Hitting Times in Markov Chains with Restart and their Application to Network Centrality
Abstract
Motivated by applications in telecommunications, computer scienceand physics, we consider a discretetime 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.
 Publication:

arXiv eprints
 Pub Date:
 March 2015
 arXiv:
 arXiv:1503.08548
 Bibcode:
 2015arXiv150308548A
 Keywords:

 Computer Science  Performance;
 Computer Science  Networking and Internet Architecture;
 Computer Science  Systems and Control