Enhanced Birkhoff–von Neumann decomposition algorithm for input queued switches

Li, J.; Ansari, Nirwan

doi:10.1049/ip-com:20010618

Cited by 17 publications

(19 citation statements)

References 5 publications

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“…Even for the region where both DOUBLE and ADAPT are feasible (i.e., ), from (15) and (16), it is easy to prove that is always true. Therefore, for the same set of switch parameters , , and , the overall speedup required by ADAPT is always smaller than that required by DOUBLE (except or , where ).…”

Section: B Performance Comparison With Doublementioning

confidence: 99%

“…in (16), in (15), and in (22). For simplicity, we focus on an optical switch with a given switch size and a given reconfiguration overhead .…”

Section: Where (22)mentioning

confidence: 99%

“…Since DOUBLE uses configurations to achieve , from (2) we have (16) ADAPT and DOUBLE are feasible only if and are positive. From (15) and (16) Fig. 2) will be fully occupied by the times of switch reconfigurations, and no time can be left for packet switching.…”

Section: B Performance Comparison With Doublementioning

confidence: 99%

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Minimizing Internal Speedup for Performance Guaranteed Switches With Optical Fabrics

Yeung

Hamdi

et al. 2009

IEEE/ACM Trans. Networking

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Abstract-We consider traffic scheduling in an packet switch with an optical switch fabric, where the fabric requires a reconfiguration overhead to change its switch configurations. To provide 100% throughput with bounded packet delay, a speedup in the switch fabric is necessary to compensate for both the reconfiguration overhead and the inefficiency of the scheduling algorithm. In order to reduce the implementation cost of the switch, we aim at minimizing the required speedup for a given packet delay bound. Conventional Birkhoff-von Neumann traffic matrix decomposition requires 2 2 + 2 configurations in the schedule, which lead to a very large packet delay bound. The existing DOUBLE algorithm requires a fixed number of only 2 configurations, but it cannot adjust its schedule according to different switch parameters. In this paper, we first design a generic approach to decompose a traffic matrix into an arbitrary number of ( 2 2 + 2 ) configurations.Then, by taking the reconfiguration overhead into account, we formulate a speedup function. Minimizing the speedup function results in an efficient scheduling algorithm ADAPT. We further observe that the algorithmic efficiency of ADAPT can be improved by better utilizing the switch bandwidth. This leads to a more efficient algorithm SRF (Scheduling Residue First). ADAPT and SRF can automatically adjust the number of configurations in a schedule according to different switch parameters. We show that both algorithms outperform the existing DOUBLE algorithm.

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Section: B Performance Comparison With Doublementioning

confidence: 99%

“…in (16), in (15), and in (22). For simplicity, we focus on an optical switch with a given switch size and a given reconfiguration overhead .…”

Section: Where (22)mentioning

confidence: 99%

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Minimizing Internal Speedup for Performance Guaranteed Switches With Optical Fabrics

Yeung

Hamdi

et al. 2009

IEEE/ACM Trans. Networking

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“…In the ILP, and are general integer variables [27], is a binary variable, and is the maximum line sum of the matrix The sum of the weights is minimized in (17). Constraints (18) and (19) define each configuration as a permutation matrix.…”

Section: Appendix a Ilp Formulationmentioning

confidence: 99%

“…In fact, traffic matrix decomposition is a classic problem [8]- [17]. Algorithms based on Hall's theorem [14] or Birkhoff-von Neumann decomposition [12], [13], [15]- [17] generate a large number of configurations (e.g., in Birkhoff-von Neumann decomposition), and thus are only favorable in scheduling problems without reconfiguration overhead. For scheduling problems with reconfiguration overhead, greedy algorithms such as LIST [7], [8], [18] and decompositions based on graph theory [7]- [9] are invented with a smaller number of configurations in the schedule.…”

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confidence: 99%

Minimum Delay Scheduling for Performance Guaranteed Switches With Optical Fabrics

Wu¹,

Yeung²,

et al. 2009

J. Lightwave Technol.

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Abstract-We consider traffic scheduling in performance guaranteed switches with optical fabrics to ensure 100% throughput and bounded packet delay. Each switch reconfiguration consumes a constant period of time called reconfiguration overhead, during which no packet can be transmitted across the switch. To minimize the packet delay bound for an arbitrary traffic matrix, the number of switch configurations in the schedule should be no larger than the switch size . This is called minimum delay scheduling, where the ideal minimum packet delay bound is determined solely by the total overhead of the switch reconfigurations. A speedup in the switch determines the actual packet delay bound, which decreases toward the ideal bound as the speedup increases. Our objective is to minimize the required speedup schedule under a given actual packet delay bound. We propose a novel minimum delay scheduling algorithm quasi largest-entry-first (QLEF) to solve this problem. Compared with the existing minimum delay scheduling algorithms MIN and -SCALE, QLEF dramatically cuts down the required schedule bound. For example, QLEF only requires schedule = 17 89 for = 450, whereas MIN and -SCALE require schedule = 37 13 and 27.82, respectively. This gives a significant performance gain of 52% over MIN and 36% over -SCALE.

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A fast hierarchical arbitration scheme for multi-tb/s packet switches with shared memory switching

Popa¹,

Post²,

Noirie³

2009

Bell Labs Tech. J.

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Corporate Alcatel-Lucent journal, Special Issue on Core and Wireless NetworksInternational audienceOne challenge in multi-terabit per second packet switches is the design of low latency and high performance arbitration schemes. In this regard, we propose a hierarchical multi-cell arbiter, which interconnects multiple parallel processing devices. By comparison with iterative non-hierarchical multi-cell arbiters, we show that our scheme significantly decreases the signaling overhead and arbitration processing time. Performance evaluation results show the proposed solution maximizes the switch throughput and delay performance

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Enhanced Birkhoff–von Neumann decomposition algorithm for input queued switches

Cited by 17 publications

References 5 publications

Minimizing Internal Speedup for Performance Guaranteed Switches With Optical Fabrics

Minimizing Internal Speedup for Performance Guaranteed Switches With Optical Fabrics

Minimum Delay Scheduling for Performance Guaranteed Switches With Optical Fabrics

A fast hierarchical arbitration scheme for multi-tb/s packet switches with shared memory switching

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