An approximation for the mean response time for shortest queue routing with general interarrival and service times

Nelson, Randolph; Philips, Thomas K.

doi:10.1016/0166-5316(93)90004-e

Cited by 57 publications

(20 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Prior work on exploiting parallelism has traditionally been split between several disparate communities. The SIG-METRICS/Performance community frequently considers scheduling a stream of incoming jobs for execution across several servers with the goal of minimizing mean response time, e.g., [15,17,24,26,31]. Job sizes are assumed to be random variables drawn from some general distribution, and arrivals are assumed to occur according to some stochastic arrival process.…”

Section: Prior Workmentioning

confidence: 99%

See 1 more Smart Citation

Towards Optimality in Parallel Job Scheduling

Berg

Dorsman

2019

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

To keep pace with Moore's law, chip designers have focused on increasing the number of cores per chip rather than single core performance. In turn, modern jobs are often designed to run on any number of cores. However, to effectively leverage these multi-core chips, one must address the question of how many cores to assign to each job. Given that jobs receive sublinear speedups from additional cores, there is an obvious tradeoff: allocating more cores to an individual job reduces the job's runtime, but in turn decreases the efficiency of the overall system. We ask how the system should schedule jobs across cores so as to minimize the mean response time over a stream of incoming jobs.To answer this question, we develop an analytical model of jobs running on a multi-core machine. We prove that EQUI, a policy which continuously divides cores evenly across jobs, is optimal when all jobs follow a single speedup curve and have exponentially distributed sizes. EQUI requires jobs to change their level of parallelization while they run. Since this is not possible for all workloads, we consider a class of "fixed-width" policies, which choose a single level of parallelization, k, to use for all jobs. We prove that, surprisingly, it is possible to achieve EQUI's performance without requiring jobs to change their levels of parallelization by using the optimal fixed level of parallelization, k * . We also show how to analytically derive the optimal k * as a function of the system load, the speedup curve, and the job size distribution.In the case where jobs may follow different speedup curves, finding a good scheduling policy is even more challenging. In particular, we find that policies like EQUI which performed well in the case of a single speedup function now perform poorly. We propose a very simple policy, GREEDY * , which performs near-optimally when compared to the numerically-derived optimal policy. ACM Reference Format:

show abstract

Section: Prior Workmentioning

confidence: 99%

“…R(ρ) is an experimentally derived error correction term. The Manuscript submitted to ACM mean response time in the M/M/c/JSQ system given in[26] is:E[T ] J SQ ≈ W M /M /c (ρ)S(ρ)R(ρ) + 1µ Proof of Lemma 5.Given any GREEDY policy, P, for any (x 1 , x 2 ) ∈ S, V P (x 1 + 1, x 2 ) > V P (x 1 , x 2 + 1).…”

mentioning

confidence: 99%

Towards Optimality in Parallel Job Scheduling

Berg

Dorsman

2019

SIGMETRICS Perform. Eval. Rev.

View full text Add to dashboard Cite

show abstract

“…Identical parameters are used in our approximation. Figures 13 and 14 compare the simulation results with analytical ones for N=4, 8, 16 and 32. The analytical and simulation results are plotted using lines and special symbols, respectively.…”

Section: Waiting Time Distributionmentioning

confidence: 99%

Allocating Soft Real-Time Tasks on Cluster

Zhu

2001

SIMULATION

View full text Add to dashboard Cite

We consider distributing soft real-time tasks on a cluster of multiple homogeneous servers. The question considered here is how to assign incoming soft real-time tasks to these servers for better performance, measured by the fraction of tasks that miss their deadlines. In this paper, two architectures are taken into account-centralized and distributed. Within the distributed architecture, four dispatching policies-round robin, Bernoulli splitting, joining the shortest queue, and chopping-are analyzed and evaluated under the same condition. In the analysis, an approximate method is proposed and evaluated for the joining the shortest queue policy. The results show that for the distributed architecture, the joining the shortest queue policy performs the best. The chopping policy previously proposed has its limitation and when workload exceeds a moderate level, it performs worse than round robin. In addition, we investigated the impact of using the earliest deadline first to schedule tasks assigned to the same server, and found it can further improve performance.

show abstract

“…A comparison of several balancing methods is provided by Willebeek-LeMair and Reeves [6]. Approaches based on queuing theory appear in [7], [8]. Control theory has shown promise in information technology applications, including web services [9], [10] and databases [11], [12].…”

Section: Introductionmentioning

confidence: 99%

Hybrid optimal control for load balancing in a cluster of computer nodes

Moerdyk

DeCarlo

Birdwell

et al. 2006

2006 IEEE Conference on Computer Aided Control System Design, 2006 IEEE International Conference on Control Applications, 2006

View full text Add to dashboard Cite

This paper develops a hybrid optimal control technique and resulting experimental data using a previously reported deterministic dynamic nonlinear system model for load balancing in a cluster of computer nodes used for parallel computations in the presence of time delays and resource constraints. The model accounts for the trade-off between using processor resources to process tasks and transferring tasks to distribute the load evenly between the nodes to reduce overall processing time. The desired performance is achieved using hybrid optimal control techniques in a model predictive control context. Results demonstrate superior performance.

show abstract

An approximation for the mean response time for shortest queue routing with general interarrival and service times

Cited by 57 publications

References 13 publications

Towards Optimality in Parallel Job Scheduling

Towards Optimality in Parallel Job Scheduling

Allocating Soft Real-Time Tasks on Cluster

Hybrid optimal control for load balancing in a cluster of computer nodes

Contact Info

Product

Resources

About