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In this paper, we present exact shock solutions of a coupled system of delaydifferential equations, which was introduced as a traffic-flow model called{\it the car-following model}. We use the Hirota method, originally developedin order to solve soliton equations. %While, with a periodic boundarycondition, this system has % a traveling-wave solution given by ellipticfunctions. The relevant delay differential equations have been known to allowexact solutions expressed by elliptic functions with a periodic boundaryconditions. In the present work, however, shock solutions are obtained withopen boundary, representing the stationary propagation of a traffic jam.Comment: 6 pages, 2 figure

Exact Shock Solution of a Coupled System of Delay Differential Equations: A Car-Following Model