Queue inference from periodic reporting data

Frey, Jesse; Kaplan, Edward H.

doi:10.1016/j.orl.2010.05.005

Cited by 12 publications

(6 citation statements)

References 10 publications

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“…The temporal pattern of such state changes may give insight into the number of hidden units. Properties of waiting times to an event have been exploited to estimate the number of units in studies of terrorism, crime, and estimation of epidemiological risk population sizes [45,[95][96][97]. Suppose U is a set of N hidden units in existence at time 0, each of which is at risk of "failure" at some future time.…”

Section: Waiting Timesmentioning

confidence: 99%

Estimating the size of a hidden finite set: Large-sample behavior of estimators

Cheng¹,

Eck²,

Crawford³

2020

Statist. Surv.

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A finite set is "hidden" if its elements are not directly enumerable or if its size cannot be ascertained via a deterministic query. In public health, epidemiology, demography, ecology and intelligence analysis, researchers have developed a wide variety of indirect statistical approaches, under different models for sampling and observation, for estimating the size of a hidden set. Some methods make use of random sampling with known or estimable sampling probabilities, and others make structural assumptions about relationships (e.g. ordering or network information) between the elements that comprise the hidden set. In this review, we describe models and methods for learning about the size of a hidden finite set, with special attention to asymptotic properties of estimators. We study the properties of these methods under two asymptotic regimes, "infill" in which the number of fixed-size samples increases, but the population size remains constant, and "outfill" in which the sample size and population size grow together. Statistical properties under these two regimes can be dramatically different.

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Section: Waiting Timesmentioning

confidence: 99%

Estimating the size of a hidden finite set: Large-sample behavior of estimators

Cheng¹,

Eck²,

Crawford³

2020

Statist. Surv.

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“…[88], [21], [42], [43], [77], [79], [44], [45], [47], [90], [54], [56], [78], [101], [71] Bayesian Approaches: In most of the Bayesian work to date the parameter estimation utilises known queueing performance analysis formulas, considering their posterior distributions given a sensible choice of priors.…”

Section: (T)mentioning

confidence: 99%

“…In [56], Frey and Kaplan considered the case of periodic reporting data, where the arrivals follow a Poisson process with period-specific arrival rates and the data is the number of departures during each period. However, the results of this paper were challenged by Jones in [78] where he showed that queue inference cannot be carried out without knowing service start or stop times.…”

Section: Queue Inference Engine Problemsmentioning

confidence: 99%

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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“…Finally, there are also a number of studies inspired by the "queue inference engine" by Larson (1990). But, instead of inferring the input models, many of these studies use transaction data to estimate the performance of a queueing system directly and hence do not take on the form of an inverse problem (see Mandelbaum and Zeltyn (1998) for a good survey of the earlier literature and Frey and Kaplan (2010) and its references for more recent progress). Several papers estimate both the queueing operational performance and the constituent input models (e.g., Daley and Servi (1998), Kim andPark (2008), Park et al (2011)), and can be considered to belong to both this stream and the aforementioned first stream of literature.…”

Section: Literature Related To Our Problem Settingmentioning

confidence: 99%

Optimization-Based Calibration of Simulation Input Models

Goeva

Lam

Qian

et al. 2019

Operations Research

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Studies on simulation input uncertainty often built on the availability of input data. In this paper, we investigate an inverse problem where, given only the availability of output data, we nonparametrically calibrate the input models and other related performance measures of interest. We propose an optimization-based framework to compute statistically valid bounds on input quantities. The framework utilizes constraints that connect the statistical information of the real-world outputs with the input-output relation via a simulable map. We analyze the statistical guarantees of this approach from the view of data-driven robust optimization, and show how the guarantees relate to the function complexity of the constraints arising in our framework.We investigate an iterative procedure based on a stochastic quadratic penalty method to approximately solve the resulting optimization. We conduct numerical experiments to demonstrate our performance in bounding the input models and related quantities. Daley D, Servi L (1998) Moment estimation of customer loss rates from transactional data. International Journal of Stochastic Analysis 11(3):301-310. Dang CD, Lan G (2015) Stochastic block mirror descent methods for nonsmooth and stochastic optimization. SIAM Journal on Optimization 25(2):856-881. Delage E, Ye Y (2010) Distributionally robust optimization under moment uncertainty with application to data-driven problems. Operations Research 58(3):595-612. Donoho DL, Johnstone IM, Hoch JC, Stern AS (1992) Maximum entropy and the nearly black object. Journal of the Royal Statistical Society. Series B (Methodological) 41-81. Duchi J, Glynn P, Namkoong H (2016) Statistics of robust optimization: A generalized empirical likelihood approach. arXiv preprint arXiv:1610.03425 . Durrett R (2010) Probability: Theory and Examples (Cambridge university press). Esfahani PM, Kuhn D (2015) Data-driven distributionally robust optimization using the wasserstein metric: Performance guarantees and tractable reformulations. arXiv preprint arXiv:1505.05116 . Fan W, Hong LJ, Zhang X (2013) Robust selection of the best. Gao R, Kleywegt AJ (2016) Distributionally robust stochastic optimization with wasserstein distance. arXiv preprint arXiv:1604.02199 . Ghadimi S, Lan G (2013) Stochastic first-and zeroth-order methods for nonconvex stochastic programming. SIAM Journal on Optimization 23(4):2341-2368. Ghadimi S, Lan G (2015) Accelerated gradient methods for nonconvex nonlinear and stochastic programming. Mathematical Programming 1-41. Ghadimi S, Lan G, Zhang H (2016) Mini-batch stochastic approximation methods for nonconvex stochastic composite optimization. Mathematical Programming 155(1-2):267-305. Ghosh S, Lam H (2015a) Computing worst-case input models in stochastic simulation. Available at http://arxiv.org/pdf/1507.05609v1.pdf . Ghosh S, Lam H (2015b) Mirror descent stochastic approximation for computing worst-case stochastic input models. Proceedings of the 2015 Winter Simulation Conference, 425-436 (IEEE Press). 35 Ghosh S, Lam H (2015c) Robust...

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Queue inference from periodic reporting data

Cited by 12 publications

References 10 publications

Estimating the size of a hidden finite set: Large-sample behavior of estimators

Estimating the size of a hidden finite set: Large-sample behavior of estimators

A Survey of Parameter and State Estimation in Queues

Optimization-Based Calibration of Simulation Input Models

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