P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal of Statistical Computation, 9(6):11141132, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....is allowed to arbitrarily subdivide a root problem into a given number of subproblems subject Throughout this paper ilogj stands for the logarithm base 2. There are some applications where modeling loads as independent random variables is very accurate (e.g. for some Monte Carlo simulation [6, 1]) to a bound on the maximum subproblem size s max . We show that by randomization good load balancing is achieved with high probability if 1=s max 2 Omega (n log n) We then switch to a more specialized setting and look at a model for parallel tree search based on splitting subproblems into ....

P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal of Statistical Computation, 9(6):11141132, 1988.

....our simpler approach of always bisecting the tree. into subproblems of size c and w Gamma c. Depending on w, the splitting factor can get arbitrarily close to 0 here. For other load models, it is a quite common technique to assign several pieces of work with independent sizes to each processor [8, 4, 14]. Often it is tried to justify the independence assumption by assigning subtasks to a PE which are in some sense as far apart as possible [14] 18, 6] use this rule for trees and it works well for them but in general true randomization is safer because it is easy to construct plausible looking ....

....bad. A general problem for the analysis of the algorithms considered here is that assumptions about statistical properties are required which cannot really hold because the underlying computation is unknown but quite deterministic. With the notable exception of probabilistic simulations [4]. 5 Analysis In Section 3 we did not specify how the parameter k in Algorithm 1 should be chosen in order to get good performance. This is a crucial question. If k is too small, the load will turn out to be unevenly distributed. If k is too large, the algorithm spends most of its time ....

P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal of Statistical Computation, 9(6):1114--1132, 1988.

....which scenarios to simulate, and even how long to run the simulation of each scenario, requires experimentation. Independent replications avoids some of the difficulties associated with multiple scenarios and indeed it seems to have great promise; see Heidelberger (1986a,b) Glynn and Heidelberger (1990a,b) and Heidelberger and Stone (1990) Many stochastic systems require large experiments in order to obtain reliable estimates; e.g. this is true of even a single queue with high traffic intensity; see Whitt (1989) Moreover, in many cases independent replications are as effective as one long ....

....and related problems. University of California, Irvine. Chandy, K. M. and Sherman, B. 1989) Space time and simulation. Distributed Simulation 1989. The Society for Computer Simulation, 53 57. Fujimoto, R. M. 1991) Parallel discrete event simulation. Commun. ACM 33, 31 53. Glynn, P. W. and Heidelberger, P. 1990a) Analysis of parallel, replicated simulations under a completion time constraint. IBM Research Report RC 15466 (#68774) Glynn, P. W. and Heidelberger, P. 1990b) Experiments with initial transient deletion for parallel, replicated steady state simulations. IBM Research Report RC 15700 ....

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Heidelberger, P. (1986a). Discrete event simulations and parallel processing: statistical properties. SIAM J. Sci. Statist. Comput. 9, 1114-1132.

.... under study is usually large (e.g. thousands of cells) A typical sequential PCS simulation run takes over 20 hours, while the corresponding PCS PDES takes less than 3 hours using 8 processors [4] ffl Another popular parallel approach, the parallel independent replicated simulation [27] [28], 29] running multiple simulation replications concurrently) does not work for PCS simulation. In most cases, the PCS designer only is interested in the behavior of the PCS network at the engineered workload (e.g. the workload at which the blocking probability is 1 ) To calibrate the ....

....1. If portable p 2 arrives at cell C (LPC ) at time 10 and leaves cell C at time 28 without making any phone call (see Figure 14(a) then the arrival of m 5 in Figure 13 (a) will not affect the executions of m 1 ; m 2 , and m 3 . Note that in PDES, whether a call for p 2 occurs in the interval [10,28] can be detected in the portable object. Thus messages m 1 ; m 2 , and m 3 do not need to be reexecuted after m 5 is executed. This is called jump forward or lazy reevaluation [1] Figure 14 about here. In this case, LPC .ReceiveMessage( simply inserts m 5 in the input queue, and the pointer ....

Heidelberger, P., "Discrete Event Simulations and Parallel Processing: Statistical Properties", SIAM Journal on Scientific and Statistical Computing, vol. 9, no. 6, pp. 1114--1132, November 1988.

.... in mind the limitations of current network environments, we have designed the EcliPSe toolkit primarily to ease the task of parallelizing replication based simulation applications (those where a simulation must be run several times to obtain confidence intervals for some desired parameters; see [5]) We describe in [7, 8] some performance experiments of the toolkit using replication based applications. EcliPSe, however, also provides features that support more general forms of distributed computing. Here, we plan to demonstrate the utility of these features. In this work we use EcliPSe to ....

P. Heidelberger. Discrete event simulations and parallel processing: statistical properties. SIAM Journal on Scientific and Statistical Computing, 9(6):1114--1132, November 1988.

.... of the high computational cost (see, e.g. 18] 19] By contrast, multiple run methods address the computational issues that relate, for example, to cases where a large number of statistical replications of a system is required to achieve a desired level of accuracy (see, e.g. 16] 17] [20]) In recent years, another set of multiple run methods have been developed where variants of a discrete event system with different system parameter settings or different operational policies are simulated concurrently on multiple processors (see, e.g. 4] 5] 6] 7] 24] 30] 31] ....

Heidelberger, P., Discrete Event Simulations and Parallel Processing : Statistical Properties, SIAM J. Sci Stat. Comput. 9, 1114-1132, 1988.

....by a special preprocessor, which allows the user to make declarations using a C like syntax. For example, suppose that each sampler generates a result array of 10 double precision numbers for the monitor. This data item is declared in a main program as follows: eclipse decls double type result[10]; The eclipse decls block defines the region that the preprocessor must act on. The preprocessor declares an integer variable called type result which, at run time, will contain a handle used in all subsequent EcliPSe references to this double precision array (analogous to the notion of a file ....

....number of results from each sampler. For an n sampler system, D[MC (j) generally corresponds to a state in which the monitor has received a cumulative total of j i results from sampler i, 1 i n. In the special case of tree combining for replicative simulation applications, bias free estimation [10] requires that j i = j for 1 i n. In other words, tree combining forces the monitor to obtain the same number of samples from each sampler at the end of each phase. For simplicity, and also because our emphasis is on describing our implementation of fault tolerance, we restrict our discussion to ....

[Article contains additional citation context not shown here]

P. Heidelberger. Discrete event simulations and parallel processing: statistical properties. SIAM journal on scientific computing, 9(6):1114--1132, November 1988.

....modelling efficiently and accurately. Another approach of parallelism applied to simulation is to run multiple serial simulation programs on multiple processors in parallel and average the results at the end of the runs. This approach is referred to as replicated serial simulation (RSS) 1] [4], 7] which belongs to a wide class of parallelism known as serial program, parallel subsystem (SPPS) 11] The major advantage of this approach is providing a simple implementation to reduce the overall turnaround time A shorter version will appear in the Proc. of European Conference on ....

....CS, AB, and Grains AB and inform remote CSs to update their status of the RPS. The next simulation run restarts when the grains receive a new grain to workstation mapping from the AB. 3. 3 Scheduling Policies of the RPSs Like the RSS, the first N replications initiated (FNI) scheduling method [1] [4], 7] is applied by the RPSs to obtain statistically accurate simulation results. In this scheduling policy, N results of simulation runs are recorded from the first N replications initiated. The value of N is determined by the termination condition of simulation, for example when a desirable ....

P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal on Scientific and Statistical Computing, 9(6):1114--1132, November 1988.

....the DTMC simulation because there exists a correlation between the L and the maximum possible length of sample trajectory between the selected recurrent state. By setting a short L, we may in fact severely misrepresent the dynamics of the DTMC. For this reason, we take an approach suggested in [Heid88], and we enforce on each LP to complete at least one complete regeneration (from a back to a) even if this entails exceeding the limit on the recorded trajectory, L. In practice, a large value of L, implies that this exception is rarely (if ever) used. In our experience, with runs ranging from a ....

P. Heidelberger. Discrete event simulations and parallel processing: statistical properties. SIAM Journal on Scientific and Statistical Computing, 9(6):1114-- 1132, November 1988.

....is allowed to arbitrarily subdivide a root problem into a given number of subproblems subject 1 Throughout this paper ilogj stands for the logarithm base 2. 2 There are some applications where modeling loads as independent random variables is very accurate (e.g. for some Monte Carlo simulation [6, 1]) to a bound on the maximum subproblem size s max . We show that by randomization good load balancing is achieved with high probability if 1=s max 2 Omega (n log n) We then switch to a more specialized setting and look at a model for parallel tree search based on splitting subproblems into ....

P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal of Statistical Computation, 9(6):11141132, 1988.

....our simpler approach of always bisecting the tree. into subproblems of size c and w Gamma c. Depending on w, the splitting factor can get arbitrarily close to 0 here. For other load models, it is a quite common technique to assign several pieces of work with independent sizes to each processor [8, 4, 14]. Often it is tried to justify the independence assumption by assigning subtasks to a PE which are in some sense as far apart as possible [14] 18, 6] use this rule for trees and it works well for them but in general true randomization is safer because it is easy to construct plausible looking ....

....bad. A general problem for the analysis of the algorithms considered here is that assumptions about statistical properties are required which cannot really hold because the underlying computation is unknown but quite deterministic. With the notable exception of probabilistic simulations [4]. 5 Analysis In Section 3 we did not specify how the parameter k in Algorithm 1 should be chosen in order to get good performance. This is a crucial question. If k is too small, the load will turn out to be unevenly distributed. If k is too large, the algorithm spends most of its time generating ....

P. Heidelberger. Discrete event simulations and parallel processing: Statistical properties. SIAM Journal of Statistical Computation, 9(6):1114--1132, 1988.

....is to distribute these multiple runs among the various processors, rather than sequentially running parallel simulations. We note, however, that computing confidence intervals by running sequential simulations on n processors does not necessarily give a speedup of n; as one might expect [9]. Yet another alternative is possible when multiple simulation experiments are to be run (e.g. under different parameter values) In this case, one could divide the experiments among the various processors and perform the different experiments in parallel. In such a case, a speedup of close to n ....

Phil Heidelberger, Discrete Event Simulations and Parallel Processing: Statistical Properties, SIAM Journal on Scientific and Statistical Computing. 9, 1114-1132.

....simulation model is restricted. Each processor must be able to simulate the whole model. The research papers have considered primarily the correctness and speedup of the simulation. On the other hand, statistical aspects of simulation have attained only minor attention. Notable exceptions include Heidelberger (1986 and 1988) and Glynn and Heidelberger (1990 and 1992) However, if we simulate a system having random input processes, the simulation study is only a programming exercise if the analysis of output processes is not properly carried out; see e.g. Pawlikowski (1990, p. 124) and Schruben (1987) In this paper ....

Heidelberger, P. 1988. "Discrete Event Simulation and Parallel Processing: Statistical Properties. " SIAM J. Stat. Comput. 9, 6 (Nov.), 1114--1132.

....and also complementary approach to model distribution is model replication, which is the approach adopted by the EcliPSe toolkit. This fact was already recognized by simulation researchers investigating the statistical consequences of parallel sampling (e.g. see Biles et al. [1] and Heidelberger [6]) Instead of distributing a single model over n processors, n replications of the same model are made to run on the n distinct processors. This is useful for the most general stochastic simulation paradigm: several sample paths are required in order that a statement with some statistical basis ....

P. Heidelberger, Discrete event simulations and parallel processing: statistical properties, SIAM Journal on Scientific and Statistical Computing, 9 (6) (1988) 1114--1132.

....themselves and program characteristics are reported in [16] In this section we present one representative example, with empirical measurements and speedup data. In the experiment described below, the combining method used was to require an equal number of samples from each replicated instance [6]. Because of this, achievable speedup is governed by the sampling rate of the slowest executing instance, or the instance whose intervals between sample reports are dominating. Prior to describing this application and our results on executing it under EcliPSe, a brief note on the interpretation of ....

....combining strategies are provided by the toolkit, along with some facilities for constructing unbiased estimates. It is particularly useful to pay attention to obtaining proper estimates because the added dimensionality brought about by parallel sampling in simulation can cause significant bias [6] through order statistic related problems. 4.1 On EcliPSing Polymer Computations To demonstrate the ease with which a production run can be made, starting with a sequential program, we give a brief description of the process of parallelizing the polymer code. As explained in section 2.2, the code ....

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Heidelberger, P., "Discrete Event Simulations and Parallel Processing: Statistical Properties, " SIAM J. Statist. Comput., Vol. 9, No. 6, pp. 1114-1132, 1988.

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Heidelberger, P., Discrete event simulations and parallel processing: statistical properties, SIAM Journal Stat. Comput., vol.9, pp.1114-- 1132, November 1988.

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