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.