A Necessary and Sufficient Condition for the Construction of 2-to-1 Optical FIFO Multiplexers by a Single Crossbar Switch and Fiber Delay Lines

Abstract-Recently, there has been a lot of attention on the constructions of optical queues by using optical Switches and fiber Delay Lines (SDL). In this paper, we consider the constructions of optical queues with a limited number of recirculations through the fibers in such SDL constructions. Such a limitation on the number of recirculations comes from practical feasibility considerations, such as crosstalk, power loss, amplified spontaneous emission (ASE) from the Erbium doped fiber amplifiers (EDFA), and the pattern effect of the optical switches.We first transform the design of the fiber delays in such SDL constructions to an equivalent integer representation problem. Specifically, given 1 ≤ k ≤ M , we seek for an M -sequence d such that there are at most k 1-entries in their C-transforms. Then we give a class of greedy constructions so that d1, d2, . . . , dM are obtained recursively and the maximum number of representable consecutive integers by using d1, d2, . . . , di is larger than that by using d1, d2, . . . , di−1 for all i. Furthermore, we obtain an explicit recursive expression for d1, d2, . . . , dM given by a greedy construction. Finally, we show that an optimal M -sequence (in the sense of achieving the maximum number of representable consecutive integers) can be given by a greedy construction. The solution of such an integer representation problem can be applied to the construction of optical 2-to-1 FIFO multiplexers with a limited number of recirculations. We show that the complexity of searching for an optimal construction can be greatly reduced from exponential time to polynomial time by only considering the greedy constructions instead of performing an exhaustive search. Similar results can be obtained for linear compressors and linear decompressors with a limited number of recirculations.

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“…the constraint that each packet can be routed through at most k of the M fibers by using the packet routing policy in [13].…”

Section: A Class Of Greedy Constructionsmentioning

confidence: 99%

“…For certain optical queues, including 2-to-1 FIFO multiplexers, linear compressors, and linear decompressors, the delay x of a packet is known upon its arrival and the routing of the packet is according to the C-transform [13] C(x) = (I 1 (x), I 2 (x), . .…”

Section: Introductionmentioning

confidence: 99%

On Constructions of Optical Queues with a Limited Number of Recirculations

Cheng

Chang

Chao

et al. 2008

IEEE INFOCOM 2008 - The 27th Conference on Computer Communications

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“…We refer the reader to [1], [2], [3], [4], [5], [6], [7] and the references cited therein. A discrete-time queue with a single input and a single output can be viewed as a switch that maps the time sequence of arrivals to the time sequence of departures.…”

Section: Introductionmentioning

confidence: 99%

Emulation and Approximation of a Flexible Delay Line by Parallel Non-Overtaking Delay Lines

et al. 2009

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Abstract-In this paper we propose to construct an flexible delay line with maximum delay d by parallel non-overtaking delay lines. We show that for a fixed number of non-overtaking delay lines, an optimal policy to minimize packet losses is to assign arriving packets to the non-overtaking delay line that has the largest residual service time while maintaining the FIFO order for each non-overtaking delay lines. Based on this optimal policy we show that to exactly emulate an flexible delay line, one needs (d + 1)/2 non-overtaking delay lines. We also show that if one can tolerate a small packet loss probability, one just needs O( √ d) non-overtaking delay lines. In this case, we show that the residual service times of the non-overtaking delay lines behaved as if they followed the order statistics of uniform random variables.Index Terms-optical buffer, flexible delay line, non-overtaking delay line, optimal policy, order statistics

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“…A multiplexer works like a 'hopper', i.e., it always has a departure packet whenever it is nonempty. It has been proved in [14] that an ( + 2) × ( + 2) feedback switch has the capability to emulate a 2-to-1 FIFO multiplexer of size (2 ).…”

Section: Introductionmentioning

confidence: 99%

A construction of shared optical buffer queue with switched delay lines

Wang

Jiang

Horiguchi

2008

2008 International Conference on High Performance Switching and Routing

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Abstract-Optical buffering is fundamental to contention resolution in optical networks. The current works on this line mainly focus on the emulation of dedicated input/output buffer queue by using switched fiber delay lines (SDL). It is notable that the shared buffer queue, where a common buffer pool is shared by all the input/output ports of a switch, has the potential to significantly reduce the overall buffer capacity requirement. As far as we know, however, no related work is available yet on the exact emulation of a shared optical buffer queue with SDLs.In this paper, we focus on the design of first in first out (FIFO) shared optical buffer queue based on the optical feedback SDL construction. The construction considered consists of an ( + 2) × ( + 2) switch fabric and fiber delay lines FDL1, . . ., FDL , where FDL connects the ℎ output of the switch fabric with its ℎ input. We show that by setting the length of FDL as min( + 1 − , ), = 1, . . . , , such a construction can actually work as an 1-to-2 shared buffer queue. We then extend this emulation to the more general -to-2 case.Index Terms-Shared buffer queue, optical buffer, switched delay line (SDL), fiber delay line (FDL), optical packet switching (OPS).

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A Necessary and Sufficient Condition for the Construction of 2-to-1 Optical FIFO Multiplexers by a Single Crossbar Switch and Fiber Delay Lines

Cited by 53 publications

References 16 publications

On Constructions of Optical Queues with a Limited Number of Recirculations

On Constructions of Optical Queues with a Limited Number of Recirculations

Emulation and Approximation of a Flexible Delay Line by Parallel Non-Overtaking Delay Lines

A construction of shared optical buffer queue with switched delay lines

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