#### Presentation Title

Shortest Remaining Processing Time Queues and the Fréchet Distribution

#### Faculty Mentor

Amber L Puha

#### Start Date

23-11-2019 10:00 AM

#### End Date

23-11-2019 10:45 AM

#### Location

241

#### Session

poster 3

#### Type of Presentation

Poster

#### Subject Area

physical_mathematical_sciences

#### Abstract

Given a list of tasks in a queue, the order in which these tasks are processed by a server is determined by the queue's service disciple. In other words, a service disciple is a set of criteria that helps sort the queue so that the server knows what task to serve next. We are interested in studying a single-server queue using the Shortest Remaining Processing Time (SRPT) service disciple with i.i.d. Pareto remaining processing times under heavy traffic conditions. Since the SRPT Queue is processing all the shorter jobs first, the large jobs with maximum service times are left in the queue. There is a theorem (Resnick 1987) that states that, as n goes to infinity, the cumulative distribution function (CDF) of the maximums of n i.i.d. Pareto random variables becomes the Fréchet CDF. Due to this, one might think that the remaining processing times obey a Fréchet distribution. However, our experimental data provides evidence that the Fréchet CDF does not seem to be closely connected to the remaining processing times of an SRPT Queue.

Shortest Remaining Processing Time Queues and the Fréchet Distribution

241

Given a list of tasks in a queue, the order in which these tasks are processed by a server is determined by the queue's service disciple. In other words, a service disciple is a set of criteria that helps sort the queue so that the server knows what task to serve next. We are interested in studying a single-server queue using the Shortest Remaining Processing Time (SRPT) service disciple with i.i.d. Pareto remaining processing times under heavy traffic conditions. Since the SRPT Queue is processing all the shorter jobs first, the large jobs with maximum service times are left in the queue. There is a theorem (Resnick 1987) that states that, as n goes to infinity, the cumulative distribution function (CDF) of the maximums of n i.i.d. Pareto random variables becomes the Fréchet CDF. Due to this, one might think that the remaining processing times obey a Fréchet distribution. However, our experimental data provides evidence that the Fréchet CDF does not seem to be closely connected to the remaining processing times of an SRPT Queue.