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We introduce and study the online pause and resume problem. In this problem,a player attempts to find the $k$ lowest (alternatively, highest) prices in asequence of fixed length $T$, which is revealed sequentially. At each timestep, the player is presented with a price and decides whether to accept orreject it. The player incurs a switching cost whenever their decision changesin consecutive time steps, i.e., whenever they pause or resume purchasing. Thisonline problem is motivated by the goal of carbon-aware load shifting, where aworkload may be paused during periods of high carbon intensity and resumedduring periods of low carbon intensity and incurs a cost when saving orrestoring its state. It has strong connections to existing problems studied inthe literature on online optimization, though it introduces unique technicalchallenges that prevent the direct application of existing algorithms.Extending prior work on threshold-based algorithms, we introducedouble-threshold algorithms for both the minimization and maximization variantsof this problem. We further show that the competitive ratios achieved by thesealgorithms are the best achievable by any deterministic online algorithm.Finally, we empirically validate our proposed algorithm through case studies onthe application of carbon-aware load shifting using real carbon trace data andexisting baseline algorithms.

The Online Pause and Resume Problem: Optimal Algorithms and An Application to Carbon-Aware Load Shifting