6th International Conference on Performance Evaluation Methodologies and Tools

Research Article

A New Transitory Queueing Model and its Process Limits

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  • @INPROCEEDINGS{10.4108/valuetools.2012.250299,
        author={Harsha Honnappa and Rahul Jain and Amy Ward},
        title={A New Transitory Queueing Model and its Process Limits},
        proceedings={6th International Conference on Performance Evaluation Methodologies and Tools},
        publisher={IEEE},
        proceedings_a={VALUETOOLS},
        year={2012},
        month={11},
        keywords={queueing models; transitory queueing systems; fluid and diffusion limits distributional approximations; directional derivatives m1 topology},
        doi={10.4108/valuetools.2012.250299}
    }
    
  • Harsha Honnappa
    Rahul Jain
    Amy Ward
    Year: 2012
    A New Transitory Queueing Model and its Process Limits
    VALUETOOLS
    ICST
    DOI: 10.4108/valuetools.2012.250299
Harsha Honnappa1, Rahul Jain1,*, Amy Ward1
  • 1: Univ. of Southern California
*Contact email: rahul.jain@usc.edu

Abstract

We introduce the Delta_(i)/GI/1 queue, a new queueing model. In this model, customers from a given population indepen- dently arrive according to some given distribution F . Thus, the arrival times are an ordered statistics, and the inter- arrival times are differences of consecutive ordered statis- tics. They are served by a single server which provides ser- vice according to a general distribution G, with independent service times. We develop fluid and diffusion limits for the various stochastic processes, and performance metrics. The fluid limit of the queue length is observed to be a reflected process while the diffusion limit is observed to be a func- tion of a Brownian motion and a Brownian bridge, reflected through a directional derivative of the usual Skorokhod re- flection map. We also observe what may be interpreted as a ‘transient’ Little’s law. Sample path analysis reveals various operating regimes where the diffusion limit switches between a free diffusion, a reflected diffusion process and the zero process, with possible discontinuities during regime switches.