  In living cells, motor proteins, such as kinesin and dynein can move
processively along microtubule (MT), and also detach from or attach to MT
stochastically. Experiments have found that, the traffic of motor might be
jammed, and various theoretical models have been designed to understand this
traffic jam phenomenon. But previous studies mainly focus on motor
attachment/detachment rate dependent properties. Recent experiment of Leduc
{\it et al.} found that the traffic jam formation of motor protein kinesin
depends also on the length of MT [Proc. Natl. Acad. Sci. U.S.A. {\bf 109},
6100-6105 (2012)]. In this study, the MT length dependent properties of motor
traffic will be analyzed. We found that MT length has one {\it critical value}
$N_c$, traffic jam occurs only when MT length $N>N_c$. The jammed length of MT
increases with total MT length, while the non-jammed MT length might not change
monotonically with the total MT length. The critical value $N_c$ increases with
motor detachment rate from MT, but decreases with motor attachment rate to MT.
