Toward Optimizing Latency Under Throughput Constraints for Application Workflows on Clusters

Dufossé

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

2009

In this paper, we explore the problem of mapping filtering services on large-scale heterogeneous platforms. Two important optimization criteria should be considered in such a framework. The period, which is the inverse of the throughput, measures the rate at which data sets can enter the system. The latency measures the response time of the system in order to process one single data set entirely. Both criteria are antagonistic. For homogeneous platforms, the complexity of period minimization is already known [1]; we derive an algorithm to solve the latency minimization problem in the general case with service precedence constraints; for independent services we also show that the bi-criteria problem (latency minimization without exceeding a prescribed value for the period) is of polynomial complexity. However, when adding heterogeneity to the platform, we prove that minimizing the period or the latency becomes NP-hard, and that these problems cannot be approximated by any constant factor (unless P=NP). The latter results hold true even for independent services. We provide an integer linear program to solve both problems in the heterogeneous case with independent services.For period minimization on heterogeneous platforms, we design some efficient polynomial time heuristics and we assess their relative and absolute performance through a set of experiments. For small problem instances, the results are very close to the optimal solution returned by the integer linear program.

“…That is the lower bound of the latency on this instance, according to the equation (6). That means that we have ∀i,…”

Section: Particular Instancesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the complexity of mapping pipelined filtering services on heterogeneous platforms

Dufossé

2009 IEEE International Symposium on Parallel &Amp; Distributed Processing

2009

“…The task graphs targeted by DataCutter are more general than linear pipelines or forks, but still more regular than arbitrary DAGs, which makes it possible to design efficient heuristics to solve the previous placement and replication optimization problems. However, we point out that a recent paper [31] targets workflows structured as arbitrary DAGs and considers bi-criteria optimization problems on homogeneous platforms. The paper provides many interesting ideas and several heuristics to solve the general mapping problem.…”

Section: Related Workmentioning

confidence: 99%

“…In particular, Ahmad and Kwok [1] provide a very interesting algorithm, namely the CPFD (Critical Path Fast Duplication) algorithm, which gives priority to tasks belonging to a critical path (such tasks are called CPN tasks), or to tasks belonging to a path that leads to a CPN task. It would be very interesting (and probably very challenging) to extend or modify the CPFD algorithm to deal with latency optimization for pipelined workflows made up of arbitrary DAGs (rather than just linear or fork graphs), and even to deal with bi-criteria objectives as in the paper [31] discussed above.…”

Section: Related Workmentioning

confidence: 99%

Complexity Results for Throughput and Latency Optimization of Replicated and Data-parallel Workflows

2008

Algorithmica

Mapping applications onto parallel platforms is a challenging problem, even for simple application patterns such as pipeline or fork graphs. Several antagonist criteria should be optimized for workflow applications, such as throughput and latency (or a combination). In this paper, we consider a simplified model with no communication cost, and we provide an exhaustive list of complexity results for different problem instances. Pipeline or fork stages can be replicated in order to increase the throughput by sending consecutive data sets onto different processors. In some cases, stages can also be data-parallelized, i.e. the computation of one single data set is shared between several processors. This leads to a decrease of the latency and an increase of the throughput. Some instances of this simple model are shown to be NP-hard, thereby exposing the inherent complexity of the mapping problem. We provide polynomial algorithms for other problem instances. Altogether, we provide solid theoretical foundations for the study of mono-criterion or bi-criteria mapping optimization problems.

“…The pipeline operates in synchronous mode: after a transient behavior due to the initialization delay, a new data set is completed every period. Typical performancerelated objectives for such pipelined operations are the period (which is defined as the inverse of the throughput) or the latency (also called response time) [16,17,19,20,3,4,21]. Formally, the period of a mapping is defined as the time interval required between the beginning of the execution of two consecutive data sets.…”

Section: Introductionmentioning

confidence: 99%

Performance and energy optimization of concurrent pipelined applications

Renaud-Goud

2010 IEEE International Symposium on Parallel &Amp; Distributed Processing (IPDPS)

2010

In this paper, we study the problem of finding optimal mappings for several independent but concurrent workflow applications, in order to optimize performance-related criteria together with energy consumption. Each application consists in a linear chain application with several stages, and processes successive data sets in pipeline mode, from the first to the last stage. We study the problem complexity on different target execution platforms, ranking from fully homogeneous platforms to fully heterogeneous ones. The goal is to select an execution speed for each processor, and then to assign stages to processors, with the aim of optimizing several concurrent optimization criteria. There is a clear trade-off to reach, since running faster and/or more processors leads to better performance, but the energy consumption is then very high. Energy savings can be done at the price of a lower performance, by reducing processor speeds or enrolling fewer resources.. We consider two mapping strategies: in one-to-one mappings, a processor is assigned a single stage, while in interval mappings, a processor may process an interval of consecutive stages of the same application. For both mapping strategies and all platform types, we establish the complexity of several multi-criteria optimization problems, whose objective functions combine period, latency and energy criteria. In particular, we exhibit cases where the problem is NP-hard with concurrent applications, while it can be solved in polynomial time for a single application. Also, we demonstrate the difficulty of performance/energy trade-offs by proving that the tri-criteria problem is NP-hard, even with a single application on a fully homogeneous platform.