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Kinetics of dilute heterogeneous traffic on a two lane road is formulated inthe framework of the Ben-Naim Krapivsky model and stationary state propertiesare analytically derived in the asymptotic limit. The heterogeneity isintroduced as a quenched disorder in desired speeds of vehicles. The modelassumes that each vehicle/platoon in a lane moves ballistically until itapproaches a slow moving vehicle/platoon and then joins it. Vehicles in aplatoon are assumed to escape the platoon at a constant rate by changing lanes.Each lane is assumed to have a different escape rate. As the stationary stateis approached, the platoon density in the two lanes become equal, whereas thevehicle densities and fluxes are higher in the lane with lower escape rate. Amajority of the vehicles enjoy a free-flow if the harmonic mean of the escaperates of the lanes is comparable to average initial flux on the road. Theaverage platoon size is close to unity in the free-flow regime. If the harmonicmean is lower than the average initial flux, then vehicles with desired speedslower than a characteristic speed $v^*$ still enjoy free-flow while thosevehicles with desired speeds that are greater than $v^*$ experience congestionand form platoons behind the slower vehicles. The characteristic speed dependson the mean of escape times $(R=(R_1+R_{-1})/2)$ of the two lanes (representedby 1 and -1) as $v^* \sim R^{-\frac{1}{\mu+2}}$, where $\mu$ is the exponent ofthe quenched disorder distribution for desired speed in the small speed limit.The average platoon size in a lane, when $v^* \ll 1$, is proportional to$R^{\frac{\mu+1}{\mu+2}}$ plus a lane dependent correction. Equations for thekinetics of platoon size distribution for two-lane traffic are also studied. Itis shown that a stationary state with platoons as large as road length canoccur only if the mean escape rate is independent of platoon size.

Stationary states in two lane traffic: insights from kinetic theory