Heidelberger, P., Trivedi, S. K. "Analytic queueing models for programs with internal concurrency", IEEE Trans. on Computers, 32, Jan. 1983, pp. 73 -- 82.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... of computer systems performance evaluation has also recognized fields of the research and applications of methods in parallel processing [Akyi 92] Model based performance analysis has recognized an overwhelming mass of contributions in the various paradigms: queueing network models [Heid 82, Heid 83, Funk 91, Munt 90] Petri Net modeling [Ajmo 84] and markovian stochastic performance models [Ciar 90, Smit 90b] to give some pointers. Modeling has been applied to describe interdependencies of hardware resources [Mahg 92a] to characterize the behavior of parallel program components and to ....

P. Heidelberger and K. S. Trivedi. "Analytic Queueing Models for Programs with Internal Concurrency". IEEE Transactions on Computers, Vol. C-32, No. 1, pp. 73--82, Jan. 1983.

....be introduced. This is especially true with analytical modeling techniques. To make the model be mathematically solvable, higher level of abstraction and more assumptions must be made. For example, in many analytical models only exponential distributions are allowed for time distributions (e.g. Heidelberger83; Mak90] When simulation is used, this restriction has gone. Many complex non exponential distributions can easily be used. Briefly, simulation allows more complex and detailed models, thus resulting in more accurate solutions. Because measurement is directly carried out on a real system, it ....

....focuses are mainly on two aspects. One is on looking for different methods of describing systems under consideration, and the other is on finding cost effective approximate solutions with respect to the corresponding modeling methods. The work done by Heidelberger and Trivedi [Heidelberger82; Heidelberger83] is considered to be representative of earlier work using queueing network models to predict parallel performance. In their work, analytic queueing models of programs with internal concurrency are considered. The system under investigation consists of m active resources such as processors and ....

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Heidelberger, P. and Trivedi, K. S., "Analytic queueing models for programs with internal concurrency," IEEE Transactions on Computers, vol. C-32, no. 1, pp. 73-82, January 1983.

....Performance analysis of parallel computations has been recognized as a dicult problem because existing ecient methods are generally not applicable due to the precedence constraints among tasks. Most earlier works have dealt with uniprogramming systems [9, 15, 16] restrictive task structures [6, 7, 17, 18, 19] or used methods with exponential complexity [2, 3, 25] This paper describes a prediction method which is applicable to a multiprogramming parallel processing system with a large class of task structures, and estimate the mean system performance such as tasks response time and resource ....

P. Heidelberger and K. S. Trivedi. Analytic Queueing Models for Programs with Internal Concurrency. IEEE Transactions on Computers, 32(1):73-82, January 1983.

....of equations and corresponding sets of parameters, say x and y. The two sets of equations take the form. y = f(x) and x = g(y) These equations can be reduced to a single set of fixed point equations. x = g(f(x) or y = f(g(y) Applications of the fixed point iteration method can be found in [31, 38, 56, 78, 110]. To solve the fixed point equations, the numerical iterative method, called fixed point iteration method is usually used. Iterative method is a method in which we choose an arbitrary x 0 and compute a sequence x 0 ; x 1 ; x 2 ; recursively, until there is no significant change in the ....

P. Heidelberger and K. S. Trivedi. Analytic queueing models for programs with internal concurrency. IEEE Transactions on Computers, C-32(1):73--82, Jan. 1983.

....the model presented in [13] is applicable to rendezvous based systems, the post rendezvous phase of task execution is not considered. Standard queueing theory does not deal with models of parallel execution with inter dependence between customers. A queueing theoretic approach has been used in [12] for the performance analysis of a limited variety of splits and joins in control flow but this model does not extend to general systems of concurrent tasks using a rendezvous mechanism for interaction. A direct derivation of a Markov chain model of a system characterized by tasks communicating ....

P. Heidelberger and K.S. Trivedi, "Analytic Queueing Models for Programs with Internal Concurrency," IEEE Transactions on Computers, Vol. C-32, No. 1, January 1983.

....are complementary: when used together, both synchronisation types are covered. Glamis differs from related approaches on a few important points. A major difference is the distribution of the task completion times. Most related approaches assume exponentially distributed completion times [7, 11, 14]. We assume a negligible variance in completion times. Our experiments, as well as a recent publication by Adve and Vernon [1] support this assumption, provided that certain requirements are met. The complexity of Mak s method [11] is polynomial, but its applicability is restricted to ....

P. Heidelberger and K.S. Trivedi, "Analytic queueing models for programs with internal concurrency," IEEE Tr. on Computers, vol. 32, Jan. 1983, pp. 73--82.

....underlying Markov chains when used with the condensed task graph as input; in this case, the task scheduling is incorporated when creating the condensed graph itself. 2.4. Models Restricted to Fork Join Programs A number of previous models are restricted to programs with fork join task graphs [AIA91, Cve87, DuB82, HeT83, KrW85, TRS90, TsV90, VSS88], and are all much simpler than models described so far. Of these, perhaps the most general is the seminal model of Kruskal and Weiss [KrW85] They consider a parallel program consisting of N independent parallel tasks executing on P processors, and make two simplifying assumptions about task ....

.... for three fork join programs with good load balancing (i.e. in which ignoring synchronization delays at barriers does not introduce significant error) We will not describe the other, less general, models for fork join programs here, except to note that both the models of Heidelberger and Trivedi [HeT83] and Towsley et al. [TRS90] apply to multiprogrammed parallel systems with multiple parallel jobs (each job is assumed to have the same number of tasks in each parallel phase and each task is exponentially distributed) All other models to which we refer in this paper only consider systems with a ....

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P. HEIDELBERGER and K. S. TRIVEDI, Analytic Queueing Models for Programs with Internal Concurrency, IEEE Trans. on Computers C-32, 1 (Jan. 1983), 73-82.

.... branch of computer systems performance evaluation has also recognized fields for research and application of analysis methods in parallel processing [2] Model based performance analysis has recognized an overwhelming mass of contributions in the various paradigms: queueing network models [15, 16, 11], Petri Net modeling [1] and markovian stochastic performance models [22] to give some pointers. Performance models have been devised that describe the interdependencies of hardware resources [17] that characterize the behavior of parallel program components and the workload for parallel systems ....

P. Heidelberger and K. S. Trivedi. Analytic Queueing Models for Programs with Internal Concurrency. IEEE Transactions on Computers, C-32(1):73--82, January 1983.

....model that represents the system is shown in Figure 4. The delay center in the network represents time during which either the scan process or the join process blocks due to synchronization on the buffer that they use to communicate. A similar approach was used to model synchronization delays in [HT83] The scan process blocks if the buffer is full, whereas the join process blocks if the buffer is empty, as described in Section 2. Since the processes are fairly tightly synchronized (i.e. the size of the buffer is assumed to be fairly small) we assume that in fact both processes complete ....

P. Heidelberger and K. S. Trivedi. "Analytic Queueing Models for Programs with Internal Concurrency". In IEEE Transactions on Computers, January 1983.

....network because messages are not conserved; a message arriving at a task may stimulate zero, one, or several further messages. In this aspect, messages are more similar to procedure call frequencies in software models (e.g. 7] Other models of distributed software (e.g. Heidelberger and Trivedi [8], Thomasian and Bay [9] have created artificial populations of customers with special behaviour which simulate the variability in the message populations. Some previous work by Woodside et al. [10, 11] has examined special cases of task networks involving rendezvous only. It was found that task ....

Heidelberger, P.; Trivedi, K.S.; "Analytic Queueing Models for Programs with Internal Concurrency", I.E.E.E. Transactions on Computers, Vol. C-32, No. 1, January 1983.

....However, the completion time of the long jobs is not known in advance, so that the value to be chosen for the synchronisation delay cannot be determined. This problem can be solved by using the following iterative method (which resembles Heidelberger and Trivedi s method of complementary delays [14], but in contrast to this method applies to sections with a constant completion time) Consider a Glamis machine model with L blocks hC 1 ; CL i, where C i (i 2 f1; Lg) can be any block Q m k (D i ) or I(D i ) A program consisting of one parallel section with two types of jobs ....

P. Heidelberger and K.S. Trivedi, "Analytic queueing models for programs with internal concurrency," IEEE Tr. Comp., vol. C-32, no. 1, Jan. 1983, pp. 73--82.

....for computing communication costs with resource contention. His analysis has been validated only against synthetic series parallel task graphs. Models Restricted to Fork Join Programs There a number of previous models restricted to programs with fork join task graphs [Dubois and Briggs 1982; Heidelberger and Trivedi 1983; Towsley et al. 1990; Ammar et al. 1990; Kruskal and Weiss 1985; Vrsalovic et al. 1988; Cvetanovic 1987; Tsuei and Vernon 1990] divide and conquer task graphs [Madala and Sinclair 1991] or pipelined task graphs [Lewandowski et al. 1996] Of these, perhaps the most important is the seminal model ....

Heidelberger, P. and Trivedi, K. S. 1983. Analytic Queueing Models for Programs with Internal Concurrency. IEEE Trans. on Computers C-32, 1 (January), 73--82.

....is not stalled in the MB submodel. USB = M RSB UMB UMB = M RMB USB The alternating solution of each submodel is repeated until the estimated throughputs converge. This approach might be named the method of surrogate service time inflation, analogous to the method of surrogate delays [4, 6]. The equations for R peMB and R peSB are shown below. The processor residence time consists of the customer s service time and the amount of time that the customer waits for the M Gamma 1 other customers that might be either waiting or in service at the same processor. The first term, Rpe R ....

P. Heidelberger and K. Trivedi. Analytic Queueing Models for Programs with Internal Concurrency. IEEE Trans. on Computers, C-32(1):73--82, Jan. 1982.

....is not stalled in the SB model. Once the measures are computed from the MB model, the SB model is solved again using SB = UMB . The alternating solution of the submodels is repeated until the estimated throughputs converge. This approach is similar to the method of complementary delays [9, 13]. The SB and MB submodels are each similar to Willick and Eager s model [27] except that: 1) transaction routing is according to the cache coherence protocol, 2) the switching network is configured as a two dimensional mesh and the delay per switch is modeled as an average quantity measured ....

P. Heidelberger and K. Trivedi. Analytic Queueing Models for Programs with Internal Concurrency. IEEE Trans. on Computers, C-32(1):73--82, Jan. 1982.

....Rendezvous Network with Two Reference Tasks (the numbers in square brackets are execution times of each entry, by phase, while those in round brackets are the mean numbers of messages from entry to entry, by the phase of the sender. in the context of split join patterns in the execution flow [12, 14, 32]. However (as discussed in [13] splitting and joining of flows is just one of many forms of interdependence in the execution of related tasks. A more detailed approach is to model the tasks and their interactions with Petri Nets [17] and to analyze performance via an appropriate form of Timed ....

P. Heidelberger and K.S. Trivedi, "Analytic Queueing Models for Programs with Internal Concurrency," IEEE Transactions on Computers, Vol. C-32, No. 1, pp. 73--82, January 1983.

....recurrence equations about program timings using Hoare style axioms. Analytic methods include complexity analysis (e.g. 7] micro analysis using difference equations (e.g. 21] Petri nets (e.g. 8, 22] stochastic processes (e.g. 16] stochastic automata [29] queueing networks (e.g. [19]) and analysis of graphs whose nodes represent code segments (e.g. 17, 32] Of these, consistent Petri nets (i.e. nets that return to their initial marking) in which a deterministic firing time is associated with each transition are most related to this paper. Ramamoorthy and Ho [30] consider ....

P. Heidelberger and K. S. Trivedi. Analytic queueing models for programs with internal concurrency. IEEE Trans. on Computers, C-32(1):73--82, Jan. 1983.

....parallel queueing systems. The tightness of these bounds is not investigated. Heidelberger and Trivedi [12] developed an approximate solution with bounds for a queueing network with jobs having computation graphs with a fork phase only (i.e. no synchronization of the completion of the tasks) In [13], the model is extended to contain a fork and join node and two approximation techniques are presented: one is based on a decomposition approach and other is based on an iterative solution method. Stability conditions for fork join queueing networks were investigated by Konstantopoulos and Walrand ....

P. Heidelberger and K.S. Trivedi. Analytic queueing models for programs with internal concurrency. IEEE Trans. Computer, Vol. C-32, pp.73-82, Nov, 1983.

....analysis, hence they can be used for combined hardware software analysis. Some aspects of system hardware are indeed represented in the models described in this paper. Several papers are relevant to our study. Performance modeling of concurrent software has been carried out using Markov chains [11, 12], series parallel graphs [16] queueing networks [28] stochastic rendezvous networks [31, 30] and SPNs [18, 5, 26] A recent study by Leu et al. uses SPNs to model fault tolerant aspects of software [15] Section 2 gives a brief review of the SRN concepts; it also contains an explanation for ....

Heidelberger, P., and Trivedi, K. S. Analytic queueing models for programs with internal concurrency. IEEE Transactions on Computers. C-32, 1 (Jan. 1983), 73-82.

....analysis, hence they can be used for combined hardware software analysis. Some aspects of system hardware are indeed represented in the models described in this paper. Several papers are relevant to our study. Performance modeling of concurrent software has been carried out using Markov chains [11, 12], series parallel graphs [16] queueing networks [28] stochastic rendezvous networks [31, 30] and SPNs [18, 5, 26] A recent study by Leu et al. uses SPNs to model fault tolerant aspects of software [15] Section 2 gives a brief review of the SRN concepts; it also contains an explanation for the ....

Heidelberger, P., and Trivedi, K. S. Analytic queueing models for programs with internal concurrency. IEEE Transactions on Computers. C-32, 1 (Jan. 1983), 73--82.

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Heidelberger, P., Trivedi, S. K. "Analytic queueing models for programs with internal concurrency", IEEE Trans. on Computers, 32, Jan. 1983, pp. 73 -- 82.

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Heidelberger, P., Trivedi, S. K. "Analytic queueing models for programs with internal concurrency", IEEE Trans. on Computers, 32, Jan 1983, pp. 73 -- 82.

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P. Heidelberder and K. S. Trivedi, Analytic Queueing Models for Programs with Internal 25 Concurrency, IEEE Transactions on Computers, pp. 73-82, January 1983.

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P. Heidelberger and K. S. Trivedi. Analytic queueing models for programs with internal concurrency. IEEE Trans. Comp., C-32(1):73-82, Jan. 1983.

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P. Heidelberger and K. S. Trivedi. Analytic queueing models for programs with internal concurrency. IEEE Trans. Comp., C-32(1):73--82, Jan. 1983.

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P. Heidelberger and K.S. Trivedi, #Analytic queueing models for programs with internal concurrency," IEEE Tr. Comp.,vol. C-32, no. 1, Jan. 1983, pp. 73#82.

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