Geodesic
Stability conditions for queueing systems with regenerative flow of interruptions
Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 623-653

Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is focused on the multichannel queueing system with heterogeneous servers, regenerative input flow, and a regenerative process of interruptions. Two service disciplines are studied: preemptive-repeat-different service discipline and preemptive resume service discipline. We consider discrete as well as continuous-time cases. We introduce an auxiliary service flow, which does not depend on the input flow, and construct the common points of regeneration for these two flows. Using such a synchronization method, we establish necessary and sufficient conditions for stability of the system under some additional assumptions. Additionally, under weaker assumptions, we also find the conditions needed for the queue length process to be stochastically bounded.
Keywords: multichannel queueing system, stability, priority, regeneration, synchronization.
Mots-clés : interruption 
@article{TVP_2018_63_4_a0,
     author = {L. G. Afanas'eva and A. W. Tkachenko},
     title = {Stability conditions for queueing systems with regenerative flow of interruptions},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {623--653},
     publisher = {mathdoc},
     volume = {63},
     number = {4},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a0/}
}
TY  - JOUR
AU  - L. G. Afanas'eva
AU  - A. W. Tkachenko
TI  - Stability conditions for queueing systems with regenerative flow of interruptions
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2018
SP  - 623
EP  - 653
VL  - 63
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a0/
LA  - ru
ID  - TVP_2018_63_4_a0
ER  - 
%0 Journal Article
%A L. G. Afanas'eva
%A A. W. Tkachenko
%T Stability conditions for queueing systems with regenerative flow of interruptions
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2018
%P 623-653
%V 63
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a0/
%G ru
%F TVP_2018_63_4_a0
L. G. Afanas'eva; A. W. Tkachenko. Stability conditions for queueing systems with regenerative flow of interruptions. Teoriâ veroâtnostej i ee primeneniâ, Tome 63 (2018) no. 4, pp. 623-653. http://geodesic.mathdoc.fr/item/TVP_2018_63_4_a0/