Performance of Dynamic Pump-Wavelength Selection for Optical Packet Switch With Chained Parametric Wavelength Conversion

Nattapong Kitsuwan; Eiji Oki

doi:10.1364/JOCN.6.000165

Journal of Optical Communications and Networking
Vol. 6,
Issue 2,
pp. 165-179
(2014)
•https://doi.org/10.1364/JOCN.6.000165

Performance of Dynamic Pump-Wavelength Selection for Optical Packet Switch With Chained Parametric Wavelength Conversion

Nattapong Kitsuwan and Eiji Oki

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Nattapong Kitsuwan and Eiji Oki, "Performance of Dynamic Pump-Wavelength Selection for Optical Packet Switch With Chained Parametric Wavelength Conversion," J. Opt. Commun. Netw. 6, 165-179 (2014)

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Abstract

This paper proposes a scheme for pump-wavelength selection in an optical packet switch (OPS) with parametric wavelength converters (PWCs). In this scheme, pump wavelengths can be dynamically changed in all time slots, and more than one PWC is allowed to convert a wavelength in a chained manner. The objective of this scheme is to minimize the packet loss rates of the OPS. This scheme is called dynamic pump-wavelength selection with chained parametric wavelength conversion (DPS-C). DPS-C selects the pump wavelength for each PWC so as to maximize the number of successful requests, which refer to packets that wish to be forwarded to their requested output fibers. A PWC, which has the advantage of multiple wavelength conversion, uses a pump wavelength that can be flexibly chosen to define which wavelengths can be converted from/to. The set of original and converted wavelengths, where the pump wavelength is set in the middle of the two wavelengths, is called the conversion pair. Each PWC supports several conversion pairs. The OPS allows each wavelength to be converted using combinations of available conversion pairs, which are not used by any requests, from more than one PWC. A simulation shows that DPS-C outperforms the conventional scheme in terms of packet loss rates in both uniform and nonuniform traffic patterns.

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	One PWC for Conversion	Multiple PWCs for Conversion
Pump wavelength is fixed	SPA [10]	SPA-C [11]
Pump wavelength is adjustable	DPS [12]	DPS-C (proposed)

Symbol	Meaning
$λ_{w}$	Original wavelength
$λ_{w^{'}}$	New wavelength after conversion
$λ_{p}$	Continuous pump wavelength
$Λ_{P}$	Set of pump wavelengths
$N$	Number of input and output fibers
$M$	Number of PWCs
$W$	Number of transmission wavelengths
$m$	Index of PWCs
$w$	Index of transmission wavelengths
$i$	Index of input fibers
$j$	Index of output fibers
$S$	Maximum number of conversion stages
$s$	Index of conversion stages
$p_{m}$	Index of pump wavelength for the $m$ th PWC
$d_{s}$	Index of PWC at the $s$ th conversion stage
$w_{s}$	Converted wavelength of the $w_{s - 1}$ th wavelength produced by the $d_{s}$ th PWC
$R O (i, w, j)$	Request from input fiber $i$ with $λ_{w}$ to output fiber $j$
$R C C (i, w, d_{1}, \dots, d_{s}, j, w^{'})$	Request flag of the $i$ th input fiber at the $w$ th wavelength to $j$ th output fiber at the $w^{'}$ th wavelength via wavelength conversions through $d_{1}, \dots, d_{s}$
$I (i, w)$	Input port of the $i$ th fiber and the $w$ th wavelength
$O (j, w)$	Output port of the $j$ th fiber and the $w$ th wavelength
$C I (d_{s}, w_{s - 1})$	Input port of the $d_{s}$ th PWC carrying the $w_{s - 1}$ th wavelength
$C O (d_{s}, w_{s})$	Output port of the $d_{s}$ th PWC carrying the $w_{s}$ th wavelength
$C_{p_{m}}$	Number of different requests (index of conversion pairs) with the same $p_{m}$
$ρ$	Traffic load
$ρ_{i, j}$	Traffic load from the $i$ th input to the $j$ th output
$α$	Unbalanced probability for unbalanced traffic
$d$	Diagonal probability for diagonal traffic
$h$	Hotspot probability for hotsport traffic

Request Information	Index Pump	Conversion	Requested Pair
( $(i, w, {d}, j, w^{'})$ )	Wavelength ( $p_{1}$ )	Pair	Count ( $C_{p_{1}}$ )
$R C C (3, 3, 1, 2, 1)$	2.0	$1 \leftrightarrow 3$	1
$R C C (3, 3, 1, 2, 2)$	2.5	4 $2 \leftrightarrow 3$	1
$R C C (2, 1, 1, 3, 6)$	3.5	$1 \leftrightarrow 6$	1
$R C C (2, 1, 1, 3, 7)$	4.0	$1 \leftrightarrow 7$	1
$R C C (2, 7, 1, 1, 1)$	4.0	$1 \leftrightarrow 7$
$R C C (2, 7, 1, 1, 3)$	5.0	$3 \leftrightarrow 7$	1
$R C C (3, 3, 1, 2, 7)$	5.0	$3 \leftrightarrow 7$
$R C C (2, 7, 1, 1, 5)$	6.0	$5 \leftrightarrow 7$	1

Request Information	Index Pump	Conversion	Requested Pair
( $(i, w, {d}, j, w^{'})$ )	Wavelength ( $p_{2}$ )	Pair	Count ( $C_{p_{2}}$ )
$R C C (2, 1, 2, 1, 3, 6)$	1.5	$1 \leftrightarrow 2$	1
$R C C (3, 3, 2, 2, 1)$	2.0	$1 \leftrightarrow 3$	1
$R C C (3, 3, 2, 2, 2)$	2.5	$2 \leftrightarrow 3$	1
$R C C (3, 3, 1, 2, 2, 1)$	3.0	$1 \leftrightarrow 5$	1
$R C C (2, 1, 2, 3, 6)$	3.5	$1 \leftrightarrow 6$	2
$R C C (3, 3, 1, 2, 2, 2)$	3.5	$2 \leftrightarrow 5$
$R C C (2, 1, 2, 3, 7)$	4.0	$1 \leftrightarrow 7$	1
$R C C (3, 3, 2, 1, 2, 2)$	4.5	$3 \leftrightarrow 6$	1
$R C C (3, 3, 2, 2, 7)$	5.0	$3 \leftrightarrow 7$	1
$R C C (3, 3, 1, 2, 2, 7)$	6.0	$5 \leftrightarrow 7$	1

	One PWC for Conversion	Multiple PWCs for Conversion
Pump wavelength is fixed	SPA [10]	SPA-C [11]
Pump wavelength is adjustable	DPS [12]	DPS-C (proposed)

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Journal of Optical Communications and Networking