an:05682296
Zbl 1209.90117
Miyazawa, Masakiyo; Rolski, Tomasz
Tail asymptotics for a L??vy-driven tandem queue with an intermediate input
EN
Queueing Syst. 63, No. 1-4, 323-353 (2009).
00257141
2009
j
90B22 60K25 68M20 90B15
Summary: We consider a L??vy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper, we consider only light-tailed inputs. For the Brownian input case, we derive exact tail asymptotics for the marginal stationary distribution of the second buffer content, while weaker asymptotic results are obtained for the general L??vy input case. The results generalize those of \textit{P. Lieshout} and \textit{M. Mandjes} from recent papers [Math. Methods Oper. Res. 66, No.~2, 275--298 (2007; Zbl 1139.60045); Queueing Syst. 60, No.~3--4, 203--226 (2008; Zbl 1156.90334)] for the corresponding tandem queue without an intermediate input.
Zbl 1139.60045; Zbl 1156.90334