Linear stochastic fluid networks

We introduce open stochastic fluid networks that can be regarded as continu ous analogues or fluid limits of open networks of infinite-server queues. R andom exogenous input may come to any of the queues. At each queue, a c.d.f .-valued stochastic process governs the proportion of the input processed b y a given time after arrival. The routeing may be deterministic (a specifie d sequence of successive queue visits) or proportional, i.e. a stochastic t ransition matrix may govern the proportion of the output routed from one qu eue to another. This stochastic fluid network with deterministic c.d.f.s go verning processing at the queues arises as the limit of normalized networks of infinite-server queues with batch arrival processes when the batch size s grow. In this limit, one can think of each particle having an evolution t hrough the network, depending on its time and place of arrival, but otherwi se independent of all other particles. A key property associated with this independence is the linearity: the workload associated with a superposition of inputs, each possibly having its own pattern of flow through the networ k, is simply the sum of the component workloads. As with infinite-server qu eueing models, the tractability makes the linear stochastic fluid network a natural candidate for approximations.