How Hard are Steady-State Queueing Simulations?

Ni, Eric C.; Henderson, Shane G.

doi:10.1145/2749460

Cited by 5 publications

(4 citation statements)

References 25 publications

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“…replications of an M/G/n system observed over a time interval of length between 2,000-40,000 depending on the value of n after a warm-up period of length 50-100 to allow the system that started empty to approach steady state. (We remark that the appropriate choices depend on n, largely because the sample size is proportional to both n and t; see Srikant and Whitt 1996, Whitt 1989, and Ni and Henderson 2015 Idle times and periods between successive breaks are collected from all n servers.…”

Section: Statistical Estimationmentioning

confidence: 99%

“…For a random variable X, the first two moments m k ≡ E[X k ], k 1, 2, are estimated by the sample averagesm 1 andm 2 within each replication. Then the overall estimatesm 1 andm 2 are taken to be the sample averages of the r values, which again should be Gaussian; for example, see p. 2 of Ni and Henderson (2015). Hence, again the 95% CIs can be constructed in the same way with t 0.025 (r − 1).…”

Section: Statistical Estimationmentioning

confidence: 99%

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Creating Work Breaks from Available Idleness

Sun

Whitt

2018

M&SOM

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We develop new rules for assigning available service representatives to customers in customer contact centers and other large-scale service systems in order to create effective work breaks for the service representatives from naturally available idleness. These are unplanned breaks occurring randomly over time. We consider both announced breaks as well as unannounced breaks. Our goal is to make the mean and variance of the interval between successive breaks suitably small. Given a target break duration, we propose assigning idle servers based on the elapsed time since their last break. We show that our proposed server-assignment rules are optimal for the many-server heavy-traffic (MSHT) fluid model. Extensive simulation experiments support the proposed serverassignment rules in practical cases and confirm the MSHT approximation formulas when the number of servers is very large.

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Section: Statistical Estimationmentioning

confidence: 99%

Section: Statistical Estimationmentioning

confidence: 99%

Creating Work Breaks from Available Idleness

Sun

Whitt

2018

M&SOM

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“…This result can be used, e.g., to set simulation run lengths to obtain confidence intervals for ζ. See, e.g., [13,22,23].…”

Section: Introductionmentioning

confidence: 99%

Solving Poisson’s equation for birth–death chains: Structure, instability, and accurate approximation

Niño‐Mora

2021

Performance Evaluation

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“…Also, another crtitical decision is about the data points and run length that will provide the steady state outputs. Ni and Henderson (2015) says that the systems with higher utilization (larger ρ), need longer run length to provide accurate estimations of steady state measures.…”

Section: Chapter 2 Literature Reviewmentioning

confidence: 99%

Steady-State Co-Kriging Models

Hemmati¹

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In deterministic computer experiments, a computer code can often be run at different levels of complexity/fidelity and a hierarchy of levels of code can be obtained. The higher the fidelity and hence the computational cost, the more accurate output data can be obtained. Methods based on the co-kriging methodology Cressie (2015) for predicting the output of a high-fidelity computer code by combining data generated to varying levels of fidelity have become popular over the last two decades. For instance, Kennedy and O'Hagan (2000) first propose to build a metamodel for multi-level computer codes by using an auto-regressive model structure. Forrester et al. (2007) provide details on estimation of the model parameters and further investigate the use of co-kriging for multi-fidelity optimization based on the efficient global optimization algorithm Jones et al. (1998). Qian and Wu (2008) propose a Bayesian hierarchical modeling approach for combining lowaccuracy and high-accuracy experiments. More recently, Gratiet and Cannamela (2015) propose sequential design strategies using fast cross-validation techniques for multi-fidelity computer codes. This research intends to extend the co-kriging metamodeling methodology to study steady-state simulation experiments. First, the mathematical structure of co-kriging is extended to take into account heterogeneous simulation output variances. Next, efficient steady-state simulation experimental designs are investigated for co-kriging to achieve a high prediction accuracy for estimation of steady-state parameters. Specifically, designs consisting of replicated longer simulation runs at a few design points and replicated shorter simulation runs at a larger set of design points will be considered. Also, design with no replicated simulation runs at long simulation is studied, along with different methods for calculating the output variance in absence of replicated outputs. Stochastic co-kriging (SCK) method is applied to an M/M/1, as well as an M/M/5 queueing system. In both examples, the prediction performance of the SCK model is promising. It is also shown that the SCK method provides better response surfaces compared to the SK method. "The moving finger writes, and having written moves on. Nor all thy piety nor all thy wit, can cancel half a line of it. " Omar Khayyam iii First, I would like to thank my dear parents, for all the support and love that they have had for me through every single stage of my personal and academic life. They have always made me believe in myself and fly high. I send my gratitude to Professor Majid Jaridi, who has been beyond a professor, my "Patient Stone", making me feel the relief of having a trustworthy and caring person when I am thousands of miles away from my family. I also thank Dr Feng Yang, my advisor and Dr Xi Chen, my committee member, for being really helpful thorough my master studies at West Virginia University and being academically supportive of me through this research.

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How Hard are Steady-State Queueing Simulations?

Cited by 5 publications

References 25 publications

Creating Work Breaks from Available Idleness

Creating Work Breaks from Available Idleness

Solving Poisson’s equation for birth–death chains: Structure, instability, and accurate approximation

Steady-State Co-Kriging Models

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