Performance Models For Master/Slave Parallel Programs

Baldo, Lucas; Brenner, Léonardo; Fernandes, Luiz Gustavo; Fernandes, Paulo; Sales, Afonso

doi:10.1016/j.entcs.2005.01.015

Cited by 19 publications

(15 citation statements)

References 12 publications

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“…The tests were executed in a cluster architecture containing seven homogeneous nodes connected in a Gigabit Ethernet network. Each node is composed of two processors Intel Itanium Table 1 shows that for a SAN model [2] containing e.g., ten automata representing workers (N=10) and a buffer automaton of forty positions (K=40), is generated a total of 43 Kronecker product terms in the descriptor to be multiplied by a vector. For each Kronecker product term j, a different σ is determined resulting in various sets of AUNFs.…”

Section: Preliminary Resultsmentioning

confidence: 99%

Kronecker descriptor partitioning for parallel algorithms

Czekster

Rose

Fernandes

et al. 2010

Proceedings of the 2010 Spring Simulation Multiconference

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The key operation to obtain stationary and transient solutions of transition systems described by Kronecker structured formalisms is the Vector-Descriptor product. This operation is usually performed with shuffling operations and matrices aggregations to reduce the floating point multiplications inside iterative methods. Due to the flexibility of the Split method treating Kronecker product terms, it is a natural alternative to decompose descriptors within parallel environments. The main problem is to define the correct task size to assign to each node and also the shared memory size, since sending a small task per time can lead to a larger communication overhead. In this paper we are investigating data partitioning strategies for a parallel solution of transition systems obtained from Kronecker descriptors using the Split algorithm.

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Section: Preliminary Resultsmentioning

confidence: 99%

Kronecker descriptor partitioning for parallel algorithms

Czekster

Rose

Fernandes

et al. 2010

Proceedings of the 2010 Spring Simulation Multiconference

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“…The prototype was compiled using g++ compiler with optimizations (−O3). The methods were executed for practical examples of SAN models [13,3], running all tensor product terms in all possible cut-parameters, collecting outputs for 100 runs. The results were obtained in time intervals with 95% of confidence.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…This SAN model in the Figure 2 refers to an evaluation of the master-slave parallel implementation of the Propagation algorithm considering asynchronous communication [3], indicating to parallel program developers what are the possible execution bottlenecks before the implementation. This model contains one Master automaton, one huge Buffer automaton, and S automata Slave (i) , where i = 1 .…”

Section: Master-slave Parallel Modelmentioning

confidence: 99%

Split: a flexible and efficient algorithm to vector-descriptor product

Czekster¹,

Fernandes²,

Vincent³

et al. 2007

Proceedings of the 2nd International ICST Conference on Performance Evaluation Methodologies and Tools

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Many Markovian stochastic structured modeling formalisms like Petri nets, automata networks and process algebra represent the infinitesimal generator of the underlying Markov chain as a descriptor instead of a traditional sparse matrix. A descriptor is a compact and structured storage based on a sum of tensor (Kronecker) products of small matrices that can be handled by many algorithms allowing affordable stationary and transient solutions even for very large Markovian models. One of the most efficient algorithms used to compute iterative solutions of descriptors is the Shuffle algorithm which is used to perform the multiplication by a probability vector. In this paper we propose an alternative algorithm called Split, since it offers a flexible solution between the pure sparse matrix approach and the Shuffle algorithm using a hybrid solution. The Split algorithm puts the Shuffle approach in perspective by presenting a faster execution time for many cases and at least the same efficiency for the worst cases. The Split algorithm is applied to solve two SAN models based on real problems showing the practical contribution of this paper.

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“…Assynchronously, the master polls the buffer and processes final computations. For more information regarding this particular model, please refer to [3]. The model descriptor presents (3S − 3) synchronizing events, in a total of (7S − 8) tensor terms.…”

Section: Numerical Analysismentioning

confidence: 99%

Efficient vector-descriptor product exploiting time-memory trade-offs

Czekster

Fernandes

Webber

2011

SIGMETRICS Perform. Eval. Rev.

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The description of large state spaces through stochastic structured modeling formalisms like stochastic Petri nets, stochastic automata networks and performance evaluation process algebra usually represent the infinitesimal generator of the underlying Markov chain as a Kronecker descriptor instead of a single large sparse matrix. The best known algorithms used to compute iterative solutions of such structured models are: the pure sparse solution approach, an algorithm that can be very time efficient, and almost always memory prohibitive; the Shuffle algorithm which performs the product of a descriptor by a probability vector with a very impressive memory efficiency; and a newer option that offers a trade-off between time and memory savings, the Split algorithm. This paper presents a comparison of these algorithms solving some examples of structured Kronecker represented models in order to numerically illustrate the gains achieved considering each model's characteristics.

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Performance Models For Master/Slave Parallel Programs

Cited by 19 publications

References 12 publications

Kronecker descriptor partitioning for parallel algorithms

Kronecker descriptor partitioning for parallel algorithms

Split: a flexible and efficient algorithm to vector-descriptor product

Efficient vector-descriptor product exploiting time-memory trade-offs

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