AIMD scheduling and resource allocation in distributed computing systems

Abstract

We consider the problem of simultaneous scheduling and resource allocation of an incoming flow of requests to a set of computing units. By representing each computing unit as a node, we model the overall system as a multiqueue scheme. Inspired by congestion control approaches in communication networks, we propose an AIMD-like (additive increase multiplicative decrease) admission control policy that is stable irrespective of the total number of nodes and AIMD parameters. The admission policy allows us to establish an event-driven discrete model, triggered by a locally identifiable enabling condition. Subsequently, we propose a decentralized resource allocation strategy via a simple nonlinear state feedback controller, guaranteeing global convergence to a bounded set in finite time. Last, we reveal the connection of these properties with Quality of Service specifications, by calculating local queuing time via a simple formula consistent with Little's Law.

Optimal Resource Scheduling and Allocation under Allowable Over-Scheduling

“…1. We model incoming requests as a continuous constant process with an arrival rate λ > 0; see also [11]. On their arrival, incoming requests are first queued in the dispatcher and then are distributed to n computing nodes.…”

“…which is the same as the one in [11]. We call it A-AIMD triggering condition as β i u i (t k ) + 0.5α i T k is the average share of each computing node between two successive jumps [14,Ch.…”

“…Since not all computing nodes need to be activated, we first focus on how to choose the computing nodes to be activated. Based on the cost function (10a), we introduce the following variable for each computing node: (11) which can be treated as the price of each computing node [16]. To show this, if the dispatcher pays one euro per unit service time and K euros per unit cost, then the price of each computing node is the expected total price that the dispatcher pays to this computing node.…”

“…Here, we introduce an averagebased AIMD (A-AIMD) algorithm which tackles a scheduling task from an average perspective and ensures bounded waiting time for all requests. Our proposed AIMD-based scheduling mechanism is motivated by recently introduced AIMD-like algorithms utilized for scheduling [8], [11]. First, the over-scheduling is embedded into an optimization problem, whose objective is to minimize the sum of the response time and cost of all computing nodes.…”

“…Although convergence and stability of typical AIMD schemes are well-studied in literature, see, e.g., [11], these properties need to be revisited here, primarily, due to a different triggering condition which is, to the best of our knowledge, novel in the context of event-triggered distributed systems. Due to its definition, the proposed A-AIMD scheduling mechanism is intuitively transformed to a switching system the stability of which is shown by boundedness of the joint spectral radius of symmetric matrices [12].…”