Optimal remapping in dynamic bulk synchronous computations via a stochastic control approach

Abstract

Abstract-A bulk synchronous computation proceeds in phases that are separated by barrier synchronization. For dynamic bulk synchronous computations that exhibit varying phase-wise computational requirements, remapping at runtime is an effective approach to ensure parallel efficiency. This paper introduces a novel remapping strategy for computations whose workload changes can be modeled as a Markov chain. The use of Markovian model allows us to treat statistical dependence and more complex structure than the usual independent identically distributed random variable assumptions. Our models are quite general and we do not need to impose conditions on the dynamics of the underlying process other than the transition probability matrix. It is shown that optimal remapping can be formulated as a binary decision process: remap or not at a given synchronizing instant. The optimal strategy is then developed for long lasted computations by employing optimal stopping rules in a stochastic control framework. The existence of optimal controls is established. Necessary and sufficient conditions for the optimality are obtained. Furthermore, a policy iteration algorithm is devised to reduce computational complexity and enhance fast convergence to the desired optimal control.

Mean Exit Times and the Multilevel Monte Carlo Method

“…Such exit times are important in many applications, including air traffic management (using the Markov chain approach) [23], manufacturing flexibility [37], quantum electrodynamics [4], the adoption of technological innovation [20], electronic systems [22,30], optimal decision making [27,33], and finance, insurance, and economics [8,25,36,38].…”

Migration decision for hybrid mobility in reconfigurable distributed virtual machines

“…The scaled workload is described by a Markov chain, which is assumed in many other studies on bulk synchronous computations [8,16]. As a result of the agents' workload change between phases, the computation of a server becomes non-deterministic.…”

“…It is possible to find a feasible optimal solution to agent migration with some global information. We relate the coordinated decision problem of agent migration to the remapping problem in parallel computing and use dynamic programming to derive a globally optimal solution, similar to the discussion in [16].…”

Stochastic Recursive Algorithms for Networked Systems with Delay and Random Switching: Multiscale Formulations and Asymptotic Properties

“…This model turns out to be a special version of a model introduced in [23] for simulating animation of flocking and schooling behaviors. Technically, the problem considered is related to the asynchronous and parallel computation model considered by [25], which was substantially generalized in [11]; see also related works in [1], [3], [5], [14], [15], [17], [18], [21], [33]. During the past decades, a host of researchers have devoted their efforts to the study of the consensus problems, and many results have been obtained; see [6], [7], [8], [9], [19], [20], [22], [24], [28], and many references therein.…”