Geodesic
Asymptotic characteristics of output flows in queueing networks
Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 1, pp. 36-43

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This paper is devoted to a construction of tail asymptotics of interdeparture intervals in queuing systems. These asymptotics are considered in a case when interarrival intervals and serving times have subexponential distributions. It is shown that such asymptotics depends mainly on heavier considered tail. An influence of the queuing system structure (one-server, multi-server, multi-phase and etc.) on the tails is investigated. Asymptotic of free period tail is investigated. It is proved that in wide assumptions this asymptotic is equivalent to interarrival tail asymptotic independently on the queuing system structure. 
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G. Sh. Tsitsiashvili; N. V. Markova. Asymptotic characteristics of output flows in queueing networks. Dalʹnevostočnyj matematičeskij žurnal, Tome 4 (2003) no. 1, pp. 36-43. http://geodesic.mathdoc.fr/item/DVMG_2003_4_1_a4/