On guaranteed smooth scheduling for input-queued switches.

Input-queued switches are used extensively in the design of high-speed routers. As switch speeds and sizes increase, the design of the switch scheduler becomes a primary challenge, because the time interval for the matching computations needed for determining switch configurations becomes very small. Possible alternatives in scheduler design include increasing the scheduling interval by using envelopes [19], and using a frame-based scheduler that guarantees fixed rates between input-output pairs. However, both these alternatives have significant jitter drawbacks: the jitter increases with the envelope size in the first alternative, and previously-known methods do not guarantee tight jitter bounds in the second. In this paper, we propose a hybrid approach to switch scheduling. Traffic with tight jitter constraints is first scheduled using a frame-based scheduler that achieves low jitter bounds. Jitter-insensitive traffic is later scheduled using an envelope-based scheduler. The main contribution of this paper is a scheduler design for generating low-jitter schedules. The scheduler uses a rate matrix decomposition designed for low jitter and different from the minimum-bandwidth Birkhoff-Von Neumann (BV) decomposition. In addition to generating low-jitter schedules, this decomposition in the worst case yields fewer switch configuration matrices (O(n)) than the BV decomposition (O(n(2))), and so requires far less high-speed switch memory. We develop an efficient algorithm for decomposing the rate matrix and for scheduling the permutation matrices. We prove that our low-jitter algorithm has an O(log n) factor bound on its bandwidth consumption in comparison to the minimum-bandwidth BV decomposition. Experimentally, we find that the bandwidth increase in practice is much lower than the theoretical bound. We also prove several related performance bounds for our scheduler. Finally, we propose a practical algorithm for bandwidth-guaranteed algorithm, and show how our findings could even be extended to systems with large tuning time.