Dynamic Stackelberg games are a broad class of two-player games in which the leader acts first, and the follower chooses a response strategy to the leader's strategy. Unfortunately, only stylized Stackelberg games are explicitly solvable since the follower's best-response operator (as a function of the control of the leader) is typically analytically intractable. This paper addresses this issue by showing that the follower's best-response operator can be approximately implemented by an attention-based neural operator, uniformly on compact subsets of adapted open-loop controls for the leader. We further show that the value of the Stackelberg game where the follower uses the approximate best-response operator approximates the value of the original Stackelberg game. Our main result is obtained using our universal approximation theorem for attention-based neural operators between spaces of square-integrable adapted stochastic processes, as well as stability results for a general class of Stackelberg games.

Current data centers require storage capacities of hundreds of terabytes to petabytes. Time-critical applications such as online transactions processing depend on getting adequate performance from the storage subsystem: otherwise, they fail. It is difficult to provide predictable quality of service at this level of complexity, because I/O workloads are extremely variable and device behavior is poorly understood. Ensuring that unrelated but competing workloads do not affect each other's performance is still more difficult, and equally necessary. We present SLEDS (Service Level Enforcement Discipline for Storage), a distributed controller that provides statistical performance guarantees on a storage system built from commodity components. SLEDS can adaptively handle unpredictable workload variations so that each client continues to get the performance it needs even in the presence of misbehaving, competing peers. After evaluating the SLEDS on a heterogeneous mid-range storage system, we found that it is vastly superior to the raw system in its ability to provide performance guarantees, while only introducing a negligible overhead.

Enterprise-scale storage systems, which can contain hundreds of host computers and storage devices and up to tens of thousands of disks and logical volumes, are difficult to design. The volume of choices that need to be made is massive, and many choices have unforeseen interactions. Storage system design is tedious and complicated to do by hand, usually leading to solutions that are grossly over-provisioned, substantially under-performing or, in the worst case, both.To solve the configuration nightmare, we present minerva: a suite of tools for designing storage systems automatically. Minerva uses declarative specifications of application requirements and device capabilities; constraint-based formulations of the various sub-problems; and optimization techniques to explore the search space of possible solutions.This paper also explores and evaluates the design decisions that went into Minerva, using specialized micro- and macro-benchmarks. We show that Minerva can successfully handle a workload with substantial complexity (a decision-support database benchmark). Minerva created a 16-disk design in only a few minutes that achieved the same performance as a 30-disk system manually designed by human experts. Of equal importance, Minerva was able to predict the resulting system's performance before it was built.

This paper investigates the placement of data and parity on redundant disk arrays. Declustered organizations have been traditionally used to achieve fast reconstruction of a failed disk's contents. In previous work, Holland and Gibson identified six desirable properties for ideal layouts; however no declustered layout satisfying all properties has been published in the literature. We present a complete, constructive characterization of the collection of ideal declustered layouts possessing all six properties. Given that ideal layouts exist only for a limited set of configurations, we also present two novel layout families. PRIME and RELPR can tolerate multiple failures in a wide variety of configurations with slight deviations from the ideal. Our simulation studies show that the new layouts provide excellent parallel access performance and reduced incremental loads during degraded operation, when compared with previously published layouts. For large accesses and under high loads, response times for the new layouts are typically smaller than those of previously published declustered layouts by a factor of 2.5.

We describe a centralized approach to testing that distributed fault-tolerant protocols satisfy their safety and timeliness specifications in the presence of the very failures they are designed to tolerate. CESIUM is a testing environment based on the centralized simulation of distributed executions and failures. Processes are run in a single address space while providing the appearance of a truly distributed execution. The human tester can force the occurrence of arbitrary failures and security attacks. The implementations under test are not instrumented for testing purposes, and their source codes need not be available. We prove that CESIUM can execute exactly the set of runs feasible in the real distributed system being simulated. We also show that there are safety and timeliness properties in the specifications of many existing distributed protocols that cannot be tested in practical distributed systems. All of these properties can, however, be accurately tested by CESIUM without introducing any perturbation in test experiments.

We present DATUM, a novel method for tolerating multiple disk failures in disk arrays. DATUM is the first known method that can mask any given number of failures, requires an optimal amount of redundant storage space, and spreads reconstruction accesses uniformly over disks in the presence of failures without needing large layout tables in controller memory. Our approach is based on information dispersal, a coding technique that admits an efficient hardware implementation. As the method does not restrict the configuration parameters of the disk array, many existing RAID organizations are particular cases of DATUM. A detailed performance comparison with two other approaches shows that DATUM'S response times are similar to those of the best competitor when two or less disks fail, and that the performance degrades gracefully when more than two disks fail.

The paper illustrates how the CESIUM simulation tool can be used for design and performance evaluation of fault tolerant and real time systems, in addition to testing the correctness of protocol implementations. We calibrate three increasingly accurate simulation models of a network of workstations using independently obtained data. For a sample group membership protocol, the predictions of the simulator are very close to the actual performance measured in the real system. We also apply CESIUM to the evaluation of two potential improvements for the protocol, performing experiments that would have been difficult to implement in the real system. The results of the simulations give us valuable insight on how to tune configuration parameters, as well as on the performance gains of the improved versions. Our experience shows that CESIUM can be used to develop best effort services which adapt their quality of service according to the failures that occur during operation.