Schedule disturbances in public transport operations have a tendency to intensify along the line and propagate to successive vehicles due to the uneven accumulation of passengers. This phenomenon, affecting efficiency and reliability of service, occurs frequently with surface services due to street congestion, as well as with rapid transit when It approaches capacity volumes. In recent years, considerable attention has been given to this problem.
Newell and Potts  (*), using a deterministic model, derived an expression for the behavior of delays both along the line and of subsequent vehicles at individual stations due to passenger accumulation. They gave a theoretical explanation of the phenomenon of pairing of buses, which later Potts and Tamlin tried to verify through observations of bus operations . While they did observe the tendency for pairing of vehicles, their experiment indicated that numerous other factors in street operation (signals, traffic, etc.) make it difficult to distinguish individual causes of delays. Rapid transit is more convenient for these observations since passenger boarding is the dominant variable factor in operation. Tiercin  described a new method of schedule control tested by RATP in Paris for one of the principal « Metro » lines, and London Transport, in planning for « Victoria Line», used computer simulation of rapid transit operation at minimum intervals to derive operational measures to increase stability of service. This work was reported by Welding and Day (4) and in an unpublished Research Report . Recently, Lehmann  and Sudmeyer  gave an Interesting theoretical analysis of propagation of delays along the line; their discussion was followed by a paper by this author  which is incorporated and somewhat expanded here.
In this paper a theoretical analysis of the behavior of disturbances is extended to include the changes of disturbances with time (for subsequent vehicles at any given station). Practical implications are discussed and measures to minimize this phenomenon in public transport operations are suggested. A diagram for easy evaluation of stability of any service is also given here.
Date of this Version
Posted with permission from UITP.
Date Posted: 09 January 2017