ABSTRACT
QBD processes were considered. The former work dealt with the case of m < 00 . Later ,
the results were generalized to the case of m � 00 . Besides , they also obtained the counterpart results when A2 has a similar special structure. In this paper , we generalize the results in Gillent and Latouche [2] and Ramaswami and Latouche [ 1 0] to those
Markov chains of the GI/M/l type and the M/G/l type. Many interesting problems
in applications can be formulated into either a GI/M/ l type Markov chain or a M/G/ l
type Markov chain with the special structure. The results in this paper provide an
unified treatment of the shortest queue model with jockeying. This kind of queueing
system has been tackled for many years by using different methods (e .g . Kao and Lin
[3] , Zhao and Grassmann [ 1 2] , Adan , Wessels and Zijm [ 1 ] , Zhao and Grassmann [ 1 3] .
The main results from these papers will b e discussed later i n the paper as an example
