SOAP Bubbles: Robust Scheduling Under Adversarial Noise

A great many scheduling policies for the M/G/1 queue are so-called SOAP policies [1], meaning they assign each job a priority based on its age, the amount of service it has received so far. Perhaps the most notable example is the Gittins policy, which minimizes mean response time when job sizes are unknown. However, in some computer systems even job ages, let alone job sizes, are not precisely known by the scheduler. This can occur when scheduling in a time-shared system or over a network. Given that the Gittins policy relies on knowing exact job ages, it is not clear how to minimize mean response time in such settings.In this paper we study scheduling for the M/G/1 when the scheduler knows only approximate job ages. We find that naively using the traditional Gittins policy is not robust, meaning that introducing even an infinitesimal amount of noise in job ages can cause a large jump in mean response time. By examining the ways in which this naive policy fails, we construct a simple variation of the Gittins policy, called the shift-flat Gittins policy, which is indeed robust to noise and therefore has near-optimal mean response time. Moreover, we show that our shift-flat construction generalizes, yielding a robust variation of any SOAP policy.