Estimation of the traffic intensity in a piecewise-stationary Mt/Gt/1 queue with probing

Antunes, Nelson; Jacinto, Gonçalo; Pacheco, Antònio; Wichelhaus, Cornelia

doi:10.1145/3003977.3003979

Cited by 5 publications

(6 citation statements)

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“…(P) [36], [117], [1], [72], [73], [96], [39], [98], [16], [117], [103], [70], [80], [2], [3], [86], [25], [69], [104] Inference for Non-Interacting Systems: This paradigm deals with models where customers don't interact such as the M/G/∞ queue and generalisations.…”

Section: Key Referencesmentioning

confidence: 99%

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A Survey of Parameter and State Estimation in Queues

Asanjarani¹,

Nazarathy²,

Taylor³

2020

Preprint

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We present a broad literature survey of parameter and state estimation for queueing systems. Our approach is based on various inference activities, queueing models, observations schemes, and statistical methods. We categorize these into branches of research that we call estimation paradigms. These include: the classical sampling approach, inverse problems, inference for noninteracting systems, inference with discrete sampling, inference with queueing fundamentals, queue inference engine problems, Bayesian approaches, online prediction, implicit models, and control, design, and uncertainty quantification. For each of these estimation paradigms, we outline the principles and ideas, while surveying key references. We also present various simple numerical experiments. In addition to some key references mentioned here, a periodically-updated comprehensive list of references dealing with parameter and state estimation of queues will be kept in an accompanying annotated bibliography.

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Section: Key Referencesmentioning

confidence: 99%

“…considered the problem of estimating the arrival rate and the service rate of an M/G/1 queue with probing. They also studied the timevarying M t /G t /1 queues in [3]. In [86] Kim et.…”

Section: Inverse Problem Estimationmentioning

confidence: 99%

A Survey of Parameter and State Estimation in Queues

Asanjarani¹,

Nazarathy²,

Taylor³

2020

Preprint

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“…Estimation of the model primitives from queue observations also has important managerial applications, for example in the contexts of demand estimation [4] and dynamic pricing [1]. In [3] the traffic intensity of a non-homogeneous-in-time queue was estimated using a (non-Poisson) probing scheme that depends on the service time of the probes. This list of papers on statistical inference of queueing systems is by no means exhaustive; see [5] for an extensive bibliography of this strand of research.…”

Section: Introductionmentioning

confidence: 99%

Estimating the input of a Lévy-driven queue by Poisson sampling of the workload process

Ravner¹,

Boxma

Mandjes³

2019

Bernoulli

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This paper aims at semi-parametrically estimating the input process to a Lévy-driven queue by sampling the workload process at Poisson times. We construct a method-ofmoments based estimator for the Lévy process' characteristic exponent. This method exploits the known distribution of the workload sampled at an exponential time, thus taking into account the dependence between subsequent samples. Verifiable conditions for consistency and asymptotic normality are provided, along with explicit expressions for the asymptotic variance. The method requires an intermediate estimation step of estimating a constant (related to both the input distribution and the sampling rate); this constant also features in the asymptotic analysis. For subordinator Lévy input, a partial MLE is constructed for the intermediate step and we show that it satisfies the consistency and asymptotic normality conditions. For general spectrally-positive Lévy input a biased estimator is proposed that only uses workload observations above some threshold; the bias can be made arbitrarily small by appropriately choosing the threshold. * To appear in Bernoulli.

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“…The analysis of a queueing system with additional input (probes) is a difficult problem [8]. A small number of works have provided rigorous results for classical queueing systems (e.g., M/M/1, M/G/1, G/M/1), see e.g., [1,2,4]. The idea consists in sending a stream of probes, according to a point process, with a given size distribution.…”

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confidence: 99%