It is well known that size-based scheduling policies, which take into account job size (i.e., the time it takes to run them), can perform very desirably in terms of both response time and fairness. Unfortunately, the requirement of knowing a priori the exact job size is a major obstacle which is frequently insurmountable in practice. Often, it is possible to get a coarse estimation of job size, but unfortunately analytical results with inexact job sizes are challenging to obtain, and simulation-based studies show that several size-based algorithm are severely impacted by job estimation errors. For example, Shortest Remaining Processing Time (SRPT), which yields optimal mean sojourn time when job sizes are known exactly, can drastically underperform when it is fed inexact job sizes. Some algorithms have been proposed to better handle size estimation errors, but they are somewhat complex and this makes their analysis challenging. We consider Shortest Processing Time (SPT), a simplification of SRPT that skips the update of "remaining" job size and results in a preemptive algorithm that simply schedules the job with the shortest estimated processing time. When job size is inexact, SPT performs comparably to the best known algorithms in the presence of errors, while being definitely simpler. In this work, SPT is evaluated through simulation, showing near-optimal performance in many cases, with the hope that its simplicity can open the way to analytical evaluation even when inexact inputs are considered.
While many works have studied scheduling for single-server queues, most of them focused on the extreme cases where job size is either completely unknown ( algorithms) or known perfectly. When the job size distribution is skewed---meaning that resources are occupied most of the time by a minority of large jobs---algorithms such as Least Attained Service (LAS) @cite_34 or multi-level queues @cite_17 @cite_18 can still perform well by prioritizing new jobs. LAS is evaluated experimentally in this work; for more details about it, see .
@cite_18 @cite_34 @cite_17
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Recent studies of Internet traffic have shown that flow size distributions often exhibit a high variability property in the sense that most of the flows are short and more than half of the total load is constituted by a small percentage of the largest flows. In the light of this observation, it is interesting to revisit scheduling policies that are known to favor small jobs in order to quantify the benefit for small and the penalty for large jobs. Among all scheduling policies that do not require knowledge of job size, the least attained service (LAS) scheduling policy is known to favor small jobs the most. We investigate the M G 1 LAS queue for both, load ? < 1 and ? = 1. Our analysis shows that for job size distributions with a high variability property, LAS favors short jobs with a negligible penalty to the few largest jobs, and that LAS achieves a mean response time over all jobs that is close to the mean response time achieved by SRPT.Finally, we implement LAS in the ns-2 network simulator to study its performance benefits for TCP flows. When LAS is used to schedule packets over the bottleneck link, more than 99 of the shortest flows experience smaller mean response times under LAS than under FIFO and only the largest jobs observe a negligible increase in response time. The benefit of using LAS as compared to FIFO is most pronounced at high load. Motivated by distributed schedulers that combine the power-of-d-choices with late binding and systems that use replication with cancellation-on-start, we study the performance of the LL(d) policy which assigns a job to a server that currently has the least workload among d randomly selected servers in large-scale homogeneous clusters. We consider general job size distributions and propose a partial integro-differential equation to describe the evolution of the system. This equation relies on the earlier proven ansatz for LL(d) which asserts that the workload distribution of any finite set of queues becomes independent of one another as the number of servers tends to infinity. Based on this equation we propose a fixed point iteration for the limiting workload distribution and study its convergence. We consider the dispatching problem in a size- and state-aware multi-queue system with Poisson arrivals and queue-specific job sizes. By size- and state-awareness, we mean that the dispatcher knows the size of an arriving job and the remaining service times of the jobs in each queue. By queue-specific job sizes, we mean that the time to process a job may depend on the chosen server. We focus on minimizing the mean sojourn time (i.e., response time) by an MDP approach. First we derive the so-called size-aware relative values of states with respect to the sojourn time in an M G 1 queue operating under FIFO, LIFO, SPT or SRPT disciplines. For FIFO and LIFO, the size-aware relative values turn out to be insensitive to the form of the job size distribution. The relative values are then exploited in developing efficient dispatching rules in the spirit of the first policy iteration. We consider a distributed server system in which heterogeneous servers operate under the processor sharing (PS) discipline. Exponentially distributed jobs arrive to a dispatcher, which assigns each task to one of the servers. In the so-called size-aware system, the dispatcher is assumed to know the remaining service requirements of some or all of the existing jobs in each server. The aim is to minimize the mean sojourn time, i.e., the mean response time. To this end, we first analyze an M M 1-PS queue in the framework of Markov decision processes, and derive the so-called size-aware relative value of state, which sums up the deviation from the average rate at which sojourn times are accumulated in the infinite time horizon. This task turns out to be non-trivial. The exact analysis yields an infinite system of first order differential equations, for which an explicit solution is derived. The relative values are then utilized to develop efficient dispatching policies by means of the first policy iteration (FPI). Numerically, we show that for the exponentially distributed job sizes the myopic approach, ignoring the future arrivals, yields an efficient and robust policy when compared to other heuristics. However, in the case of highly asymmetric service rates, an FPI based policy outperforms it. Additionally, the size-aware relative value of an M G 1-PS queue is shown to be sensitive with respect to the form of job size distribution, and indeed, the numerical experiments with constant job sizes confirm that the optimal decision depends on the job size distribution.