The model of stalling in queueing system (QS) with two heterogeneous severs is considered, the probabilities of steady states by means of Tchebyshev polynomials of second order are derived. The obtained expressions are stable numerically, their complexity does not depend on the number of states, and they enable us to study QS characteristics analytically. Optimization of a stalling buffer is considered as well and it was shown that stalling helps us to solve the slow server problems under an appropriate choice of stalling buffer size, making a slow server usable under various values of system load. Asymptotic conditions of optimal query distribution in servers are established, when the ratio of capacities of fast and slow channels is increasing. Application of the model developed in computer networks is discussed as well.
Accepté le :
DOI : 10.1051/ro/2018056
Mots-clés : Heterogeneous severs, stalling buffer, queueing system
@article{RO_2019__53_4_1097_0, author = {Kaklauskas, Liudvikas and Sakalauskas, Leonidas and Denisovas, Vitalijus}, title = {Stalling for solving slow server problem}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {1097--1107}, publisher = {EDP-Sciences}, volume = {53}, number = {4}, year = {2019}, doi = {10.1051/ro/2018056}, mrnumber = {3986370}, zbl = {1439.60086}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2018056/} }
TY - JOUR AU - Kaklauskas, Liudvikas AU - Sakalauskas, Leonidas AU - Denisovas, Vitalijus TI - Stalling for solving slow server problem JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2019 SP - 1097 EP - 1107 VL - 53 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2018056/ DO - 10.1051/ro/2018056 LA - en ID - RO_2019__53_4_1097_0 ER -
%0 Journal Article %A Kaklauskas, Liudvikas %A Sakalauskas, Leonidas %A Denisovas, Vitalijus %T Stalling for solving slow server problem %J RAIRO - Operations Research - Recherche Opérationnelle %D 2019 %P 1097-1107 %V 53 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2018056/ %R 10.1051/ro/2018056 %G en %F RO_2019__53_4_1097_0
Kaklauskas, Liudvikas; Sakalauskas, Leonidas; Denisovas, Vitalijus. Stalling for solving slow server problem. RAIRO - Operations Research - Recherche Opérationnelle, Tome 53 (2019) no. 4, pp. 1097-1107. doi : 10.1051/ro/2018056. http://www.numdam.org/articles/10.1051/ro/2018056/
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