INPUTS

P(r,i,s,j)

probability that a class $r$ request which completed service at center $i$ is routed to center $j$ as a class $s$ request. Class switching is allowed.

index of class $c$ reference station, $r(c)\; \backslash in\; 1,\; \dots ,\; K$, $1\; \le \; c\; \le \; C$. The class $c$ visit count to server r(c) (V(c,r(c))) is conventionally set to 1. The reference station serves two purposes: (i) its throughput is assumed to be the system throughput, and (ii) a job returning to the reference station is assumed to have completed one cycle. Default is to consider station 1 as the reference station for all classes.

OUTPUTS

V(c,i)

number of visits of class $c$ requests at center $i$.

chain number that class $c$ belongs to. Different classes can belong to the same chain. Chains are numbered sequentially starting from 1 ($1,\; 2,\; \dots$). The total number of chains is max(ch).