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60
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 5 (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.
Comparison of Buffer Usage Utilizing Single and Multiple Servers in Network Systems with PowerTail Distributions
, 1997
"... this paper, we will plot using logarithmic scales, usually multiplying by 1ae. The curves are discontinuous because N is an integer function, and have negative slopes for small ae because of the factor 1ae. Figure 5 shows that although the buffer size can become very large as ae ..."
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Cited by 5 (1 self)
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this paper, we will plot using logarithmic scales, usually multiplying by 1ae. The curves are discontinuous because N is an integer function, and have negative slopes for small ae because of the factor 1ae. Figure 5 shows that although the buffer size can become very large as ae
On the Necessity of Transient Performance Analysis in Telecommunication Networks
, 2001
"... This paper discusses potential drawbacks of steadystate parameters, in particular of the steadystate bufferoverflow or cellloss probability. The importance of transient performance analysis is demonstrated for longrange dependent (multiplexed) ON/OFF traffic. A transient parameter pair is propo ..."
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Cited by 5 (0 self)
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This paper discusses potential drawbacks of steadystate parameters, in particular of the steadystate bufferoverflow or cellloss probability. The importance of transient performance analysis is demonstrated for longrange dependent (multiplexed) ON/OFF traffic. A transient parameter pair is proposed as replacement for the steadystate overflow or loss probabilities. The indepth discussion of the behavior of those transient parameters reveals surprising results that allow for characterization and understanding of the fluctuations that are being observed in actual network behavior under traffic loads with longrange dependent properties.
Correlations Induced in a Packet Stream by Background Traffic in a Multiplexed Environment
 In Proceedings of International Teletraffic Congress (ITC
, 2003
"... this paper is the ability to completely characterize the tagged departure process in terms of both first and secondorder statistical properties. The model is also unique in that it incorporates correlations in the packet length distribution as well as the packet interarrival process for each class ..."
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Cited by 4 (2 self)
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this paper is the ability to completely characterize the tagged departure process in terms of both first and secondorder statistical properties. The model is also unique in that it incorporates correlations in the packet length distribution as well as the packet interarrival process for each class of traffic. In particular, the model allows us to study all aspects of multiplexed streams in heavy traffic, and answer the questions posed above
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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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.
Moment characterization of matrix exponential and Markovian arrival processes
 ANN OPER RES
"... This paper provides a general framework for establishing the relation between various moments of matrix exponential and Markovian processes. Based on this framework we present an algorithm to compute any finite dimensional moments of these processes based on a set of required (low order) moments. Th ..."
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Cited by 4 (1 self)
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This paper provides a general framework for establishing the relation between various moments of matrix exponential and Markovian processes. Based on this framework we present an algorithm to compute any finite dimensional moments of these processes based on a set of required (low order) moments. This algorithm does not require the computation of any representation of the given process. We present a series of related results and numerical examples to demonstrate the potential use of the obtained moment relations.
QMAM: a tool for solving infinite queues using matrixanalytic methods, in: ValueTools ’08: Proceedings of the 3rd International Conference on Performance Evaluation Methodologies and Tools, 2008, pp. 1–9. http://dx.doi.org/10.4108/ICST.VALUETOOLS2008.43
 Computer Science Department of the University of Antwerp
"... In this paper we propose a novel MATLAB tool, called QMAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1type, quasibi ..."
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In this paper we propose a novel MATLAB tool, called QMAM, to compute queue length, waiting time and sojourn time distributions of various discrete and continuous time queuing systems with an underlying structured Markov chain/process. The underlying paradigms include M/G/1and GI/M/1type, quasibirthdeath and nonskipfree Markov chains (implemented by the SMCSolver tool), as well as Markov processes with a matrix exponential distribution. We consider various single server queueing systems with phasetype, matrix exponential, Markovian, rational and semiMarkovian arrival and service processes; queues with multiple customer types, where the service depends on the customer type and where consecutive customer types may be correlated; and queues with multiple servers for which the typical dimensionality problem can be avoided. Apart from implementing various classical and more advanced solution techniques, the tool also extends and improves some of the existing solution techniques in a number of cases. 1.
Comparison Of Buffer Usage Utilizing Multiple Servers In Network Systems With PowerTail Distributions
 in Network Systems With PowerTail Distributions. INFORMS97, Boston MA, 30 June2
, 1997
"... We present the results of a parametric study of the buffer size needed to prevent overflow or loss in single and multiple server systems where data arrivals or service times are "bursty", "selfsimilar", or "fractal". Such erratic behavior can be caused (or adequately described) by renewal processes ..."
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Cited by 3 (2 self)
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We present the results of a parametric study of the buffer size needed to prevent overflow or loss in single and multiple server systems where data arrivals or service times are "bursty", "selfsimilar", or "fractal". Such erratic behavior can be caused (or adequately described) by renewal processes whose interarrival distributions are powertail (or Pareto, or L`evy, or "longtail") with infinite variance. We show that power tails can cause problems for intermediate values of the utilization parameter, ae, and become very serious (beyond the usual 1=(1 \Gamma ae) factor) when ae is close to 1, and/or when ff approaches 1. For systems with a powertail arrival distribution and multiple servers(PT/M/C), we gain no performence increase by utilizing multiple Poisson servers. However, for systems with a Poisson arrival rate and powertail service times (M/PT/C), the improvement by using multiple, slower servers over a single faster one can be great indeed. Keywords: Powertail, longtail...
Analytic Model of Performance in Telecommunication Systems, Based on OnOff Traffic Sources with SelfSimilar Behavior
 in 7th International Conference on Telecommunication Systems Modeling and Analysis
, 1999
"... 1 A short review of what we call "Linear Algebraic Queueing Theory (LAQT)" is presented, including the basic formulas for matrix representations of Phase (or `Matrix Exponential') Distributions. SemiMarkov (or Markov Renewal) Processes are then described in this formulation, with particular emphasi ..."
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1 A short review of what we call "Linear Algebraic Queueing Theory (LAQT)" is presented, including the basic formulas for matrix representations of Phase (or `Matrix Exponential') Distributions. SemiMarkov (or Markov Renewal) Processes are then described in this formulation, with particular emphasis on `Markov Modulated Poisson Processes (MMPP).' The MMPP process is then modified to represent ONOFF models with nonexponential holding times (the 1Burst model). A `Truncated PowerTail (TPT)' Distribution with a Phase representation is then described. It is the combination of ONOFF Processes with TPT ONtimes that allows telecommunications systems with selfsimilar and longrange dependent traffic to be modeled analytically as a point process. We then present some results, showing that there is a range of values for the ontime data rate where performance can go rapidly from very good to very bad even while the overall arrival rate is held constant. We then show how this can be extend...
Approximation Models of Wireless Cellular Networks Using Moment Matching
 IEEE JSAC Wireless Communications Series, Vol
, 2000
"... In this paper we present an analytical model for micro and picoceil wireless networks for any arbitrary topology in a high mobility environment. We introduce an approximation technique which uses a single ceil decomposition analysis which incorporates moment matching of handoff processes into the ..."
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In this paper we present an analytical model for micro and picoceil wireless networks for any arbitrary topology in a high mobility environment. We introduce an approximation technique which uses a single ceil decomposition analysis which incorporates moment matching of handoff processes into the ceil. The approximation technique is novel in that it can provide close approximations for nonPoisson arrival traffic and it is easily parallelized. Performance measures such as new cails blocked and handoff cails lost are presented for any general call arrival distribution in a nonhomogeneous traffic environment. We produce some numerical examples for some simple topologies with varying mobility for several call arrival distributions and compare our results to those from simulation studies.