Abstract
We present a new probabilistic analysis of distributed systems. Our approach relies on the theory of quasi-stationary distributions (QSD) and the results recently developed by the first and third authors. We give properties on the deadlock time and the distribution of the model before deadlock, both for discrete and diffusion models. Our results apply to any finite values of the involved parameters (time, numbers of resources, number of processors, etc.) and reflect the real behavior of these systems, with potential applications to deadlock prevention.
Highlights
Today’s distributed systems involve a huge number of processes sharing common resources
Our approach relies on the theory of quasi-stationary distributions (QSD) recently developed by Champagnat, Villemonais et al [3, 4, 5, 6, 28]
We provide non-asymptotic estimates on the deadlock time and the state of the system at deadlock for discrete models (Section 4.1) and asymptotic results which hold true for any numbers of processes and resources for diffusion models of distributed systems (Section 4.2)
Summary
Today’s distributed systems involve a huge (but finite) number of processes sharing common resources (i.e. are massively parallel). Let us mention that [30] is an excellent book on this topic. We recommend it strongly (as well as the references therein). We provide non-asymptotic estimates on the deadlock time and the state of the system at deadlock for discrete models (Section 4.1) and asymptotic results which hold true for any numbers of processes and resources for diffusion models of distributed systems (Section 4.2).
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