Performance bounds for feedforward queueing networks with upper-constrained inputs

We propose a simple framework for analyzing feedforward queueing networks that have the following features: each customer belongs to a (customer) flow and the route that a customer follows in the network depends on the flow to which he belongs. The amount of traffic fed by a customer flow into the network is bounded by a deterministic subadditive function, which is called a subadditive envelope in this paper. Customers are served according to a FIFO discipline at each queue. We show that the boundary of the virtual-waiting-time distribution at each queue in such networks can be analytically derived, based on the information concerning subadditive envelopes of flows. By using the proposed analysis, we investigate how the envelope of a flow changes when it traverses a series of queues.