Instability of FIFO in Session-Oriented Networks

We show that First-In-First-Out (FIFO) can be unstable in the (sigma-rho)- regulated session model for packet-switched networks. In this model packets are injected into the network in fixed sessions. The total size of the session-i packets injected during the time interval (x-y) is at most sigma sub i + rho sub i (y-x) for some burst parameter sigma sub i and rate rho sub i. The sum of the rates of sessions passing through a server is at most the server speed.