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

Hitting Times in Markov Chains with Restart and their Application to Network Centrality