Motivated by the use of high speed circuit switches in large scale data centers, we consider the problem of circuit switch scheduling. In this problem we are given demands between pairs of servers and the goal is to schedule at every time step a matching between the servers while maximizing the total satisfied demand over time. The crux of this scheduling problem is that once one shifts from one matching to a different one a fixed delay @math is incurred during which no data can be transmitted. For the offline version of the problem we present a @math approximation ratio (for any constant @math ). Since the natural linear programming relaxation for the problem has an unbounded integrality gap, we adopt a hybrid approach that combines the combinatorial greedy with randomized rounding of a different suitable linear program. For the online version of the problem we present a (bi-criteria) @math -competitive ratio (for any constant @math ) that exceeds time by an additive factor of @math . We note that no uni-criteria online algorithm is possible. Surprisingly, we obtain the result by reducing the online version to the offline one.
A range of new datacenter switch designs combine wireless or optical circuit technologies with electrical packet switching to deliver higher performance at lower cost than traditional packet-switched networks. These "hybrid" networks schedule large traffic demands via a high-rate circuits and remaining traffic with a lower-rate, traditional packet-switches. Achieving high utilization requires an efficient scheduling algorithm that can compute proper circuit configurations and balance traffic across the switches. Recent proposals, however, provide no such algorithm and rely on an omniscient oracle to compute optimal switch configurations. Finding the right balance of circuit and packet switch use is difficult: circuits must be reconfigured to serve different demands, incurring non-trivial switching delay, while the packet switch is bandwidth constrained. Adapting existing crossbar scheduling algorithms proves challenging with these constraints. In this paper, we formalize the hybrid switching problem, explore the design space of scheduling algorithms, and provide insight on using such algorithms in practice. We propose a heuristic-based algorithm, Solstice that provides a 2.9× increase in circuit utilization over traditional scheduling algorithms, while being within 14 of optimal, at scale. Using optical technology for the design of packet switches routers offers several advantages such as scalability, high bandwidth, power consumption, and cost. However, reconfiguring the optical fabric of these switches requires significant time under current technology (microelectromechanical system mirrors, tunable elements, bubble switches, etc.). As a result, conventional slot-by-slot scheduling may severely cripple the performance of these optical switches due to the frequent fabric reconfiguration that may entail. A more appropriate way is to use a time slot assignment (TSA) scheduling approach to slow down the scheduling rate. The switch gathers the incoming packets periodically and schedules them in batches, holding each fabric configuration for a period of time. The goal is to minimize the total transmission time, which includes the actual traffic-sending process and the reconfiguration overhead. This optical switch scheduling problem is defined in this paper and proved to be NP-complete. In particular, earlier TSA algorithms normally assume the reconfiguration delay to be either zero or infinity for simplicity. To this end, we propose a practical algorithm, ADJUST, that breaks this limitation and self-adjusts with different reconfiguration delay values. The algorithm runs at O( spl lambda N sup 2 logN) time complexity and guarantees 100 throughput and bounded worst-case delay. In addition, it outperforms existing TSA algorithms across a large spectrum of reconfiguration values.