From performance monitoring to timetable design

Project title:  From performance monitoring to timetable design: more reliable efficient timetables for railways

Project duration:  24 months (ending 6/1993).

Project staff:    Principal Investigator: Professor Malachy Carey

                        Research Assistant:  Paul Seckington.

EPSRC grant number: GR/H/50432.

The following is a one page summary of the Sept. 1993 Final Report to the SERC on the above research project/ grant.

This project employed one Research Assistant for 24 months. 

The objectives of the research were:

(a)    From idealized models of simple train services, derive relationships and insights into trade-offs between measures of performance and reliability on the one hand, and timetable design parameters (travel times, connection times, service frequency, etc.) on the other.

(b)     For more realistic, complex networks, use relationships such as from (a) to generate at least approximate design-performance rules, standards or models.

We achieved these objectives.  We produced several Research Reports setting out the research and conclusions.  Three of these have now been accepted for publication in refereed transportation or operational research journals, and others have been submitted for publication and are currently under review.  Some of the main contributions can be summarized as follows.  We:

(i)                  Developed a semi-analytial method for computing various measures of reliability and costs for a rail line consisting of a sequence of segments without junctions or intersections.  We show how to use this to adjust timetables to `optimize' reliability/cost measures. 

(ii)                Extended the above to allow a limited amount of real-time swapping of the train order in response to delays.  The semi-analytical approach becomes intractably complex as more train order swapping is allowed.  In view of this we:

(iii)               Developed several simpler ad hoc measures of reliability of actual or proposed train timetables, --- measures which can be computed by relatively simple `one-pass' methods.

(iv)              Investigated the properties of models of train networks which include random variation in trip times, wait times, connection times, etc.  In particular, we determine when piecemeal improvements will ensure improving the overall timetable. 

(v)                Developed methods of approximating the effects of headways on knock-on delays within a line segment.  We tested these in a large number of simulations.  Such approximations should make simulating train networks timetables very much simpler. 

(vi)              Investigated the effect of the behavioural response of train drivers, operators, etc., on punctuality/ reliability.  We found simple formulae to allow for such operator response. 

(vii)             Developed computer programs for implementing some of the above methods and models, tested these, and used them to illustrate and explore a variety of trade-offs between schedule time, reliability and travel costs. 

The problems treated here are broader than those traditional considered by or for railways.  For example, we have included explicit trade-offs among cost, revenues, trip times, etc, which are usually only considered earlier or later in the train planning process.  To be used by British Rail, or its successors, the models developed here would have to be implemented in larger scale computer models/programs and linked to their data sets.