Applications and Some Further Theory

Theorem 4.16, from Section 4.4, gives conditions under which an HL queueing network will be stable. Theorem 4.17, from the same section, gives similar conditions under which a network will be e-stable. In the first three sections of Chapter 5, we will demonstrate stability/e-stability for three families of queueing networks by using these criteria. In Section 5.1, we do this for a family of a networks that includes single class networks, and in Section 5.2, we do this for two families of SBP reentrant lines, FBFS and LBFS. In Section 5.3, we apply the same criteria to FIFO networks of Kelly type.

The material in this chapter relies on a number of papers. The material in the first three sections is mostly from [Br98a], [DaWe96], and [Br96a]. The material in Section 5.4 is mostly from [DaV00], and that in Section 5.5 is mostly from [Da96], [Br99], [DaHV04], and [GaH05].