To batch or not to batch

Alexopoulos,; Goldsman,

doi:10.1109/wsc.2003.1261459

Cited by 6 publications

(5 citation statements)

References 16 publications

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“…The main problem with the method of non-overlapping batch means is to select the batch size q, such that successive batch means are approximately uncorrelated. Different approaches have been proposed in the literature to address this problem (see for example [Chien, 1994;Alexopoulos & Goldsman, 2004;Pawlikowski, 1990]). In SimQPN, we start with a user-configurable initial batch size (by default 200) and then increase it sequentially until the correlation between successive batch means becomes negligible.…”

Section: Methods Of Non-overlapping Batch Meansmentioning

confidence: 99%

On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems

Kounev¹,

Buchmann²

2008

Petri Net, Theory and Applications

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Section: Methods Of Non-overlapping Batch Meansmentioning

confidence: 99%

On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems

Kounev¹,

Buchmann²

2008

Petri Net, Theory and Applications

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“…γji, minimal upper bound on the mean arrival rate at queue i, ρi = Γi/µi, Γ = i≥0,j≥0 γij, uniformization constant of the Markov chain (φ (n) (x, u1→n)) n∈N , τ (x, y) Coupling time of the trajectories starting in states x and y (see (2)) ei Unit vector in direction i of size M , Table 1: Summary of the notation used in the paper. …”

Section: Proof (Of Proposition 2)mentioning

confidence: 99%

Efficiency of simulation in monotone hyper-stable queueing networks

Anselmi

Gaujal

2013

Queueing Syst

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We consider Jackson queueing networks with finite buffer constraints (JQN) and analyze the efficiency of sampling from their stationary distribution. In the context of exact sampling, the monotonicity structure of JQNs ensures that such efficiency is of the order of the coupling time (or meeting time) of two extremal sample paths. In the context of approximate sampling, it is given by the mixing time.Under a condition on the drift of the stochastic process underlying a JQN, which we call hyperstability, in our main result we show that the coupling time is polynomial in both the number of queues and buffer sizes. Then, we use this result to show that the mixing time of JQNs behaves similarly up to a given precision threshold. Our proof relies on a recursive formula relating the coupling times of trajectories that start from network states having 'distance one', and it can be used to analyze the coupling and mixing times of other Markovian networks, provided that they are monotone. An illustrative example is shown in the context of JQNs with blocking mechanisms.

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“…In all subsequent discussions, these are interpreted as being given by approximating rewards computed at a large enough-but finite-time point t, for which convergence in probability does hold. In practice, steady-state rewards are estimated through stochastic simulation using the method of batch means (e.g., see [27], [28]). Equilibrium conditions for the ODE model are based on two criteria that are checked during numerical integration.…”

Section: Steady-state Rewardsmentioning

confidence: 99%

Fluid Rewards for a Stochastic Process Algebra

Tribastone

Ding

Gilmore

et al. 2012

IIEEE Trans. Software Eng.

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Abstract-Reasoning about the performance of models of software systems typically entails the derivation of metrics such as throughput, utilisation, and response time. If the model is a Markov chain, these are expressed as real functions of the chain, called reward models. The computational complexity of reward-based metrics is of the same order as the solution of the Markov chain, making the analysis infeasible when evaluating large-scale systems. In the context of the stochastic process algebra PEPA, the underlying continuous-time Markov chain has been shown to admit a deterministic (fluid) approximation as a solution of an ordinary differential equation, which effectively circumvents state-space explosion. This paper is concerned with approximating Markovian reward models for PEPA with fluid rewards, i.e., functions of the solution of the differential equation problem. It shows that (a) the Markovian reward models for typical metrics of performance enjoy asymptotic convergence to their fluid analogues, and that (b), via numerical tests, the approximation yields satisfactory accuracy in practice.

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To batch or not to batch

Cited by 6 publications

References 16 publications

On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems

On the Use of Queueing Petri Nets for Modeling and Performance Analysis of Distributed Systems

Efficiency of simulation in monotone hyper-stable queueing networks

Fluid Rewards for a Stochastic Process Algebra

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