Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Leeuwaarden, Johan S. H. van; Mathijsen, Britt W. J.; Zwart, Bert

doi:10.1137/17m1133944

Cited by 57 publications

(16 citation statements)

References 159 publications

(210 reference statements)

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“…These limiting results enable us to formulate easy-to-calculate approximations, and allow us to solve capacity allocation problems in the form of optimization problems that generate (close-to-optimal) green times. This adds to the literature of capacity allocation problems [14] and [22] and asymptotic dimensioning of queueing systems [5] and [21].…”

Section: Discussionmentioning

confidence: 99%

“…As far as we are aware, this is the first study that applies this scenario for the FCTL queue. Related scalings in continuous-time single-server queues are referred to as "nearly-deterministic regime" [17,18] and in multi-server settings as the Halfin-Whitt regime or Quality-and-Efficiency-Driven (QED) regime [10,21]. The term QED regime was coined because queueing systems in this regime can deal with high vehicleto-capacity ratios while the probability of no delay stays strictly between 0 and 1.…”

Section: Introductionmentioning

confidence: 99%

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Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Boon¹,

Janssen²,

Leeuwaarden³

et al. 2021

Preprint

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Setting traffic light signals is a classical topic in traffic engineering, and important in heavytraffic conditions when green times become scarce and longer queues are inevitably formed. For the fixed-cycle traffic-light queue, an elementary queueing model for one traffic light with cyclic signaling, we obtain heavy-traffic limits that capture the long-term queue behavior. We leverage the limit theorems to obtain sharp performance approximations for one queue in heavy traffic. We also consider optimization problems that aim for optimal division of green times among multiple conflicting traffic streams. We show that inserting heavy-traffic approximations leads to tractable optimization problems and close-to-optimal signal prescriptions.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Boon¹,

Janssen²,

Leeuwaarden³

et al. 2021

Preprint

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“…Recently, owing to the advancement in computing, different data mining models are proposed. Since the financial markets produce big data in real time, an advantage in competition is the capability to use different modes of data in real time and depict the financial market in the form of data-driven guidelines that are deliverable to business decision-makers [3]. erefore, it is essential to develop a standard process capable of deriving data-driven insights that are directly related to performance in the financial markets.…”

Section: Introductionmentioning

confidence: 99%

Design of Macroeconomic Growth Prediction Algorithm Based on Data Mining

Sun

Yang

Miao

2021

Mobile Information Systems

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With the rapid development of information technology and globalization of economy, financial data are being generated and collected at an unprecedented rate. Consequently, there has been a dire need of automated methods for effective and proficient utilization of a substantial amount of financial data to help in investment planning and decision-making. Data mining methods have been employed to discover hidden patterns and estimate future tendencies in financial markets. In this article, an improved macroeconomic growth prediction algorithm based on data mining and fuzzy correlation analysis is presented. This study analyzes the sequence of economic characteristics, reorganizes the spatial structure of economic characteristics, and integrates the statistical information of economic data. Using the optimized Apriori algorithm, the association rules between macroeconomic data are generated. Distinct features are extracted according to association rules using the joint distribution characteristic quantity of macroeconomic time series. Moreover, the Doppler parameter of macroeconomic time series growth prediction is calculated, and the residual analysis method of the regression model is used to predict the growth of macroeconomic data. Experimental results show that the proposed algorithm has better adaptability, less computation time, and higher prediction accuracy of economic data mining.

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“…In terms of the aggregate traffic load and total service capacity, this scaling corresponds to the so-called Halfin-Whitt heavy-traffic regime which was introduced in the seminal paper [11] and has been extensively studied since. The set-up in [11], as well as the numerous model extensions in the literature (see [7,8,9,11,21,22,23], and the references therein), predominantly concerned a setting with a single centralized queue and server pool (M/M/N), rather than a scenario with parallel queues. Eschenfeldt and Gamarnik [6] initiated the study of the scaling behavior for parallel-server systems in the Halfin-Whitt heavy-traffic regime.…”

Section: Introductionmentioning

confidence: 99%

Join-the-shortest queue diffusion limit in Halfin–Whitt regime: Tail asymptotics and scaling of extrema

Banerjee¹,

Mukherjee²

2019

Ann. Appl. Probab.

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Consider a system of N parallel single-server queues with unit-exponential service time distribution and a single dispatcher where tasks arrive as a Poisson process of rate λ(N). When a task arrives, the dispatcher assigns it to one of the servers according to the Join-the-Shortest Queue (JSQ) policy. Eschenfeldt and Gamarnik (2015) established that in the Halfin-Whitt regime where (N − λ(N))/ √ N → β > 0 as N → ∞, appropriately scaled occupancy measure of the system under the JSQ policy converges weakly on any finite time interval to a certain diffusion process as N → ∞. Recently, it was further established by Braverman (2018) that the convergence result extends to the steady state as well, i.e., stationary occupancy measure of the system converges weakly to the steady state of the diffusion process as N → ∞, proving the interchange of limits result.In this paper we perform a detailed analysis of the steady state of the above diffusion process. Specifically, we establish precise tail-asymptotics of the stationary distribution and scaling of extrema of the process on large time interval. Our results imply that the asymptotic steady-state scaled number of servers with queue length two or larger exhibits an Exponential tail, whereas that for the number of idle servers turns out to be Gaussian. From the methodological point of view, the diffusion process under consideration goes beyond the state-of-the-art techniques in the study of the steady state of diffusion processes. Lack of any closed form expression for the steady state and intricate interdependency of the process dynamics on its local times make the analysis significantly challenging. We develop a technique involving the theory of regenerative processes that provides a tractable form for the stationary measure, and in conjunction with several sharp hitting time estimates, acts as a key vehicle in establishing the results. The technique and the intermediate results might be of independent interest, and can possibly be used in understanding the bulk behavior of the process.

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Economies-of-Scale in Many-Server Queueing Systems: Tutorial and Partial Review of the QED Halfin--Whitt Heavy-Traffic Regime

Cited by 57 publications

References 159 publications

Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Optimal capacity allocation for heavy-traffic fixed-cycle traffic-light queues and intersections

Design of Macroeconomic Growth Prediction Algorithm Based on Data Mining

Join-the-shortest queue diffusion limit in Halfin–Whitt regime: Tail asymptotics and scaling of extrema

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