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Longlasting transient conditions in simulations with heavytailed workloads
, 1997
"... Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is nonnegligible. For example, ..."
Abstract

Cited by 73 (5 self)
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Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is nonnegligible. For example, such distributions have been found to describe the lengths of bursts in network traffic and the sizes of files in some systems. As a result, system designers are increasingly interested in employing heavytailed distributions in simulation workloads. Unfortunately, these distributions have properties considerably different from the kinds of distributions more commonly used in simulations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achieving stability in such simulations, using tools from the theory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow convergence to steady state, and high variability at steady state. As a result, we argue that such simulations must be treated as effectively always in a transient condition. One way to address this problem is to introduce the notion of time scale as a parameter of the simulation, and we discuss methods for simulating such systems while explicitly incorporating time scale as a parameter. 1
An Analytic Performance Model Of Parallel Systems That Perform Tasks Using Processors That Can Fail
 IEEE NCA 01 International Symposium on Network Computing and Applications
, 2001
"... We present a family of Markov models for analyzing the performance of parallel /distributed processors that execute a job consisting of N independent tasks in parallel using P processors. The model is a Markov Chain with states representing service and failure rates with k (0 ! k P ) active proc ..."
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Cited by 6 (4 self)
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We present a family of Markov models for analyzing the performance of parallel /distributed processors that execute a job consisting of N independent tasks in parallel using P processors. The model is a Markov Chain with states representing service and failure rates with k (0 ! k P ) active processors. The tasktimes and processor failures are both exponentially distributed. We derive a number of expressions to determine the mean execution time, probability of success, work, and other measurable quantities, all conditioned on the job finishing successfully. A prototype, implemented using an extended version of ACMPI, is used for actual experiments that are based on simulated tasktimes and processor failures. We present our results comparing the analytic model with the prototype for a range of values of processor failure rates. We then discuss extensions of the model and issues related to communication costs, approximations and effect of tasktime distributions.
Transient Model for Jackson Networks and its Application
 Journal of Cluster Computing
, 2003
"... Abstract. Jackson networks have been very successful in so many areas in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since Jackson networks do not apply to systems where there are population ..."
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Cited by 4 (2 self)
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Abstract. Jackson networks have been very successful in so many areas in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since Jackson networks do not apply to systems where there are population size constraints. Also, the productform solution of Jackson networks assumes steady state systems exponential service centers with FCFS queueing discipline. In this paper, we present a transient model for Jackson networks. The model is applicable under any population size. This model can be used to study the transient behavior of Jackson networks and if the number of customers in the network is large enough, the model accurately approaches the productform solution (steady state solution). Finally, an approximation to the transient model using the steady state solution is presented. 1.
Modeling Parallel and Distributed Systems with Finite Workloads
 Journal of Performance Evaluation
, 2004
"... In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determines the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, the ability of Ja ..."
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Cited by 2 (1 self)
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In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determines the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since they do not apply to systems where there are population size constraints. Also, the productform solution of Jackson networks assumes steady state and exponential service centers or certain specialized queueing disciplines. In this paper, we present a transient model for Jackson networks that is applicable to any population size and any finite workload (no new arrivals). Using several Erlangian and Hyperexponential distributions we show to what extent the exponential distribution can be used to approximate other distributions and transient systems with finite workloads. When the number of tasks to be executed is large enough, the model approaches the productform solution (steady state solution). We also, study the case where the nonexponential servers have queueing (Jackson networks can’t be applied). Finally, we show how to use the model to analyze the performance of parallel and distributed systems.
How to Model Telecommunications (and Other) Systems Where "SelfSimilar" Behavior is Observed
, 1997
"... This report gives an overview of Prof. Lipsky's contribution to our current project on traffic statistics during his stay at TUM in June and July 1997. It covers the background review on modeling techniques for selfsimilar behavior and our latest article on demonstrating the importance of powe ..."
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Cited by 2 (1 self)
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This report gives an overview of Prof. Lipsky's contribution to our current project on traffic statistics during his stay at TUM in June and July 1997. It covers the background review on modeling techniques for selfsimilar behavior and our latest article on demonstrating the importance of powertail distributions for such a modeling approach. We primarily concentrated our work on the development and analysis of the socalled N  Burst Process. However, beside that main topic we also investigated other topics which seem to be preliminary to the project's goals at first glance but are essential for developing a deeper insight and understanding of modeling selfsimilar behavior in broadband networks: Among these are ffstable distributions, order statistics of powertail distributions, and last but not least the analysis of correlation on system performance.
Transient Performance Model for Parallel and Distributed Systems
 Proceedings of the 10 th IEEE International Conference on Parallel and Distributed Systems (ICPADS04
, 2004
"... In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determines the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, Jackson networks ..."
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Cited by 1 (0 self)
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In studying or designing parallel and distributed systems one should have available a robust analytical model that includes the major parameters that determines the system performance. Jackson networks have been very successful in modeling parallel and distributed systems. However, Jackson networks have their limitations. In particular, the productform solution of Jackson networks assumes steady state and exponential service centers with certain specialized queueing discipline. In this paper, we present a performance model that can be used to study the transient behavior of parallel and distributed systems with finite workload. When the number of tasks to be executed is large enough, the model approaches the productform of Jackson networks (steady state solution). We show how to use the model to analyze the performance of parallel and distributed systems. We also use the model to show to what extent the productform solution of Jackson networks can be used.
Dynamic Resource Allocation of Computer Clusters With Probabilistic Workloads
"... In many parallel processing systems, particularly realtime systems, it is desirable for jobs to finish as close to a target time as possible. This work examines a method of controlling the variance of job completion times by dynamically allocating resources to jobs that are behind schedule and taki ..."
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In many parallel processing systems, particularly realtime systems, it is desirable for jobs to finish as close to a target time as possible. This work examines a method of controlling the variance of job completion times by dynamically allocating resources to jobs that are behind schedule and taking resources from jobs that are ahead of schedule. Emphasis is placed on where variance enters the system and how well it can be controlled. Controlling the variance also helps meet deadlines because the number of standard deviations between the target and the deadline determines the probability of missing the deadline. 1
LONGLASTING TRANSIENT CONDITIONS IN SIMULATIONS WITH HEAVYTAILED WORKLOADS
"... Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is nonnegligible. For example, s ..."
Abstract
 Add to MetaCart
Recent evidence suggests that some characteristics of computer and telecommunications systems may be well described using heavy tailed distributions — distributions whose tail declines like a power law, which means that the probability of extremely large observations is nonnegligible. For example, such distributions have been found to describe the lengths of bursts in network traffic and the sizes of files in some systems. As a result, system designers are increasingly interested in employing heavytailed distributions in simulation workloads. Unfortunately, these distributions have properties considerably different from the kinds of distributions more commonly used in simulations; these properties make simulation stability hard to achieve. In this paper we explore the difficulty of achieving stability in such simulations, using tools from the theory of stable distributions. We show that such simulations exhibit two characteristics related to stability: slow convergence to steady state, and high variability at steady state. As a result, we argue that such simulations must be treated as effectively always in a transient condition. One way to address this problem is to introduce the notion of time scale as a parameter of the simulation, and we discuss methods for simulating such systems while explicitly incorporating time scale as a parameter. 1