IoT 15(4): e5

Research Article

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

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  • @ARTICLE{10.4108/icst.valuetools.2014.258149,
        author={Misikir Eyob Gebrehiwot and Samuli Aalto and Pasi Lassila},
        title={Optimal sleep-state control of energy-aware M/G/1 queues},
        journal={EAI Endorsed Transactions on Internet of Things},
        volume={1},
        number={4},
        publisher={EAI},
        journal_a={IOT},
        year={2015},
        month={2},
        keywords={performance-energy trade-off, m/g/1, setup delay},
        doi={10.4108/icst.valuetools.2014.258149}
    }
    
  • Misikir Eyob Gebrehiwot
    Samuli Aalto
    Pasi Lassila
    Year: 2015
    Optimal sleep-state control of energy-aware M/G/1 queues
    IOT
    EAI
    DOI: 10.4108/icst.valuetools.2014.258149
Misikir Eyob Gebrehiwot1,*, Samuli Aalto1, Pasi Lassila1
  • 1: Aalto University
*Contact email: misikir.gebrehiwot@aalto.fi

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 specifi c 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 benefi t 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.