[en] The dynamics of N particles with hard core exclusion performing biased random walks is studied on a one-dimensional lattice with a reflecting wall. The bias is toward the wall and the particles are placed initially on the N sites of the lattice closest to the wall. For N = 1 the leading behavior of the first passage time T /sub fp/ to a distant site iota is known to follow the kramers escape time formula T /sub fp/ similar to λ where λ is the ratio of hopping rates toward and away from the wall. For N>1 Monte Carlo and analytical results are presented to show that for the particle closest to the wall, the Kramers formula generalizes to T /sub fp/ similar to λ /sup in/. First passage times for the other particles are studied as well. A second question that is studied pertains to survival times T /sub s/ in the presence of an absorbing barrier place at site 1. In contrast to the first passage time, it is found that T /sub s/ follows the leading behavior λ /sub l/ independent of N