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The asymptotic variance rate of the output process of finite capacity birth-death queues

Yoni Nazarathy, Gideon Weiss
2008 Queueing systems  
We analyze the output process of finite capacity birth-death Markovian queues.  ...  We develop a formula for the asymptotic variance rate of the form λ * + v i where λ * is the rate of outputs and v i are functions of the birth and death rates.  ...  Asymptotic variance rate of birth-death queues We now consider a birth and death queue with generator , stationary distribution π and flow rate λ * , as in (3) (4) (5) .  ... 
doi:10.1007/s11134-008-9079-4 fatcat:2hfwv3ja2jbfhoha7df5yggo7i

On the Biological Signalling, Information and Estimation Limits of Birth Processes [article]

Kris Varun Parag
2018 bioRxiv   pre-print
Birth-following is therefore an important reference strategy when the maximum signalling rate is high and the mean rate is no smaller than that of the target molecule.  ...  We investigate these bounds as a function of signalling rate constraints, for problems in which information about a target molecular species, to be estimated, is encoded in the birth rate of a signalling  ...  ACKNOWLEDGEMENTS This work was funded by the Gates Cambridge Trust and the Control Group in the Department of Engineering, University of Cambridge.  ... 
doi:10.1101/319889 fatcat:gy7anljzlzhnbk7rpw5keizzfm

Finite block-length achievable rates for queuing timing channels

Thomas J. Riedl, Todd P. Coleman, Andrew C. Singer
2011 2011 IEEE Information Theory Workshop  
and σ 2 is the asymptotic variance of the underlying Markov chain.  ...  Here, we discuss practical finite-length restrictions on the codewords and attempt to understand the amount of maximal rate that can be achieved for a target error probability.  ...  ACKNOWLEDGEMENTS The authors thank Rüdiger Urbanke for hosting one of the authors at his lab at the École Polytechnique Fédérale de Lausanne for several month and providing great guidance.  ... 
doi:10.1109/itw.2011.6089377 dblp:conf/itw/RiedlCS11 fatcat:ujg2yn7rtffvpew4edylf633dy

The Second Order Terms of the Variance Curves for Some Queueing Output Processes [article]

Sophie Hautphenne, Yoav Kerner, Yoni Nazarathy, Peter Taylor
2013 arXiv   pre-print
We consider queueing output processes of some elementary queueing models such as the M/M/1/K queue and the M/G/1 queue.  ...  insight regarding the BRAVO effect (Balancing Reduces Asymptotic Variance of Outputs).  ...  The linear asymptote is then given by formulas based on the matrix Λ − := (1π − Λ) −1 , where Λ is the generator matrix of the (finite) birth-death process, π is its stationary distribution taken as a  ... 
arXiv:1311.0069v1 fatcat:tjcy3ftpfvei5kidguk67glnbq

The intercept term of the asymptotic variance curve for some queueing output processes

Sophie Hautphenne, Yoav Kerner, Yoni Nazarathy, Peter Taylor
2015 European Journal of Operational Research  
regarding the BRAVO (Balancing Reduces Asymptotic Variance of Outputs) effect.  ...  Further, the discovery of the BRAVO effect (Balancing Reduces Asymptotic Variance of Outputs) has motivated research on the variability of departure processes of queues, particularly in critically loaded  ...  The linear asymptote is then given by formulas based on the matrix − = (1π − ) −1 , where is the generator matrix of the (finite) birth-death process, π is its stationary distribution taken as a row vector  ... 
doi:10.1016/j.ejor.2014.10.051 fatcat:te2zc6k64behjcqz76r55bc7ti

Timing Channel: Achievable Rate in the Finite Block-Length Regime [article]

Thomas J. Riedl, Todd P. Coleman, Andrew C. Singer
2016 arXiv   pre-print
The bound is approximated by C- n^-1/2σ Q^-1(ϵ) where Q denotes the Q-function and σ^2 is the asymptotic variance of the underlying Markov chain. A closed form expression for σ^2 is given.  ...  The exponential server timing channel is known to be the simplest, and in some sense canonical, queuing timing channel. The capacity of this infinite-memory channel is known.  ...  Grassmann proposed this approach in [13] to obtain the asymptotic variance of a continuous time finte state birth death process.  ... 
arXiv:1605.07905v1 fatcat:qpdsdfnt3vfxnc6rgzns2e2fkq

Parameter and State Estimation in Queues and Related Stochastic Models: A Bibliography [article]

Azam Asanjarani, Yoni Nazarathy, Philip K. Pollett
2017 arXiv   pre-print
The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to explore the various types of results that exist.  ...  This bibliography attempts to include all known works that satisfy both of these requirements: -Works that deal with queueing models.  ...  Heckmuller and Wolfinger [127] : Proposes methods to estimate the parameters of arrival processes to G/D/1 queueing systems only based on observed departures from the system.  ... 
arXiv:1701.08338v1 fatcat:57wwewuifndblp7aqkmf6l2aim

BRAVO for many-server QED systems with finite buffers [article]

Daryl J. Daley and Johan S.H. van Leeuwaarden and Yoni Nazarathy
2013 arXiv   pre-print
The results are based on evaluating the limit of a formula for the asymptotic variance of death counts in finite birth--death processes.  ...  This paper demonstrates the occurrence of the feature called BRAVO (Balancing Reduces Asymptotic Variance of Output) for the departure process of a finite-buffer Markovian many-server system in the QED  ...  Consider a finite, irreducible, birth-death process Q(·) on {0, 1, . . . , J} with birth rates λ 0 , λ 1 , . . . , λ J−1 and death rates µ 1 , µ 2 , . . . , µ J .  ... 
arXiv:1308.0933v1 fatcat:asciy6lpxzgnbjqtcnyxqm352y

The variance of departure processes: puzzling behavior and open problems

Yoni Nazarathy
2011 Queueing systems  
Previous results have shown the so-called BRAVO effect occurring in M/M/1/K and GI/G/1 queues: Balancing Reduces Asymptotic Variance of Outputs.  ...  We consider the variability of queueing departure processes.  ...  The bulk of this research was conducted while the author was a post-doctoral researcher at EURANDOM, Eindhoven University of Technology, partly supported by NWO-VIDI grant 639.072.072.  ... 
doi:10.1007/s11134-011-9249-7 fatcat:aymbjnbjdfedbl5q7arbyksnsa

Page 1580 of Mathematical Reviews Vol. 50, Issue 5 [page]

1975 Mathematical Reviews  
Suppose that the number of busy devices can be described by a birth-and-death process I(t).  ...  50 #/11529-11536 An examination is made of the many-dimensional increments of a semi-Markov birth-and-death process. Recursion formulas are obtained for the first two moments of the increment vector.  ... 

BRAVO for Many-Server QED Systems with Finite Buffers

D. J. Daley, Johan S. H. Van Leeuwaarden, Yoni Nazarathy
2015 Advances in Applied Probability  
The results are based on evaluating the limit of an equation for the asymptotic variance of death counts in finite birth-death processes.  ...  This paper demonstrates the occurrence of the feature called BRAVO (balancing reduces asymptotic variance of output) for the departure process of a finite-buffer Markovian many-server system in the QED  ...  Consider a finite, irreducible, birth-death process Q(·) on {0, 1, . . . , J} with birth rates λ 0 , λ 1 , . . . , λ J−1 and death rates µ 1 , µ 2 , . . . , µ J .  ... 
doi:10.1239/aap/1427814589 fatcat:ajjpbebljnc2np6kbyxnnb4vvq

BRAVO for Many-Server QED Systems with Finite Buffers

D. J. Daley, Johan S. H. Van Leeuwaarden, Yoni Nazarathy
2015 Advances in Applied Probability  
The results are based on evaluating the limit of an equation for the asymptotic variance of death counts in finite birth-death processes.  ...  This paper demonstrates the occurrence of the feature called BRAVO (balancing reduces asymptotic variance of output) for the departure process of a finite-buffer Markovian many-server system in the QED  ...  Consider a finite, irreducible, birth-death process Q(·) on {0, 1, . . . , J} with birth rates λ 0 , λ 1 , . . . , λ J−1 and death rates µ 1 , µ 2 , . . . , µ J .  ... 
doi:10.1017/s0001867800007783 fatcat:mpgw4egbnjhzhnmkfr3b44b6ky

The asymptotic variance of departures in critically loaded queues

A. Al Hanbali, M. Mandjes, Y. Nazarathy, W. Whitt
2011 Advances in Applied Probability  
encountered in finite-capacity birth-death queues.  ...  We consider the asymptotic variance of the departure counting process D(t) of the GI/G/1 queue; D(t) denotes the number of departures up to time t.  ...  Núñez Queija (University of Amsterdam) and B. Zwart (CWI) for useful discussions and advice.  ... 
doi:10.1239/aap/1300198521 fatcat:sm2vomrn4ff5bfxmfamitpttsa

statistical multiplexing [chapter]

Martin H. Weik
2000 Computer Science and Communications Dictionary  
A first order autoregressive (AR) process was proposed for the number of bits in successive video frames of a single source. The multiplexed video was modeled by a birth-death Markov process.  ...  The reduction process involved the quantization of the rates and the fundamental rate was chosen to yield the best match to the mean and variance of the rate.  ... 
doi:10.1007/1-4020-0613-6_18211 fatcat:mjo6ctlkqjhcjgjsqfbhbjsxkm

Statistical multiplexing

1982 Microprocessors and microsystems  
A first order autoregressive (AR) process was proposed for the number of bits in successive video frames of a single source. The multiplexed video was modeled by a birth-death Markov process.  ...  The reduction process involved the quantization of the rates and the fundamental rate was chosen to yield the best match to the mean and variance of the rate.  ... 
doi:10.1016/0141-9331(82)90703-7 fatcat:m2wv235qmrcolofj5rfaqlyfc4
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