Stability of Data Networks: Stationary and Bursty Models

This paper studies stability of network models that capture macroscopic features of data communication networks, including the Internet. The network model consists of a set of links and a set of possible routes that are fixed subsets of links. A connection is dynamically established along one of the routes to transmit data as requested and is terminated after the transmission is over. The transmission bandwidth of a link is dynamically allocated, according to specific bandwidth allocation policy, to ongoing connections that traverse the link. A network model is said to be stable under a given bandwidth allocation policy if, roughly, the number of ongoing connections in the network will not blow up over time. We consider a stationary and a bursty network model; the former assumes stochastically stationary arrival processes of connections as did many theoretical studies, while the latter allows more realistic bursty and correlated arrival processes. For both models under a necessary stability condition (i.e., the average offered transmission load on each link is within its bandwidth capacity), we show that the proportionally fair, the minimum potential delay, the max-min fair, and a class of utility-maximizing bandwidth allocation policies ensure network model stability, while some priority-oriented and maximum throughput policies do not. Interestingly, the bandwidth allocation policy that maximizes the arctan(·) utility ensures the stability of the stationary model but not the bursty model. This raises a serious concern about the current practice in the Internet protocol design, since such a policy is thought of as a good approximation of one of the most widely used TCP in the Internet.