Time Dependent Biased Random Walks

We study the biased random walk where at each step of a "controller" can, with certain small probability, move to an arbitrary neighbour. This model was introduced by Azar et al. [STOC'1992]; we extend their work time dependent setting and consider cover times this walk. obtain new bounds on hitting times. conjectured that controller can increase stationary probability vertex from $p$ $p^{1-\epsilon}$; while conjecture is not true in full generality, propose best-possible amended version confirm it for broad class graphs. also problem computing optimal strategy minimise show directed graphs determining PSPACE-complete.