Line Planning on Path Networks with Application to the Istanbul Metrobüs

Abstract

Bus rapid transit systems in developing and newly industrialized countries often consist of a trunk with a path topology. On this trunk, several overlapping lines are operated which provide direct connections. The demand varies heavily over the day, with morning and afternoon peaks typically in reverse directions. The construction of a line plan for such a system can be seen as a multi-period covering problem on an interval graph. We propose an integer programming model for this problem, derive a structural property of line plans in the static (or single period) "unimodal demand" case, and consider approaches to the solution of the multi-period version that rely on clustering the demand into peak and off-peak service periods. An application to the Metrobüs system of Istanbul is discussed.

Line Planning in Public Transport: Bypassing Line Pool Generation

“…Theorem 11. If T is a tree, d fix = 0, and f max is bounded by a constant b, then the minimal cost for (LPAL) can be computed in O(nb 3 ). An optimal line concept can be computed in O(n 3 b 3 ).…”

“…For this case, the line planning problem was shown to be NP-hard on planar graphs. See [3,24] for further results on the complexity of the problem using terminal stations in path networks representing Istanbul Metrobüs and trees representing the Quito Trolebús. In [18], an integer programming formulation which includes line planning on all lines is presented and applied to small instances while in [17], line planning on all circular lines in a specific class of graphs is considered.…”

“…Since we are on a tree, this is enough to unambiguously define them. The invocation of Algorithm 2 can be done in O(deg(v) 3 ). Since L v has at most n elements, the for-loop at line 7 iterates at most n 2 times.…”

“…Overall, an iteration of the outer for-loop on a vertex v takes O(deg(v)n 2 ). Using the fact that on a tree v∈V deg(v) = 2n − 2, the total runtime of the algorithm is O v∈V deg(v) 3 + n 2 v∈V deg(v) = O(n 3 ).…”

Fluctuating Demand-Oriented Optimization of Train Line Planning Considering Carriage Resources Transfer under Flexible Compositions

“…When this variation and fluctuation are observed in both time and space, it is crucial to develop line plans that are responsive to demand. Then, some scholars questioned the appropriateness of using the same line plan over the day [8,20]. When formulating the train line planning, the railway department always considers the impact of the fluctuation characteristics in both time and space of the passenger demand.…”