A mathematical model of an urban bus route

The present paper is a mathematical description of an urban bus route in peak hour traffic. “Bus route” is here used in a collective sense to denote a set of more or less parallel-going sub-routes, here called “service variants”. The deterministic and stochastic mechanisms of bus operation are analysed—with focus on time evolution—and general models for route structure, boarding and alighting events, link travel times and stop times are formulated. Various measures of goodness of fit are defined, for validation and model choice. The models are primarily intended for use in an interactive simulation program (see Andersson et al., 1979).