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| Authors | I. Adan, M. Mandjes, W. Scheinhardt, E. Tzenova | | Title | On a generic class of two-node queueing systems |
| Journal | Queueing Systems |
| Volume | 61 |
| Year | 2009 |
| Issue | 1 |
| Pages | 37-63 |
| ISSN | 02570130 |
| Faculty | Faculty of Economics and Business |
| Institute/dept. | FEB: Research Institute in Economics and Econometrics Amsterdam (RESAM) |
| Abstract | This paper analyzes a generic class of two-node queueing systems. A first
queue is fed by an on–off Markov fluid source; the input of a second queue is a
function of the state of the Markov fluid source as well, but now also of the first queue
being empty or not. This model covers the classical two-node tandem queue and
the two-class priority queue as special cases. Relying predominantly on probabilistic
argumentation, the steady-state buffer content of both queues is determined (in terms
of its Laplace transform). Interpreting the buffer content of the second queue in terms
of busy periods of the first queue, the (exact) tail asymptotics of the distribution of the
second queue are found. Two regimes can be distinguished: a first in which the state
of the first queue (that is, being empty or not) hardly plays a role, and a second in
which it explicitly does. This dichotomy can be understood by using large-deviations
heuristics. |
| Document type | Article |
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