Complex Dynamics of Bus, Tram, and Elevator Delays in Transportation Systems

Abstract

Delayed map modelNonlinear map with a time lag. The delayed map model is a dynamic model of bus motion described by the delayed map where the delay of acceleration or deceleration is taken into account. Extended circle map modelThe circle map is a one-dimensional map which maps a circle onto itself.A nonlinear map including sin function. The extended circle map model is a dynamic model of a bus with the periodic inflow at a transfer point Combined map modelThe combined map is a nonlinear map combined with two nonlinear maps. The combined map model is a dynamic model of a single bus in which both effects of speed control and periodic inflow is taken into account. Deterministic chaosThe future behavior of dynamics involved no random elements does not make predictable. The behavior is known as deterministic chaos. The chaos occurs in the nonlinear map models of buses, trams, and elevators. Definition of the SubjectIt is necessary and important to operate buses and trams on time. The bus schedule is closely related to the dynamic motion of buses. In this part, we introduce the nonlinear maps for describing the dynamics of shuttle buses in the transportation system. The complex motion of the buses is explained by the nonlinear-map models. The transportation system of shuttle buses without passing is similar to that of the trams. The transport of elevators is also similar to that of shuttle buses with freely passing. The complex dynamics of a single bus is described in terms of the piecewise map, the delayed map, the extended circle map and the combined map. The dynamics of a few buses is described by the model of freely passing buses, the model of no passing buses, and the model of increase or decrease of buses. The nonlinear-map models are useful to make an accurate estimate of the arrival time in the bus transportation. IntroductionThe traffic science aims to discover the fundamental properties and laws and the traffic engineering aims at making the planning and implementation In the public transportation system, it is important and necessary to make a schedule of public transport, for example bus schedule. It is well known that passengers using buses are served best when buses arrive at stations on time and there is no congestion. Frequently, buses are delayed or go faster in the bus transport system. Thus, it is hard to operate buses on time. Bus schedules are closely related to the dynamic motion of buses. The bus dynamics depends highly on the control method and the system. The arrival time of buses is not determined only by serving passengers but also by the speed control method of buses. The dynamics of trams and elevators is also similar to that of the bus transport system.In the morning and evening peaks, the bus transport system exhibits severe congestion problems. The maximum rate of serving passengers increases with the number of buses. In managing the bus operation, the usual criterion for deciding the number of buses is that one should be able to transport everyone from the starting point to his destin...