Anthony G Lauck

Time scale analysis and scalability issues for explicit rate allocation in ATM networks

End-to-end rate based congestion management has been extensively studied for control of computer communication networks. We examine some of the properties of end-to-end rate based algorithms for congestion management using explicit rate feedback, to achieve maxmin fair rate allocation in the network. We formulate a requirement on a switchs local rate allocation computation sufficient to ensure convergence of the distributed algorithm to the global maxmin fair rate allocation. We provide an upper bound on the convergence time when the switch algorithm satisfies this requirement. We propose a requirement of feasibility of the transmission rates, maintaining which results in oscillation-free operation of the algorithm while maintaining small queues at the switches. Feasibility implies that the capacity of any of the resources is not exceeded at any time. We suggest a source policy to ensure feasibility of transmission rates, the essence of which is to delay a rate increase by a certain time, while decreasing the transmission rate immediately upon receiving the appropriate feedback. Finally, we seek ways of improving scalability of the computation of maxmin fair rates in the presence of a large number of flows. We suggest using a discrete set of rates, which as we show, reduces the computational complexity and the state requirement at the switches.

Hashed and hierarchical timing wheels: efficient data structures for implementing a timer facility

The performance of timer algorithms is crucial to many network protocol implementations that use timers for failure recovery and rate control. Conventional algorithms to implement an operating system timer module take O(n) time to start or maintain a timer, where n is the number of outstanding timers: this is expensive for large n. This paper shows that by using a circular buffer or timing wheel, it takes O(1) time to start, stop, and maintain timers within the range of the wheel. Two extensions for larger values of the interval are described. In the first, the timer interval is hashed into a slot on the timing wheel. In the second, a hierarchy of timing wheels with different granularities is used to span a greater range of intervals. The performance of these two schemes and various implementation tradeoffs are discussed. We have used one of our schemes to replace the current BSD UNIX callout and timer facilities. Our new implementation can support thousands of outstanding timers without much overhead. Our timer schemes have also been implemented in other operating systems and network protocol packages.