  We prove an exact solution of a multi-lane totally asymmetric simple
exclusion process (TASEP) with heterogeneous lane-changing rates on a torus.
The solution is given by a factorized form; that is, the TASEP in each lane and
lane-changing transition can be separable because of the detailed balance
conditions in lane-changing transition. Using the saddle point method, the
current of particles is calculated in a simple form in a thermodynamic limit.
It is notable that the current depends only on a set of lane-changing
parameters, not on the configuration of lanes.
