The periodic service intention as a conceptual framework for generating timetables with partial periodicity

Abstract

Many railway companies in Europe operate periodic timetables. Yet most timetables are not entirely periodic but have a mixture of different periodicities and many exceptions to cope with changing demand. Current approaches for automatic timetable generation are not able to deal with such partially periodic structures but consider only fully periodic inputs. We therefore introduce the periodic Service Intention (pSI) as a framework where customer-relevant information about train services can be described, including their periodicity information. We then address the problem of finding a feasible timetable that fulfills the requirements specified in a pSI without the need for manual postprocessing. We solve this problem by projecting intended train runs over equivalence classes and thereby reducing the pSI to an augmented instance of periodic timetabling. Thus it is possible to use existing models for periodic scheduling, such as Periodic Event Scheduling Problem, to generate periodic timetables with partial periodicity, which are finally rolled out to obtain the desired daily schedule according to the commercial requirements of the pSI. Results for a test case from the timetable for central Switzerland in 2008 show that this approach needs only slightly longer computation time than for a fully periodic instance, but the additional time is compensated by the fact that postprocessing becomes unnecessary and by the better quality of the solution. The approach is particularly well suited for offers with a strong periodicity but some irregularities, which could not be treated properly by existing methods.

Modeling cascade dynamics of railway networks under inclement weather

“…On the other hand, it is also easy to transform periodic to non-periodic timetables using the unfolding technique, where the dependency between events in different periods is still reserved (Goverde, 2007;van der Meer, 2008). Additionally, partially periodic and non-periodic train services are also being adopted in practical train operations in Europe and China to cope with the non-uniformly distributed demand and exceptional situations, where the non-periodic expression would be applicable (Caimi et al, 2011;Forsgren et al, 2011;Wong et al, 2008;Canca et al, 2014;Cacchiani et al, 2014).…”

A multi-level framework for generating train schedules in highly utilised networks

“…In (c) a periodic timetable is generated and in (d) it is rolled out to a complete day T should therefore be chosen to reduce the problem size as much as possible without violating the equivalence condition. The equivalence always holds for T > 2W , where W is the size of the largest time slot (see Caimi et al 2011c for details).…”

“…minimising total travel time) in the projection will be rolled out to an optimal original solution if the equivalence is guaranteed. It can be shown that the equivalence depends on the length T of the time period on which the problem is projected: the smaller the period length, the more probable the violation of the equivalence (Caimi et al 2011c). The value of Fig.…”

“…In addition, we present a case study to illustrate the proposed procedure on a real-world setting for a part of the Swiss railway network. For detailed but isolated technical descriptions of the different models and algorithms, we refer to the specific papers (Caimi et al 2009(Caimi et al , 2011a(Caimi et al , 2011b(Caimi et al , 2011c and well as Caimi (2009).…”

Line planning in public transportation: models and methods

“…We remark that lines together with a rough time frame have been also denoted as (periodic) service intensions (see Caimi et al 2009) as the line concept contains the customer-relevant information about the public transport system.…”