Optimal sleep-state control of energy-aware M/G/1 queues

Abstract

We study the problem of optimally controlling the use of sleep states in an energy-aware M/G/1 queue. In our model, we consider a family of policies where the server upon becoming idle can wait for a random period before entering, potentially randomly, any of a finite number of possible sleep states to save energy. The server becomes busy again after a possibly random number of jobs have arrived. However, jobs are served only after a random setup time. This kind of an energy-aware queuing system has been analyzed in recent papers under specific assumptions regarding the cost metrics and the distributions of the random variables. In this paper, we consider an essentially more general model. Notably we show that the optimal control of the idle time and sleep states is deterministic and does not benefit from randomization: either the system only uses the idle state and no sleep states, or the idle state is not used at all and the server immediately goes to some fixed sleep state and waits until a fixed number of jobs have arrived before starting the setup. We prove this result for two popular cost metrics, namely weighted sum of energy and response time (ERWS) and their product ERP.

Fluid-Flow Approximation in the Analysis of Vast Energy-Aware Networks

“…A review of existing data centers modeled as queuing systems, including classical and energy-aware performance, can be found in [60]. A general model of energy-aware server based on M/G/1 queue is shown in [61]. In the case of network nodes, the authors of [62] study the use of queuing theory to identify the number of bands needed to service the incoming traffic in multi-band WiFi routers; unused bands are put into a sleep mode to save energy.…”

State of the Art and Research Challenges in the Area of Autonomous Control for a Reliable Internet of Services

“…For example, server farms are vital components in cloud computing and advanced multi-server queueing models that include features essential for characterizing scheduling performance as well as energy efficiency need to be developed. Recent results in this area include [29,40,41] and analyze fundamental structural properties of policies that optimize the performance-energy trade-off. On the other hand, several works exist [20,67] that employ energy-driven Markov Decision Process (MDP) solutions.…”

On Optimal Control for Energy-Aware Queueing Systems

“…Furthermore, where exact expressions were found, the assumption of server setups being interruptible was imposed. These models were extended in [10], [14], [16] to specifically look at single server systems. Due to the decreased complexity of the model, the optimal policy was found under general cost functions as well as general underlying distributions for the setup and service times.…”