Stability of Networks with Age-Based Scheduling

Aged based scheduling policies, as proposed for network routers or links, give priority to packets belonging to connections having sent a smaller volume of data. Examples of such policies are least attained service (LAS) and multi-level processor sharing (MLPS). These policies have been shown to be efficient in the context of an isolated queue when the distribution of connection sizes has a large variance or a decreasing failure rate. This is the case of Internet connections. The motivation to use such policies is to reduce the mean transfer times for connections, to reduce the number of ongoing connections, and to give precedence to interactive transactions for which users have higher expectation. However it has been argued recently that these policies may lead to network instabilities: the network may become unstable although the average load offered to each resource is smaller than one. In this paper we introduce a packet level model in contrast to flow level models used recently to model resource sharing policies in networks. We extend and generalize former stability properties in queueing networks where priority decreases. These results are used to obtain stability conditions for aged-based policies in data networks. We compare our conclusions with those obtained with flow level models and explain the differences obtained.