of different fleets, increasing frequencies in those groups of stops with larger passenger inflow. In this paper we develop a model that combines short turning and deadheading in an integrated strategy for a single transit line, where the optimization variables are both of a continuous and discrete nature: frequencies within and outside the high demand zone, vehicle capacities, and those stations where the strategy begins and ends. We show that closed solutions can be obtained for frequencies in some cases, which resembles the classical “square root rule”. Unlike the existing literature that compares different strategies with a given normal operation (no strategy – single frequency), we use an optimized base case, in order to assess the potential benefits of the integrated strategy on a fair basis. We found that the integrated strategy can be justified in many cases with mixed load patterns, where unbalances within and between directions are observed. In general, the short turning strategy may yield large benefits in terms of total cost reductions, while low benefits are associated with deadheading, due to the extra cost of running empty vehicles in some sections.

Integrating short turning and deadheading in the optimization of transit services

An optimization framework for intermediate-level planning of bus operations on a given corridor is presented. Service patterns over different operation periods, which include short-turn strategies (full-length and short-turn line) and variable vehicle size, are considered. Variables optimized are: positions where turn-backs are operated, vehicle size, frequencies (by operation period) and, where bus arrivals are regular, relative offset (by operation period) of full-length and short-turn line, and fare. The objective function is the net benefit represented by benefits that accrue to the users for lower average waiting times minus operator's costs not covered by fares. A numerical procedure to solve the problem is provided. An application of it to a case representative of radial corridor conditions shows the effects on service patterns and the trade-offs over operation periods between users' and operator's costs, stemming from different design criteria according to the weights attached to the two players.

Service optimization for bus corridors with short-turn strategies and variable vehicle size

This paper presents a partway deadheading strategy for transit operations to improve transit service of the peak directions of transit routes. This strategy consists of two phases: reliability assessment of further transit service and optimization of partway deadheading operation. The reliability assessment of further transit service, which is based on the current and recent service reliability, is used to justify whether or not to implement a partway deadheading operation. The objective of the second phase is to determine the beginning stop for a new service for the deadheaded vehicle by maximizing the benefit of transit system. A heuristic algorithm is also defined and implemented to estimate reliability of further transit service and to optimize partway deadheading operation. Then, the partway deadheading strategy proposed in this paper is tested with the data from a transit route in Dalian city of China. The results show the partway deadheading strategy with the reasonable parameters can improve transit service.

Real-time partway deadheading strategy based on transit service reliability assessment

We develop a short turning model using demand information from station to station within a single bus line-single period setting, aimed at increasing the service frequency on the more loaded sections to deal with spatial concentration of demand considering both operators’ and users’ costs. We find analytical expressions for optimal values of the design variables, namely frequencies (inside and outside the short cycle), capacity of vehicles and the position of the short turn limit stations. These expressions are used to analyze the influence of different parameters in the final solution. The design variables and the corresponding cost components for operators and users (waiting and in-vehicle times) are compared against an optimized normal operation scheme (single frequency). Applications on actual transit corridors exhibiting different demand profiles are conducted, calculating the optimal values for the design variables and the resulting benefits for each case. Results show the typical demand configurations that are better served using a short turn strategy.

Optimal design and benefits of a short turning strategy for a bus corridor

This article deals with bus fleet assignment on a route to meet a required timetable pattern on the route. The conditions under which a saving of a few buses in the fleet is possible by inserting express and partial services in the schedule with alternative fleet assignment strategies are discussed. An application of the case of an urban route in Madras, India is also discussed.

K.M. Anantharamaiah

Papers

Fleet assignment strategies in urban transportation using express and partial services