Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
We consider a two-station cascade system in which waiting or externally arriving customers at station 1 move to the station 2 if the queue size of station 1 including an arriving customer itself and a customer being served is greater than a given threshold level
c
1
≥
1
and if station 2 is empty. Assuming that external arrivals are subject to independent renewal processes satisfying certain regularity conditions and service times are
i
.
i
.
d
. at each station, we derive necessary and sufficient conditions for a Markov process describing this system to be positive recurrent in the sense of Harris. This result is extended to the cascade system with a general number
k
of stations in series. This extension requires certain traffic intensities of stations
2
,
3
,
…
,
k
-
1
for
k
≥
3
to be defined. We finally note that the modeling assumptions on the renewal arrivals and
i
.
i
.
d
. service times are not essential if the notion of the stability is replaced by a certain sample path condition. This stability notion is identical with the standard stability if the whole system is described by the Markov process which is a Harris irreducible
T
-process.