Abstract
High performance computing clusters are increasingly operating under a shared/buy-in paradigm. Under this paradigm, users choose between two tiers of services: shared services and buy-in services. Shared services provide users with access to shared resources for free, while buy-in services allow users to purchase additional buy-in resources in order to shorten job completion time. An important feature of shared/buy-in computing systems consists of making unused buy-in resources available to all other users of the system. Such a feature has been shown to enhance the utilization of resources. Alongside, it creates strategic interactions among users, hence giving rise to a non-cooperative game at the system level. Specifically, each user is faced with the questions of whether to purchase buy-in resources, and if so, how much to pay for them. Under quite general conditions, we establish that a shared/buy-in computing game yields a unique Nash equilibrium, which can be computed in polynomial time. We provide an algorithm for this purpose, which can be implemented in a distributed manner. Moreover, by establishing a connection to the theory of aggregative games, we prove that the game converges to the Nash equilibrium through best response dynamics from any initial state. We justify the underlying game-theoretic assumptions of our model using real data from a computing cluster, and conduct numerical simulations to further explore convergence properties and the influence of system parameters on the Nash equilibrium. In particular, we point out potential unfairness and abuse issues and discuss solution venues.
Highlights
I N ORDER to achieve economy of scale, major research institutions are increasingly consolidating their IT services into High Performance Computing (HPC) clusters
We establish that the game considered in this study does admit a unique Nash equilibrium, and, we show that it can be computed in polynomial time
Our results provide the following insights: (i) the Nash equilibrium can be computed faster using best response dynamics; (ii) increasing the amount of buy-in resources that a user gets per currency unit may lead some users to pay less and other users to pay more; (iii) users with small workloads generally benefit more from the system than users with larger workloads, which may lead to the emergence of free-riders
Summary
I N ORDER to achieve economy of scale, major research institutions are increasingly consolidating their IT services into High Performance Computing (HPC) clusters. We show that each player can compute its best response in a distributed manner This result implies that the unique Nash equilibrium exists, but is likely to be reached. We discuss how the system parameters influence the game’s Nash equilibrium, and indicate the existence of opportunities for users to abuse resources in shared/buyin computing systems along with guidelines for addressing such problems. Our results provide the following insights: (i) the Nash equilibrium can be computed faster using best response dynamics; (ii) increasing the amount of buy-in resources that a user gets per currency unit may lead some users to pay less and other users to pay more; (iii) users with small workloads generally benefit more from the system than users with larger workloads, which may lead to the emergence of free-riders.
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