Instability Phenomena in Underloaded Packet Networks with QoS Schedulers

Instability in packet 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 appeared in the literature. Underload instabilities can be produced either by customer routes that visit several times the same queues; or by variations of the customer service times at the different queues; or by complex scheduling algorithms, that bear significant resemblance to the Quality of Service (QoS) schedulers considered today for packet networks, and to the scheduling algorithms used in Input Queued (IQ) switches. Instability phenomena in networks of IQ switches were previously studied. In this paper, we study with fluid models and with adversarial queueing theory the possible underload instabilities due to QoS schedulers in packet networks, focusing on strictpriority schedulers, as well as Generalized Processor Sharing (GPS) schedulers. The considered scenarios always refer to the case of acyclic packet routes, and consider customer service times that vary only according to channel capacities, so that they model the approaches being currently considered to provide QoS in the Internet. Our (in)stability results are rather surprising: packet networks with strict-priority schedulers appear to be more robust than networks with GPS schedulers, whenever exact information on the effective average packet flow rates is not available.