Optimal Allocation of Service Frequencies over Transit Network Routes and Time Periods

Abstract

This study proposes a formulation for the transit network frequency setting problem. The formulation provides an optimal allocation of resources over space and time while recognizing the existence of multiple service patterns along each bus route. Transit agencies must allocate their limited resources optimally to maximize user benefits, operator benefits, or a combination of the two. The coupling of the routes with the service patterns provided along all or portions of the routes is effectively captured, and the user perspective and the operator perspective are merged into one formulation. The service patterns may be scheduled with different subsets of stops for a given route. Users see the resulting combined route headways at the stops. The number of riders varies with the prevailing number of bus trips at a given stop, which is the combination of different pattern dispatch frequencies. Two main formulations are introduced. The first extends work of Furth and Wilson and seeks to maximize the number of riders and the total wait time savings under budget, fleet, policy headway, and bus loading constraints. The second minimizes the net cost under fleet, policy headway, bus loading, minimum ridership, and minimum wait time savings constraints. In both formulations, pattern headways in different time-of-day intervals are the decision variables. This paper provides the mathematical formulation underlying the proposed methodology, describes the solution method and implementation, and demonstrates, by example, important properties of the frequency setting problem in this context, including some that may at first appear counterintuitive.

Planning, operation, and control of bus transport systems: A literature review

“…They claim that these moderate headways provide a better balance between the bus operational costs and the passengers' satisfaction. Verbas and Mahmassani (2013) and extend the model presented by Furth and Wilson (1981) considering demand variation along time and line route. The authors re-define a line as a set of ''line patterns''-consisting of subset of stops of the normal line-for which a frequency must be set in order to properly satisfy demand patterns in specific time intervals.…”

“…The problem is formulated with a non-linear program which minimizes the weighted sum of ridership and wait time savings over all stops, lines, and time intervals subject to constraints such as budget, fleet size, headway bounds for each line pattern, and bounds for load factors. Verbas and Mahmassani (2013) test the model on an example in order to analyze the impact of the constraints. Numerical results show that increasing the fleet size may lead to reduce operational costs since vehicles may be assigned to low-cost, high-ridership line patterns.…”

Efficiency and effectiveness in the urban public transport sector: A critical review with directions for future research

“…the last four rows of Table 1, are much less consistently studied, as in the economic efficiency literature, but some notable exceptions could be spotted. In particular, congestion issues are at least indirectly considered whenever competing travel means are analysed (Michaelis and Schöbel, 2009;Verbas and Mahmassani, 2013). Gallo et al (2011) show how sustainability issues, in particular related to environmental external costs, can be embedded into an objective function formulation within the tactical design process of a public transport service, whereas Ferguson et al (2012) exclusively focus on equity, social inclusion and accessibility issues, considering service production costs issues ancillary.…”

“…literature is therefore equally addressing the operator and the customer viewpoint, a first difference from economic efficiency studies reviewed so far. From a transport planning viewpoint, it is particularly interesting that some works are addressing relative performances rather than absolute ones within a multimodal network setting (Michaelis and Schöbel, 2009;Verbas and Mahmassani, 2013).…”

Exploring trade-offs in frequency allocation in a transit network using bus route patterns: Methodology and application to large-scale urban systems

“…All the other parameters are obtained from the data are constants. For more detailed derivations of this aspect, see Verbas and Mahmassani (2013).…”