A mathematical theory of trac hysteresis
نویسنده
چکیده
This paper presents a mathematical theory for modeling the hysteresis phenomenon observed in trac ̄ow. It proposes that acceleration, deceleration and equilibrium ̄ow should be distinguished in obtaining speed-concentration and/or occupancy relationships, such that the phase transitions from one phase to another can be correctly identi®ed. The analysis shows that the speed±concentration curves obtained following this approach are hysteresis loops, as predicted by the theory. The paper also gives a discussion of the general properties of the proposed modeling equations and examines the relationship between trac hysteresis and stop-start waves observed in trac ̄ow. # 1998 Elsevier Science Ltd. All rights reserved.
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