Underload instabilities in packet networks with flow schedulers

Instability in packet-switching networks is normally associated with overload conditions, since queueing network models show that, in simple configurations, only overload generates instability. However, some results showing that instability can happen also in underloaded queueing networks began to appear about a decade ago. Underload instabilities can be produced by: 1) customer routes that visit the same queues several times; 2) variations of the customer service times at the different queues; and 3) complex scheduling algorithms. We study, using fluid models and adversarial queueing theory, possible underload instabilities due to flow schedulers in packet networks, focusing on output queued switches with strict priority (SP) schedulers and Generalized Processor Sharing (GPS) schedulers. The considered scenarios always refer to acyclic packet routes and consider customer service times that vary only according to channel capacities, thus resembling the approaches being currently considered to provide QoS in the Internet. Our (in)stability results are rather surprising: SP schedulers appear to be more robust than GPS schedulers whenever exact information on the effective average packet flow rates is not available.