Even Slot Transmission in Slotted Optical Packet-Switched Networks

Akbar GhaffarPour Rahbar; Oliver W.W. Yang

doi:10.1364/JOCN.1.00A219

Journal of Optical Communications and Networking
Vol. 1,
Issue 2,
pp. A219-A235
(2009)
•https://doi.org/10.1364/JOCN.1.00A219

Even Slot Transmission in Slotted Optical Packet-Switched Networks

Akbar GhaffarPour Rahbar and Oliver W.W. Yang

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Akbar GhaffarPour Rahbar and Oliver W.W. Yang, "Even Slot Transmission in Slotted Optical Packet-Switched Networks," J. Opt. Commun. Netw. 1, A219-A235 (2009)

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Related Topics
Table of Contents Category
- Optical Networks for the Future Internet
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: November 6, 2008
- Revised Manuscript: January 26, 2009
- Manuscript Accepted: January 29, 2009
- Published: July 1, 2009
Virtual Issues
Journal of Optical Networking Optical Networks for the Future Internet (2009)

Abstract

The issue of transmitting optical packets (called slots in this paper) smoothly toward an egress switch appears to be overlooked in bandwidth access schemes proposed for optical packet-switched (OPS) networks. Here, we explain the benefits of providing an even (smooth) slot transmission and propose four basic metrics and three hybrid metrics to achieve an even slot transmission from an ingress switch of a multiwavelength/fiber slotted OPS network. The even slot transmission can help improve network performance parameters required for Internet applications. An index parameter is also introduced for each method, and a formulation is provided to gauge how even a transmission is among different combinations of frame periods, wavelengths, and fibers. These formulations can provide us with a new approach to relatively compare different bandwidth access schemes in order to determine which scheme can provide an even transmission of traffic to an OPS network. An example is provided for the comparison of two existing bandwidth access schemes in terms of even transmission of traffic.

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Evenness Problem	No. of Items in Set B	No. of Items in Set A
EDF density $({EDF}_{de})$	$β = Z_{i}$	$α = τ$
Load balanced (LB)	$β = \sum_{j = 0}^{n_{e} - 1} Z_{j}$	$α = τ$
Fair dissemination (FD)	$β = \sum_{j = 0}^{n_{e} - 1} Z_{j}$	$α = n_{e}$

	Distribution-a				Distribution-b				Distribution-c
	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index
$X_{DI}^{*}$	0.000	1.714	0.000	—	2.667	1.714	1.714	—	2.400	0.000	1.714	—
$X_{DI}$	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	2.400	2.000	0.000	1.333
$X_{DI}^{\max}$	0.000	0.000	0.000	—	0.667	0.000	0.000	—	2.400	6.000	0.000	—
$X_{DI}^{Norm}$	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	1.000	0.333	0.000	0.444
$X_{DE}^{*}$	3.000	3.750	3.000	—	1.750	4.000	3.750	—	1.750	1.750	3.750	—
$X_{DE}$	0.000	2.000	0.000	0.667	3.750	2.000	2.000	2.583	5.500	5.250	4.500	5.083
$X_{DE}^{\max}$	12.000	12.750	12.000	—	11.750	14.000	12.750	—	11.750	8.750	13.750	—
$X_{DE}^{Norm}$	0.000	0.157	0.000	0.052	0.319	0.143	0.157	0.206	0.468	0.600	0.327	0.465
$X_{LB}^{*}$	—			1.750	—			0.000	—			3.750
$X_{LB}$	—			3.500	—			10.000	—			5.250
$X_{LB}^{\max}$	—			19.500	—			20.000	—			18.000
$X_{LB}^{Norm}$	—			0.179	—			0.500	—			0.292
$X_{FD}^{*}$	—			1.333	—			1.333	—			1.333
$X_{FD}$	—			0.000	—			2.000	—			5.333
$X_{FD}^{\max}$	—			40.000	—			41.333	—			37.333
$X_{FD}^{Norm}$	—			0.000	—			0.048	—			0.143
$H 1$	—			0.026	—			0.103	—			0.455
$H 2$	—			0.077	—			0.235	—			0.400
$H 3$	—			0.058	—			0.189	—			0.336

Evenness Problem	No. of Items in Set B	No. of Items in Set A
EDF density $({EDF}_{de})$	$β = Z_{i}$	$α = τ$
Load balanced (LB)	$β = \sum_{j = 0}^{n_{e} - 1} Z_{j}$	$α = τ$
Fair dissemination (FD)	$β = \sum_{j = 0}^{n_{e} - 1} Z_{j}$	$α = n_{e}$

	Distribution-a				Distribution-b				Distribution-c
	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index	Index for Torrent 1	Index for Torrent 2	Index for Torrent 3	Overall Index
$X_{DI}^{*}$	0.000	1.714	0.000	—	2.667	1.714	1.714	—	2.400	0.000	1.714	—
$X_{DI}$	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	2.400	2.000	0.000	1.333
$X_{DI}^{\max}$	0.000	0.000	0.000	—	0.667	0.000	0.000	—	2.400	6.000	0.000	—
$X_{DI}^{Norm}$	0.000	0.000	0.000	0.000	0.000	0.000	0.000	0.000	1.000	0.333	0.000	0.444
$X_{DE}^{*}$	3.000	3.750	3.000	—	1.750	4.000	3.750	—	1.750	1.750	3.750	—
$X_{DE}$	0.000	2.000	0.000	0.667	3.750	2.000	2.000	2.583	5.500	5.250	4.500	5.083
$X_{DE}^{\max}$	12.000	12.750	12.000	—	11.750	14.000	12.750	—	11.750	8.750	13.750	—
$X_{DE}^{Norm}$	0.000	0.157	0.000	0.052	0.319	0.143	0.157	0.206	0.468	0.600	0.327	0.465
$X_{LB}^{*}$	—			1.750	—			0.000	—			3.750
$X_{LB}$	—			3.500	—			10.000	—			5.250
$X_{LB}^{\max}$	—			19.500	—			20.000	—			18.000
$X_{LB}^{Norm}$	—			0.179	—			0.500	—			0.292
$X_{FD}^{*}$	—			1.333	—			1.333	—			1.333
$X_{FD}$	—			0.000	—			2.000	—			5.333
$X_{FD}^{\max}$	—			40.000	—			41.333	—			37.333
$X_{FD}^{Norm}$	—			0.000	—			0.048	—			0.143
$H 1$	—			0.026	—			0.103	—			0.455
$H 2$	—			0.077	—			0.235	—			0.400
$H 3$	—			0.058	—			0.189	—			0.336

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Journal of Optical Communications and Networking