  The steady-state currents and densities of a one-dimensional totally
asymmetric exclusion process (TASEP) with particles that occlude an integer
number ($d$) of lattice sites are computed using various mean field
approximations and Monte Carlo simulations. TASEP's featuring particles of
arbitrary size are relevant for modeling systems such as mRNA translation,
vesicle locomotion along microtubules, and protein sliding along DNA. We
conjecture that the nonequilibrium steady-state properties separate into low
density, high density, an maximal current phases similar to those of the
standard ($d=1$) TASEP. A simple mean field approximation for steady-state
particle currents and densities is found to be inaccurate. However, we find
{\it local equilibrium} particle distributions derived from a discrete Tonks
gas partition function yield apparently exact currents within the maximal
current phase. For the boundary-limited phases, the equilibrium Tonks gas
distribution cannot be used to predict currents, phase boundaries, or the order
of the phase transitions. However, we employ a refined mean field approach to
find apparently exact expressions for the steady state currents, boundary
densities, and phase diagrams of the $d\geq 1$ TASEP. Extensive Monte Carlo
simulations are performed to support our analytic, mean field results.
