On “jamitons,” self-sustained nonlinear traffic waves

Phantom jams,” traffic blockages that arise without apparent cause, have long frustrated transportation scientists. Herein, we draw a novel homology between phantom jams and a related class of self-sustained transonic waves, namely detonations. Through this analogy, we describe the jam structure; favorable agreement with reported measurements from congested highways is observed. Complementary numerical simulations offer insights into the jams’ development. Our results identify conditions likely to result in a dangerous concentration of vehicles and thereby lend guidance in traffic control and roadway design. Continuum traffic models whereby individual vehicles are modeled collectively have enjoyed a rich history since their popularization by M. J. Lighthill and G. B. Whitham. These models are able to explain dynamics both on open roadways and in the vicinity of traffic lights and also elucidate “phantom jams,” blockages that arise without obstructions [1]. Notwithstanding this venerated record, the possibility of self-sustained disturbances consisting of a shock matched to a transonic flow has received inadequate attention despite recent experimental evidence that such “jamitons” are ubiquitous [2]. We demonstrate herein that jamitons are structurally similar to detonation waves [3]. This insight, fascinating in its own right, lends helpful guidance in roadway design. 1 ar X iv :0 80 9. 28 28 v2 [ m at h. A P] 1 7 Se p 20 08