Geodesic
Estimation of the large deviations parameter for a single-channel queueing system with regenerative input flow
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 9-14 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A single-channel queueing system with regenerative input flow is considered. It is assumed that the stability condition is fullfilled. A statistical estimate for the parameter of large deviations of waiting time is proposed. Its consistency and asymptotic normality are proved, the asymptotic confidence interval for the parameter of large deviations is constructed. 
@article{VMUMM_2019_4_a1,
     author = {G. A. Krylova},
     title = {Estimation of the large deviations parameter for a single-channel queueing system with regenerative input flow},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {9--14},
     year = {2019},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a1/}
}
TY  - JOUR
AU  - G. A. Krylova
TI  - Estimation of the large deviations parameter for a single-channel queueing system with regenerative input flow
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2019
SP  - 9
EP  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a1/
LA  - ru
ID  - VMUMM_2019_4_a1
ER  - 
%0 Journal Article
%A G. A. Krylova
%T Estimation of the large deviations parameter for a single-channel queueing system with regenerative input flow
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2019
%P 9-14
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a1/
%G ru
%F VMUMM_2019_4_a1
G. A. Krylova. Estimation of the large deviations parameter for a single-channel queueing system with regenerative input flow. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2019), pp. 9-14. http://geodesic.mathdoc.fr/item/VMUMM_2019_4_a1/

[1] Ganesh A. J., O'Connell N., Wischik D. J., Big queues, Springer, Berlin, 2004 | MR | Zbl

[2] Afanasyeva L. G., Bashtova E. E., Tkachenko A. V., “Large deviations and statistical analysis for queueing systems with regenerative input flow”, 60th World Statistics Congress ISI2015 (Rio de Janeiro, Brazil, 2015), 1–6 | MR

[3] Sadowsky J. S., Szpankowski W., “The probability of large queue lengths and waiting times in a heterogeneous multiserver queue I: tight limits”, Adv. Appl. Probab., 27:2 (1995), 532–566 | DOI | MR | Zbl

[4] Baartfai P., “Large deviations in the queueing theory”, Period. math. hung., 2 (1972), 165–172 | DOI | MR

[5] den Hollander F., Large deviations, Fields Institute Monographs, 14, AMS, Providence, 2000 | MR | Zbl

[6] Majewski K., “Large deviations of the steady-state distribution of reflected processes with applications to queueing systems”, Queueing Systems, 29:2–4 (1998), 351–381 | DOI | MR | Zbl

[7] Wischik D., Moderate deviations in queueing theory, Preprint, 2001 https://www.cl.cam.ac.uk/d̃jw1005/Research/ucl_research/moddev.pdf | Zbl

[8] Aibatov S. Zh., Afanaseva L. G., “Subeskponentsialnaya asimptotika veroyatnostei bolshikh uklonenii dlya sistemy obsluzhivaniya s regeneriruyuschim vkhodyaschim potokom”, Teor. veroyatn. i ee primen., 62:3 (2017), 423–445 | DOI | MR

[9] Aibatov S. Zh., “Veroyatnosti bolshikh uklonenii dlya sistemy M/G/1/$\infty$ s nenadezhnym priborom”, Teor. veroyatn. i ee primen., 61:2 (2016), 378–384 | DOI | MR

[10] Borovkov A. A., Veroyatnostnye protsessy v teorii massovogo obsluzhivaniya, Fizmatlit, M., 1972

[11] Duffield N. G., Lewis J. T., O'Connell N. et al., “Entropy of ATM traffic streams: a tool for estimating QoS parameters”, IEEE J. Selected Areas Communs., 13:6 (1995), 981–990 | DOI

[12] Duffy K. R., Meyn S. P., “Estimating Loynes' exponent”, Queueing Systems, 68:3–4 (2011), 285–293 | DOI | MR | Zbl

[13] Afanasyeva L. G., Bashtova E. E., “Coupling method for asymptotic analysis of queues with regenerative input and unreliable server”, Queueing systems, 76:2 (2014), 125–147 | DOI | MR | Zbl