Author(s): H. Christian Gromoll | Łukasz Kruk | Amber L. Puha
Journal: Stochastic Systems
ISSN 1946-5238
Volume: 1;
Issue: 1;
Start page: 1;
Date: 2011;
Original page
Keywords: Heavy traffic | ueueing | shortest remaining processing time | diffusion limit
ABSTRACT
We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.
Journal: Stochastic Systems
ISSN 1946-5238
Volume: 1;
Issue: 1;
Start page: 1;
Date: 2011;
Original page
Keywords: Heavy traffic | ueueing | shortest remaining processing time | diffusion limit
ABSTRACT
We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.
