- Stoch. Syst.
- Volume 1, Number 1 (2011), 1-16.
Diffusion limits for shortest remaining processing time queues
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.
Stoch. Syst., Volume 1, Number 1 (2011), 1-16.
First available in Project Euclid: 24 February 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K25: Queueing theory [See also 68M20, 90B22] 60F17: Functional limit theorems; invariance principles
Secondary: 60G57: Random measures 68M20: Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx] 90B22: Queues and service [See also 60K25, 68M20]
Gromoll, H. Christian; Kruk, Łukasz; Puha, Amber L. Diffusion limits for shortest remaining processing time queues. Stoch. Syst. 1 (2011), no. 1, 1--16. doi:10.1214/10-SSY016. https://projecteuclid.org/euclid.ssy/1393252122