| MSC: | 60K25 | Queueing theory |
| 90B22 | Queues and service | |
| 60J10 | Makov chains with discrete parameter |
Abstract:
We introduce and study a new notion of
stability of a stochastic fluid model in terms of random stopping times (partially building
on ideas used by Stolyar \cite{kan-stoly} in his deterministic setting). It may be viewed as an
analog of the original criterion for random $T$'s (which may differ for different
$\varphi$'s). In particular, it is shown that our notion of stability is equivalent to
$L_{p}$-stability for some $p > 1 .$ We consider an example of a polling system with tow
stations and two servers in which the corresponding fluid model may be unstable in the sense
as it was written in (\cite{kan-stoly}) but stable from the generalised viewpoint that we adopt.