Size-based scheduling strategies such as Shortest Remaining Processing Time first (SRPT) and Least Attained Service first (LAS) provide popular mechanisms for improving the overall delay performance by favoring smaller service requests over larger ones. The performance gains from these disciplines have been thoroughly investigated for single-server systems, and have also been experimentally dem...

We consider the problem of scheduling n jobs on m parallel machines. Each job has a deterministic processing time and a weight associated with it. For uniform machines we show that discounted flowtime is minimized by serving jobs preemptively in increasing order of their remaining processing times, assigning the job with the shortest remaining processing time to the fastest available machine. 2...

The optimality of shortest remaining processing time (SRPT) and its variants with respect to minimizing mean sojourn times are well known. Some recent studies have further argued that SRPT does not unfairly penalize large customers in order to benefit small customers, and thus have proposed the use of SRPT to improve performance in computer systems under various applications such as Web sites a...

This paper focuses on the competitive analysis of scheduling disciplines in a large deviations setting. Though there are policies that are known to optimize the sojourn time tail under a large class of heavy-tailed job sizes (e.g. Processor Sharing and Shortest Remaining Processing Time) and there are policies known to optimize the sojourn time tail in the case of light-tailed job sizes (e.g. F...

This note briefly summarizes some results from two papers: [4] and [23]. These papers pose the following question: Is it possible to reduce the expected response time of every request at a web server, simply by changing the order in which we schedule the requests? In [4] we approach this question analytically via an M/G/1 queue. In [23] we approach the same question via implementation involving...

For a system with a dispatcher and several identical servers in parallel, we propose a policy consisting of modified multi-layered round robin routing followed by shortest remaining processing time scheduling. We show that this policy has a heavy traffic limit that is identical to one in which there is a single queue (no routing) and optimal scheduling. Under light traffic, this policy is asymp...

We present a new strategy for the allocation of requests in clustered web servers, based on the size distribution of the requested documents. This strategy, EquiLoad, manages to achieve a balanced load to each of the back-end servers, and its parameters are obtained from the analysis of a trace’s past data. To study its performance, we use phase-type distribution fittings and solve the resultin...

We consider the problem of designing a preemptive protocol that is both fair and efficient when one is only concerned with the sojourn time of the job and not intermediate results. Our Fair Sojourn Protocol (FSP) is both efficient, in a strong sense (similar to the shortest remaining processing time protocol – SRPT), and fair, in the sense of guaranteeing that it outperforms processor sharing (...

We consider the problem of scheduling jobs on-line on a single machine and on identical machines with the objective to minimize total completion time. We assume that the jobs arrive over time. We give a general 2-competitive algorithm for the single machine problem. The algorithm is based on delaying the release time of the jobs, i.e., making the jobs artificially later available to the on-line...

Shortest Remaining Processing time (SRPT) has long been known to optimize the queue length distribution and the mean response time (a.k.a. flow time, sojourn time). As such, it has been the focus of a wide body of analysis. However, results about the heavy-traffic behavior of SRPT have only recently started to emerge. In this work, we characterize the growth rate of the mean response time under...