Mean-performance of Sharp Restart II: Inequality Roadmap

Abstract

Restarting a deterministic process always impedes its completion. However, it is known that restarting a random process can also lead to an opposite outcome -- expediting completion. Hence, the effect of restart is contingent on the underlying statistical heterogeneity of the process' completion times. To quantify this heterogeneity we bring a novel approach to restart: the methodology of inequality indices, which is widely applied in economics and in the social sciences to measure income and wealth disparity. Using this approach we establish an `inequality roadmap' for the mean-performance of sharp restart: a whole new set of universal inequality criteria that determine when restart with sharp timers (i.e. with fixed deterministic timers) decreases/increases mean completion. The criteria are based on a host of inequality indices including Bonferroni, Gini, Pietra, and other Lorenz-curve indices; each index captures a different angle of the restart-inequality interplay. Utilizing the fact that sharp restart can match the mean-performance of any general restart protocol, we prove -- with unprecedented precision and resolution -- the validity of the following statement: restart impedes/expedites mean completion when the underlying statistical heterogeneity is low/high.

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Cited by in corpus (7)

• The inspection paradox in stochastic resetting
• Mitigating long queues and waiting times with service resetting
• Diversity of Sharp Restart
• Stochastic resetting prevails over sharp restart for broad target distributions
• Universal performance bounds of restart
• Entropy of Sharp Restart
• Arcsine laws for Brownian motion with Poissonian resetting