ELA, Volume 13, pp. 72-89, March 2005, abstract.
Two-station Queueing Networks with Moving Servers,
Blocking, and Customer Loss
Winfried K. Grassmann and Javad Tavakoli
This paper considers a rather general model involving
two exponential servers, each having its own line.
The first line is unlimited, whereas the second line
can only accommodate a finite number of customers.
Arrivals are Poisson, and they can join either line, and
once finished, they can either leave the system, or they
can join the other line. Since the space for the second
line is limited, some rules are needed to decide what
happens if line 2 is full. Two possibilities are considered
here: either the customer leaves prematurely, or he blocks
the first server. The model also has moving servers, that is,
the server at either station, while idle, can move to help the
server of the other station. This model will be solved by an
eigenvalue method. These eigenvalue methods may also prove
valuable in other contexts.