Reliability-based equitable transit frequency design

Abstract

Fairness is an important criterion for achieving sustainable urban development, and thus, is of major concern in providing public transport services. While most existing studies focus on accessing or evaluating the fairness condition of a given transit network, this study explicitly incorporates fairness as an objective in the planning step to allocate a fleet to a set of bus lines. A multi-objective bilevel programming model is developed for the transit frequency setting problem. The lower level problem is the reliability-based transit assignment problem that captures the effects of supply-side uncertainty on passengers' route choice behaviour via the concept of travel time budget referred to as effective travel cost. The upper level problem is to determine optimal frequency settings to simultaneously minimise the total effective travel cost and maximise the network fairness condition, measured by minimum reduction in effective travel cost of all Origin-Destination (OD) pairs. A multi-objective Artificial Bee Colony algorithm (MOABC) is developed to solve the bilevel model, where non-dominated solutions are maintained by a predefined external archive. Numerical studies find that: 1) increasing the frequency may not improve the fairness condition; 2) there is a tradeoff between the objective of minimising total effective travel cost and that of maximising the fairness measurement; 3) the two objectives can be improved simultaneously using a large fleet; 4) the effect of passengers' risk aversion attitude on the fairness measurement depends on the frequency setting; it could either amplify the fairness measurements or have no impact.

A Comprehensive Survey and Future Directions on Optimising Sustainable Urban Mobility

“…Regarding how the problem was modelled, there were single and multi-objective functions, besides problems formulated at multiple levels. In terms of multiple levels, frequently the lower level relates to trip distribution, modal split and/or traffic assignment models [37,[40][41][42][43][44][45][46][47][48][49][50][51][52][53]. Moreover, the perspectives were considered related to: (i) passengers -considering their behaviour or interests (e.g., number of transfers, travel distance and time, and comfort); (ii) operators -minimising costs or investments and maximising profit; and (iii) community -environmental and external costs and integrating urban and transport planning.…”

“…Network application regards where the model was tested. Some authors applied their model to theoretical network or presented numerical examples, while others tested in benchmark networks as Sioux Falls [44,49,[52][53][54][55], Mandl [56,57] and Nguyen-Dupuis [50,58]. Nevertheless, in the vast majority of studies, the model was tested on real networks or real case studies.…”

“…For the network design, studies sought to determine public transport service area [147], bus routes [76,90,195], route length [68,74], number of lines [74], and stop/station location [74,76,199]. For time and vehicle related modelling, studies focused on frequencies setting problems [53], vehicle scheduling [62,67,110,185], and timetabling strategies [79,169]. Some authors modelled more than one aspect, for example routes and frequencies setting [194], routes and vehicle scheduling of a customised bus service [89], routes and timetabling [187], frequencies setting and timetable development [193], and service area, frequencies, and vehicle scheduling [164]; Nesheli et al [127] focused on real-time operation aspects of bus systems, as vehicle holding time and boarding limit at stops, and also deciding if the vehicle could skip certain stops.…”

“…For multi-objective or multi level problems, the most frequent combination of functions was minimising passenger's travel time and operators' costs. Nevertheless, the whole range of functions aimed at: minimising costs or maximising revenue [53,63,67,83,89,94,110,148,150,164,179,186,[194][195][196]199], minimising unsatisfied demand costs [110,196] and user costs to access the service [199], maximising covered demand or ridership [52,62,76,78,153], maximising accessibility [148] and network fairness [53], and minimising distances [78], fleet size [169], vehicle's transportation time [82], passengers' waiting time [63,79,82,169], passengers' travel time [51,90,169,193,194], vehicle mileage [193], energy consumption [79], vulnerability [51], intersection delay [70], train infeasibility [63] and train delay [172]. Lastly, only two studies considered all the three perspe...…”

Public bus transit service modeling and optimization: from conventional to autonomous vehicles

“…In the literature, one of the proposed solution algorithms for solving transit frequency design problems typically involves an iterative process or heuristic method to obtain the design variables (Schéele, 1980;Constantin and Florian, 1995;Gao et al, 2004;dell'Olio et al, 2012;Yoo et al, 2010). The other frequently adopted solution algorithms are metaheuristics, such as genetic algorithm (Yu et al, 2010;Huang et al, 2013) and artificial bee colony algorithm (Jiang, 2021). The metaheuristics require a significant number of cost function evaluations before finding a high-quality (and potentially optimal) solution (Vlahogianni, 2015).…”