Asymptotic performance of queue length based network control policies

Abstract

In a communication network, asymptotic quality of service metrics specify the probability that the delay or buffer occupancy becomes large. An understanding of these metrics is essential for providing worst-case delay guarantees, provisioning buffer sizes in networks, and to estimate the frequency of packet-drops due to buffer overflow. Second, many network control tasks utilize queue length information to perform effectively, which inevitably adds to the control overheads in a network. Therefore, it is important to understand the role played by queue length information in network control, and its impact on various performance metrics. In this thesis, we study the interplay between the asymptotic behavior of buffer occupancy, queue length information, and traffic statistics in the context of scheduling, flow control, and resource allocation. First, we consider a single-server queue and deal with the question of how often control messages need to be sent in order to effectively control congestion in the queue. Our results show that arbitrarily infrequent queue length information is sufficient to ensure optimal asymptotic decay for the congestion probability, as long as the control information is accurately received. However, if the control messages are subject to errors, the congestion probability can increase drastically, even if the control messages are transmitted often. Next, we consider a system of parallel queues sharing a server, and fed by a statistically homogeneous traffic pattern. We obtain the large deviation exponent of the buffer overflow probability under the well known max-weight scheduling policy. We also show that the queue length based max-weight scheduling outperforms some well known queue-blind policies in terms of the buffer overflow probability. Finally, we study the asymptotic behavior of the queue length distributions when a mix of heavy-tailed and light-tailed traffic flows feeds a system of parallel queues. We obtain an exact asymptotic queue length characterization under generalized max-weight scheduling. In contrast to the statistically homogeneous traffic scenario, we show that max-weight scheduling leads to poor asymptotic behavior for the light-tailed traffic, whereas a queue-blind priority policy gives good asymptotic behavior.