On guaranteed smooth scheduling for input-queued switches

Abstract

Abstract-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 [1], and using a framebased 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 yields fewer switch configuration matrices (O(n)) than the BV decomposition (O(n 2 )), and so uses 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 bandwidth-guaranteed algorithm, and show how our findings could even be extended to systems with large tuning time.

Memory requirements for future Internet routers with essentially-perfect QoS guarantees

“…Each flowscheduler selects a flow for service when the corresponding VOQ is selected for service. The problem of scheduling the VOQs in one IQ switch with zero jitter, while minimizing the switch speedup, can be formulated as an NP-HARD integer programming problem [6]. The VOQ traffic rates to be supported by one NxN crossbar switch can be specified in a doubly-stochastic NxN traffic rate matrix Λ.…”

“…This VOQ scheduling problem is NP-HARD and the solution requires a worst-case speedup of O(logN ) [6]. A tractable Greedy Low-Jitter Decomposition (GLJD) with complexity O(N 3 ) and speedup of O(logN ) was also proposed by Bell Labs.…”

“…A tractable Greedy Low-Jitter Decomposition (GLJD) with complexity O(N 3 ) and speedup of O(logN ) was also proposed by Bell Labs. [6].…”

“…A 'tiny buffer rule' [11] states that B = O(logW ), where W is the largest TCP congestion window size, i.e., B ≈ 20-50 IP packets or ≈ 30-75 Kbytes of memory, if three conditions can be met; (a) the jitter of incoming traffic is small, (b) the jitter introduced by IP routers is small, and (c) 10-20% of the throughput is sacrificed. However, the design of a low-jitter scheduling algorithm for the VOQs in an IQ switch with unity speedup is a major unsolved theoretical problem [5][6][7][8], and represents one key challenge to be solved. Furthermore, others have argued that small buffers may cause significant losses, instability or performance degradation at the application layer [12,13].…”

Interference and Power Minimization in TDMA-OFDMA Infrastructure Wireless Mesh Networks

“…Routing and scheduling are key problems in many networks [1]. For example, the problem of scheduling traffic in one crossbar switch or a network of switches to achieve essentially-perfect QoS and 100% throughput under the constraint of unity speedup has remained unsolved for several decades [4][5][6][7][8].…”