We present SPNP, a powerful GSPN package developed at Duke University. SPNP allows the modeling of complex system behaviors. Advanced constructs are available, such as marking dependent arc multiplicities, enabling functions, arrays of places or transitions, and subnets; in addition, the full expressive power of the C programming language is available to increase the flexibility of the net description.

A deterministic activity network (DAN) is a collection of activities, each with some duration, along with a set of precedence constraints, which specify that activities begin only when certain others have finished. One critical performance measure for an activity network is its makespan, which is the minimum time required to complete all activities. In a stochastic activity network (SAN), the durations of the activities and the makespan are random variables. The analysis of SANs is quite involved, but can be carried out numerically by Monte Carlo analysis. This paper concerns the optimization of a SAN, i.e., the choice of some design variables that affect the probability distributions of the activity durations. We concentrate on the problem of minimizing a quantile (e.g., 95%) of the makespan, subject to constraints on the variables. This problem has many applications, ranging from project management to digital integrated circuit (IC) sizing (the latter being our motivation). While there are effective methods for optimizing DANs, the SAN optimization problem is much more difficult; the few existing methods cannot handle large-scale problems.

In this paper, we derive bounds on the speed-up and efficiency of applications that schedule tasks on a set of parallel processors. We assume that the application runs an algorithm that consists of N iterations and before starting its i + 1'st iteration, a processor must wait for data (i.e., synchronize) calculated in the i'th iteration by a subset of the other processors of the system. Processing times and interconnections between iterations are modeled by random variables with possibly deterministic distributions. Scientific applications consisting of iterations of recursive equations are examples of applications that can be modeled within this formulation. We consider the efficiency of such applications and show that, although efficiency decreases with an increase in the number of processors, it has a nonzero limit when the number of processors increases to infinity. We obtain a lower bound for the efficiency by solving a equation which depends on the distribution of task ...

Software development in parallel/distributed environment is a non-trivial task and depends greatly on the availability of appropriate support in terms of development tools and environments. Perforamnce prediction /evaluation tools form a critical part of any software development environment as they enable the developer to visualize the effects of various design choices on the performance of the application. This paper presents an interpretive model for a source driven performance prediction framework. A prototype framework based on the proposed model has been developed for the iPSC/860 system. Numerical results obtained on this system are presented. These results confirm the potential of interpretive performance prediction techniques and their applicability. Keywords: Performance prediction, Performance interpretation, Parallel/Distributed software development, System & Application characterization. 1 Introduction Software development in any Parallel/Distributed computing environment ...

When a parallel computation is represented in a formalism that imposes series-parallel structure on its task graph, it becomes amenable to automated analysis and scheduling. Unfortunately, its execution time will usually also increase as precedence constraints are added to ensure series-parallel structure. Bounding the slowdown ratio would allow an informed tradeoff between the benefits of a restrictive formalism and its cost in loss of performance. This dissertation deals with series-parallelising task graphs by adding precedence constraints to a task graph, to make the resulting task graph series-parallel. The weak bounded slowdown conjecture for series-parallelising task graphs is introduced. This states that the slowdown is bounded if information about the workload can be used to guide the selection of which precedence constraints to add. A theory of best series-parallelisations is developed to investigate this conjecture. Partial evidence is presented that the weak slowdown bound is likely to be 4/3, and this bound is shown to be tight.

This paper addresses the issue of dynamic load imbalance in a class of synchronous iterative applications, and develops a model to represent their workload dynamics. Such models of application load dynamics help in more accurate performance prediction and in the design of efficient load balancing algorithms. Our model captures the workload dynamics across iterations, and predicts the workload distribution at any given iteration as the cumulative effect of workload dynamics during the preceding iterations. The model parameters are derived using empirical data from initial runs of the application. The model development is illustrated using data from a parallel N-body simulation application. 1

AbstractÐGiven a set of precedence constrained parallel tasks with their processor requirements and execution times, the problem of scheduling precedence constrained parallel tasks on multicomputers with contiguous processor allocation is to find a nonpreemptive schedule of the tasks on a multicomputer such that the schedule length is minimized. This scheduling problem is substantially more difficult than other scheduling problems due to precedence constraints among tasks, the inherent difficulty of task scheduling, and processor allocation in multicomputers. We present an approximation algorithm called LLB that schedules tasks level-by-level using the largest-task-first strategy supported by the binary system partitioning scheme to handle the three difficult issues in our scheduling problem. Though algorithm LLB does not have a bounded worst-case performance ratio, we show through probabilistic analysis that LLB has a quite reasonable average-case performance ratio for typical classes of parallel computations. In particular, algorithm LLB has an average-case performance ratio less than two for large scale parallel computations that have wide task graphs (i.e., that exhibit large parallelism). Index TermsÐAverage-case performance ratio, binary system partitioning, contiguous processor allocation, largest-task-first, parallel task, precedence constraint, probabilistic analysis, task scheduling.

dongarra msr.emp.ornl.gov

This research aims at creating a framework to analyze the performance of iterative algorithms in distributed environments. The parallelization of certain iterative algorithms is indeed a crucial issue for the efficient solution of large or complex optimization problems. Diverse implementation techniques for such parallelizations have become popular. They are examined here with a view to understanding their impact on the algorithm behavior in a distributed environment. Several theoretical results concerning the sufficient conditions for, and speed of, convergence for parallel iterative algorithms are available. However, there is a gap between those results and what is relevant to the user at the application level. In particular, an estimate of the algorithm execution time is often desirable. The performance characterization presented in this dissertation follows a stochastic approach partially based on a Markov process. It addresses different characteristics of the algorithmic execution...

In multiprocessor systems, iterative algorithms can be implemented synchronously or asynchronously. The choice depends mostly on performance. Unfortunately, few guidelines exist to make that decision. In this paper, we compare the execution times of an asynchronous iterative algorithm and of its synchronous counterpart for a class of asynchronous iterations which includes iterations with monotone mappings. Synchronization overhead and communication times are neglected in order to focus on the effect of asynchronism on the convergence rate. Under some assumptions, we derive an analytical model. In this model, Q tasks with identical and independently distributed execution time distributions execute on P processors. Using simulations as well as analytical models, we show the effects of execution time fluctuations, of the number of processors and tasks, of the scheduling policy and of the amount of coupling among iterate components. The models show that the asynchronous iterati...