  Motivated by applications in telecommunications, computer scienceand physics,
we consider a discrete-time Markov process withrestart. At each step the
process eitherwith a positive probability restarts from a given distribution,
orwith the complementary probability continues according to a Markovtransition
kernel. The main contribution of the present work is thatwe obtain an explicit
expression for the expectation of the hittingtime (to a given target set) of
the process with restart.The formula is convenient when considering the problem
of optimizationof the expected hitting time with respect to the restart
probability.We illustrate our results with two examplesin uncountable and
countable state spaces andwith an application to network centrality.
