Many‐server loss models with non‐poisson time‐varying arrivals

Whitt, Ward; Zhao, Junhua

doi:10.1002/nav.21741

Cited by 11 publications

(9 citation statements)

References 71 publications

(161 reference statements)

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“…Blocking probabilities and congestion measurement are the most important measures of performance in loss models. Computing these quantities in non-stationary models is rather hard to do requiring approximations [11,13]. As a direct consequence of Theorem 3.4, our next result establishes a fluid limit for the fluid-scaled cumulative number of blocked arrivals,…”

Section: Blocked Arrivalsmentioning

confidence: 64%

“…In the nonstationary setting, in a series of papers [9,10] Lu and Whitt proved a fluid limit for a G t /GI/n + GI queue that experiences alternating periods of overload and underload, by tracking the age of the jobs in the system a la [1]. More broadly, there has been a growing body of work on nonstationary loss models and various approximations, particularly for computing blocking probabilities [11,12,7,13,14]. Our results complement these works by providing fluid limits that characterize the fraction of arrivals that encounter a blocked system.…”

Section: Introductionmentioning

confidence: 99%

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A Many-Server Functional Strong Law For A Non-Stationary Loss Model

Chakraborty¹,

Honnappa²

2019

Preprint

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The purpose of this note is to show that it is possible to establish a many-server functional strong law of large numbers (FSLLN) for the fraction of occupied servers (i.e., the scaled number-in-system) without explicitly tracking either the age or the residual service times of the jobs in a non-Markovian, non-stationary loss model. This considerable analytical simplification is achieved by exploiting a semimartingale representation. The fluid limit is shown to be the unique solution of a Volterra integral equation.

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Section: Blocked Arrivalsmentioning

confidence: 64%

Section: Introductionmentioning

confidence: 99%

A Many-Server Functional Strong Law For A Non-Stationary Loss Model

Chakraborty¹,

Honnappa²

2019

Preprint

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“…Following Whitt and Zhao (2017), we assume the distribution of the arrival process for a single-station G t ∕GI∕∞ queue is approximately Gaussian any given t, by which we mean that the number of arrivals on interval [t, t + 1] is…”

Section: Heavy-traffic Variance For a Single Stationmentioning

confidence: 99%

“…where c 2 a is the variability parameter for the index of dispersion of the arrival process (c 2 a = 1 in case of the Poisson arrival process). Assuming the system starts empty in the distant past, Theorem 2.2 of Whitt and Zhao (2017) states that the workload X(t) follows a normal distribution with the same mean as the M t ∕GI∕∞ queue with arrival rate {𝜆(t)}, but with variance given by…”

Section: Heavy-traffic Variance For a Single Stationmentioning

confidence: 99%

Operations (management) warp speed: Rapid deployment of hospital‐focused predictive/prescriptive analytics for the COVID‐19 pandemic

Shi

Helm

Chen

et al. 2023

Production and Operations Management

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At the onset of the COVID‐19 pandemic, hospitals were in dire need of data‐driven analytics to provide support for critical, expensive, and complex decisions. Yet, the majority of analytics being developed were targeted at state‐ and national‐level policy decisions, with little availability of actionable information to support tactical and operational decision‐making and execution at the hospital level. To fill this gap, we developed a multi‐method framework leveraging a parsimonious design philosophy that allows for rapid deployment of high‐impact predictive and prescriptive analytics in a time‐sensitive, dynamic, data‐limited environment, such as a novel pandemic. The product of this research is a workload prediction and decision support tool to provide mission‐critical, actionable information for individual hospitals. Our framework forecasts time‐varying patient workload and demand for critical resources by integrating disease progression models, tailored to data availability during different stages of the pandemic, with a stochastic network model of patient movements among units within individual hospitals. Both components employ adaptive tuning to account for hospital‐dependent, time‐varying parameters that provide consistently accurate predictions by dynamically learning the impact of latent changes in system dynamics. Our decision support system is designed to be portable and easily implementable across hospital data systems for expeditious expansion and deployment. This work was contextually grounded in close collaboration with IU Health, the largest health system in Indiana, which has 18 hospitals serving over one million residents. Our initial prototype was implemented in April 2020 and has supported managerial decisions, from the operational to the strategic, across multiple functionalities at IU Health.

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“…The modified-offered-load (MOL) approximation has been developed to design staffing functions to control performance functions including the probability of delay (PoD), mean waiting time, and probability of abandonment (PoA). A key step of MOL is to study the corresponding infinite-server queue and to compute its offered-load function (that is the total service resource needed if there were no constraint on the capacity), see He et al (2016), Jennings et al (1996), Yom-Tov and Mandelbaum (2014), Li et al (2016), Liu and Whitt (2012a, 2014b, 2017, Whitt and Zhao (2017). Feldman et al (2008), Defraeye and van Nieuwenhuyse (2013) developed a simulation-based iterative staffing algorithm (ISA).…”

Section: Introductionmentioning

confidence: 99%

Staffing to Stabilize the Tail Probability of Delay in Service Systems with Time-Varying Demand

Liu

2018

Operations Research

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Analytic formulas are developed to set the time-dependent number of servers to stabilize the tail probability of customer waiting times for the G t /GI/s t + GI queueing model, which has a nonstationary non-Poisson arrival process (the G t ), nonexponential service times (the first GI), and allows customer abandonment according to a nonexponential patience distribution (the +GI). Specifically, for any delay target w > 0 and probability target α ∈ (0, 1), we determine appropriate staffing levels (the s t ) so that the time-varying probability that the waiting time exceeds a maximum acceptable value w is stabilized at α at all times. In addition, effective approximating formulas are provided for other important performance functions such as the probabilities of delay and abandonment, and the means of delay and queue length. Many-server heavy-traffic limit theorems in the efficiency-driven regime are developed to show that (i) the proposed staffing function achieves the goal asymptotically as the scale increases, and (ii) the proposed approximating formulas for other performance measures are asymptotically accurate as the scale increases. Extensive simulations show that both the staffing functions and the performance approximations are effective, even for smaller systems having an average of three servers.

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Many‐server loss models with non‐poisson time‐varying arrivals

Cited by 11 publications

References 71 publications

A Many-Server Functional Strong Law For A Non-Stationary Loss Model

A Many-Server Functional Strong Law For A Non-Stationary Loss Model

Operations (management) warp speed: Rapid deployment of hospital‐focused predictive/prescriptive analytics for the COVID‐19 pandemic

Staffing to Stabilize the Tail Probability of Delay in Service Systems with Time-Varying Demand

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