Networks of Queues

In this chapter we will consider networks of queues. Simple analytical results are usually only possible for Markovian queueing networks. We will start by establishing the product form solution for the equilibrium state probabilities for such networks in section 3.2. The existence of the product form solution basically means that the joint state probability can be expressed as a simple product of functions associated with a network’s individual queues. In the case of open queueing networks of state independent queues these functions are simply the marginal state probabilities so that it seems that the queues act as if they were independent. This interesting observation was first noted by J.R. Jackson [JACK 57] in the original product form paper for open networks in 1957 and later generalized in [JACK 64]. Later, in 1967, W.J. Gordon and G.F. Newell [GORD] demonstrated the existence of the product form solution for closed networks. In 1975 F. Baskett, K.M. Chandy, R.R. Muntz and F.G. Palacios [BASK 75] generalized the families of queueing networks known to have the product form solution.