3.4 Why M/G/1 processes are more difficult

For M/G/1-type processes there is no geometric relation among the various probability vectors $\mbox{\boldmath {$\pi$}}^{(i)}$ for $i \geq 1$ as in the case of QBD and GI/M/1-type processes. In this section, we first demonstrate via a simple example why such a geometric relation does not exist and then we generalize and derive Ramaswami's recursive formula, i.e., the classic methodology for the solution of M/G/1 chains.