We outline some recent results related to stability of the basic processes in Jackson type and multiclass networks.
In paricular, we discuss renewal technique in stability (ergodicity) analysis of regenerative networks including weakly regenerative ones, weak and strong instability of the network and also long-term output stability (with respect to input perturbation) of homogeneous Jackson type network. Moreover, we touch upon the simulation aspect of weakly regenerative processes. Weak regeneration assumptions in the networks are considered in details. We are mainly based on the following works:
1. E. Morozov (1997) A renewal technique in ergodic analysis of queues. Preprint 1997-46, Dept. of Mathematics, Chalmers University, Sweden.
2. E. Morozov (1997) The tightness in the ergodic analysis of regenerative queueing processes, Queueing Systems, 27, 179-203.
3. E. Morozov (1998) Instability conditions of open regenerative queueing networks, Preprint 1998:8, Dept. of Math. Statistics, Lund University, Sweden.
4. E. Morozov and S. Sigovtsev (1998) Simulation of queueing processes based on weak regeneration, Journal of Math. Sci., 89, No 5, 1517-1523.
5. E. Morozov (1999) Queueing network stability: an unified approach via renewal technique, Proceedings of the Conf. "Probabilistic Analysis of Rare Events", 125-135, Riga, Latvia.
6. E. Morozov (1999) Long-Run Stability of Queuing Network Output, Research Report 4, Dept. of Math. Statistics, Umea University, Sweden.