  Motivated by recent experimental results for the step sizes of dynein motor
proteins, we develope a cellular automata model for intra-cellular traffic of
dynein motors incorporating special features of the hindrance-dependent step
size of the individual motors. We begin by investigating the properties of the
aggressive driving model (ADM), a simple cellular automata-based model of
vehicular traffic, a unique feature of which is that it allows a natural
extension to capture the essential features of dynein motor traffic. We first
calculate several collective properties of the ADM, under both periodic and
open boundary conditions, analytically using two different mean-field
approaches as well as by carrying out computer simulations. Then we extend the
ADM by incorporating the possibilities of attachment and detachment of motors
on the track which is a common feature of a large class of motor proteins that
are collectively referred to as cytoskeletal motors. The interplay of the
boundary and bulk dynamics of attachment and detachment of the motors to the
track gives rise a phase where high and low density phases separated by a
stable domain wall coexist. We also compare and contrast our results with the
model of Parmeggiani et. al. (Phys. Rev. Lett. {\bf 90}, 086601 (2003)) which
can be regarded as a minimal model for traffic of a closely related family of
motor proteins called kinesin. Finally, we compare the transportation
efficiencies of dynein and kinesin motors over a range of values of the model
parameters.
