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A queueing model with independent arrivals, and its fluid and diffusion limits

Harsha Honnappa, Rahul Jain, Amy R. Ward
2014 Queueing systems  
We introduce the Δ(i)/GI/1 queue, a new queueing model. In this model, customers from a given population independently sample a time to arrive from some given distribution F.  ...  regime switches.  ...  As noted in the remarks after Theorem 2, the queue length process switches between being a 'free' diffusion BB+BM (when the fluid limit model is overloaded), to a 'reflected' diffusion R(BB+BM) (when the  ... 
doi:10.1007/s11134-014-9428-4 fatcat:lgwznhsq5zffxgu4mjbv5p7mgy

Page 9447 of Mathematical Reviews Vol. , Issue 2003m [page]

2003 Mathematical Reviews  
(TR-BILK; Ankara) Diffusion approximation in overloaded switching queueing models. (English summary) Queueing Syst. Theory Appl. 40 (2002), no. 2, 143-182.  ...  The aim of this paper is to extend fluid and diffusion approxi- mation type results to a general class of queueing models of a switching structure.  ... 

Achieving Rapid Recovery in an Overload Control for Large-Scale Service Systems

Ohad Perry, Ward Whitt
2015 INFORMS journal on computing  
The target ratio is chosen to be optimal in a deterministic fluid approximation, assuming a convex holding cost is incurred on the two queues during the overload incident.  ...  In recent papers we considered how two large call centers that are primarily designed to operate independently can help each other in face of an unexpected overload.  ...  sharing, since the diffusion-scaled queue in that case are of order √ n.  ... 
doi:10.1287/ijoc.2015.0642 fatcat:yrtxa2pombb2jhrp5m7glud47i

Averaging methods for transient regimes in overloading retrial queueing systems

V.V. Anisimov
1999 Mathematical and computer modelling  
This approach is based on limit theorems of averaging principle and diffusion approximation types for so-called switching processes. Two models of retrial queueing systems of the types h?  ...  A new approach is suggested to study transient and stable regimes in overloading retrial queueing systems.  ...  regimes of operating for rather complex retrial queueing systems in overloading conditions.  ... 
doi:10.1016/s0895-7177(99)00132-6 fatcat:7cnct4ysmrdm3gu7wvhiqdalye

Switching stochastic models and applications in retrial queues

Vladimir V. Anisimov
1999 TOP - An Official Journal of the Spanish Society of Statistics and Operations Research  
Applications to the asymptotic analysis of overloading state-dependent Markov and semi-Markov queueing models MSM,Q/MsM,Q/1/oo and retrial queueing systems M/G/1/w.r in transient conditions are studied  ...  Limit theorems of Averaging Principle and Diffusion Approximation types are given.  ...  (Diffusion Approximation).  ... 
doi:10.1007/bf02564720 fatcat:ibbbnbk6n5dv7ancxa5xddie5m

Achieving Rapid Recovery in an Overload Control for Large-Scale Service Systems [article]

Ohad Perry, Ward Whitt
2014 arXiv   pre-print
We consider an automatic overload control for two large service systems modeled as multi-server queues, such as call centers.  ...  of the overload suddenly shifts in the opposite direction.  ...  If there is only negligible sharing, as FQR-ART ensures, then such stochastic refinements are well approximated by diffusion limits for the Erlang A model, as in [15] . 7.2. Switching Overloads.  ... 
arXiv:1301.4713v2 fatcat:bhdha5sp4zhrvot6hwt3e4yyze

A Fluid Approximation for Service Systems Responding to Unexpected Overloads

Ohad Perry, Ward Whitt
2011 Operations Research  
Assuming that the identity of the class that will experience the overload or the timing and extent of the overload are unknown, we proposed a queue-ratio control with thresholds: When a weighted difference  ...  In this sequel we focus on the fluid approximation itself and describe its transient behavior, which depends on a heavy-traffic averaging principle.  ...  held a postdoctoral fellowship at Centrum Wiskunde & Informatica (CWI) in Amsterdam.  ... 
doi:10.1287/opre.1110.0985 fatcat:bb3qloh6vnczliivai63a6gjnm

Page 6487 of Mathematical Reviews Vol. , Issue 2000i [page]

2000 Mathematical Reviews  
This approach is based on limit theorems of averaging princi- ple and diffusion approximation types for so-called switching processes.  ...  (TR-BILK-IE; Ankara) Averaging methods for transient regimes in overloading retrial queueing systems. (English summary) Retrial queuing systems. Math. Comput. Modelling 30 (1999), no. 3-4, 65-78.  ... 

Diffusion approximation modeling for Markov modulated bursty traffic and its applications to bandwidth allocation in ATM networks

Qiang Ren, H. Kobayashi
1998 IEEE Journal on Selected Areas in Communications  
The queueing behavior of buffer content is analyzed by applying a diffusion process approximation to the aggregate arrival process.  ...  Simulation results validate our proposed approximation model, showing good fits for distributions and autocorrelation functions of the aggregate rate process and the asymptotic queueing behaviors.  ...  A DIFFUSION APPROXIMATION MODEL AND PERFORMANCE ANALYSIS FOR QUEUE PROCESS In this section we form a diffusion process to approximate the buffer content process of (3) by using the approach discussed in  ... 
doi:10.1109/49.700905 fatcat:xpuc3aimgfhxnguhlf7x5nbgki

Many-server queues with customer abandonment: A survey of diffusion and fluid approximations

J. G. Dai, Shuangchi He
2012 Journal of Systems Science and Systems Engineering  
These results include the performance insensitivity to patience time distributions and diffusion and fluid approximate models as practical tools for performance analysis.  ...  In this survey paper, we focus on / / G GI n GI  parallel-server queues that serve as a building block to model call center operations.  ...  We survey approximate models for many-server queues in Sections 4 and 5. In Section 4, we study diffusion approximations for many-server queues in the QED regime.  ... 
doi:10.1007/s11518-012-5189-y fatcat:evpj7eow4vayvju4mhnllpdpay

Fluid-Flow Approximation in the Analysis of Vast Energy-Aware Networks

Monika Nycz, Tomasz Nycz, Tadeusz Czachórski
2021 Mathematics  
The approach is based on the fluid-flow approximation, which applies first-order differential equations to analyze the evolution of queues and flows.  ...  The paper addresses two issues: (i) modeling dynamic flows transmitted in vast TCP/IP networks and (ii) modeling the impact of energy-saving algorithms.  ...  Data Availability Statement: The modeling results are presented in the article. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/math9243279 fatcat:dm4rr2hjbzgn7byhs32cbk477e

Dynamic fluid-based scheduling in a multi-class abandonment queue

M. Larrañaga, U. Ayesta, I.M. Verloop
2013 Performance evaluation (Print)  
We consider two different models: (1) customers can abandon both while waiting in the queue and while being served, (2) only customers that are in the queue can abandon.  ...  Given the complexity of the stochastic optimization problem we propose a fluid model as a deterministic approximation. For the overload case we directly obtain that thecµ/θ rule is optimal.  ...  Conclusions In this paper, we have proposed a fluid model to obtain an approximative optimal control for a multi-class single server queue with abandonments.  ... 
doi:10.1016/j.peva.2013.08.009 fatcat:is4mzjilmjaxhgdkduboys7sje

Page 4476 of Mathematical Reviews Vol. , Issue 93h [page]

1993 Mathematical Reviews  
I. (1-SUNYS-S) Diffusion approximation for G//G/1 controlled queues. (English summary) Queueing Systems Theory Appl. 12 (1992), no. 3-4, 333-367.  ...  Summary: “A queueing model is considered in which a controller can increase the service rate.  ... 

Asymptotic analysis of queueing systems with reneging: A survey of results for FIFO, single class models

Amy R. Ward
2012 Surveys in Operations Research and Management Science  
The focus of this paper is to survey diffusion approximations for GI/GI/N +GI queueing models with a single customer class and FIFO service, and to understand how the diffusion approximations can be used  ...  In this paper, we survey results for the GI/GI/N + GI queueing model. Our focus is on finding situations in which simple performance measure approximations can be developed.  ...  The proposed approximations for W s appear to be identical in both the overloaded regime for a single-server model in Jennings and Reed [49] and in the overloaded many-server regime in Whitt [90] .  ... 
doi:10.1016/j.sorms.2011.08.002 fatcat:twom2au5arfzljmj2ficyf3yg4

Diffusion Model of a Non-Integer Order PIγ Controller with TCP/UDP Streams

Dariusz Marek, Adam Domański, Joanna Domańska, Jakub Szyguła, Tadeusz Czachórski, Jerzy Klamka
2021 Entropy  
In this article, a way to employ the diffusion approximation to model interplay between TCP and UDP flows is presented.  ...  Our diffusion model allows a single TCP or UDP flow to start or end at any time, which distinguishes it from those previously described in the literature.  ...  In our article [17] , a new model of TCP NewReno based on the diffusion approximation method is developed. The combined diffusion approximation and simulation model is proposed in [25] .  ... 
doi:10.3390/e23050619 pmid:34065734 pmcid:PMC8157166 fatcat:iq2kaq4ldbek5anzfejxv6z4ti
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