# Predeployment of Transponders for Dynamic Lightpath Provisioning in Translucent Spectrally–Spatially Flexible Optical Networks

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Works

## 3. Network Model

_{1}, s

_{2}, …, s

_{|S|}}. We assume that each slice is of 12.5 GHz width. The transmission of optical signals is provided by means of spectral super-channels (SChs). A SCh can contain a number of optical carriers (OCs), each using ∆

_{OC}frequency slices, where an OC is transmitted/received by one transponder. As proposed in [26] and [27], we assume that ∆

_{OC}= 3 slices, what is equivalent to 37.5 GHz. A set of modulation formats M = {m

_{1}, …, m

_{|M|}} is defined. Each modulation format m ∊ M is characterized by a certain transmission reach and spectral efficiency. Moreover, modulation format m ∊ M can support bit rate g(m) on a single optical carrier.

_{OC}.

- {5, 5, 5, 5}, i.e., every node has 5 transponders, and the lightpath uses transponders in the following way <2, 5, 5, 2> (Figure 2a);
- {10, 0, 0, 10}, i.e., 10 transponders are placed in nodes a and d, and the lightpath uses transponders in the following way <4, 0, 0, 4> (Figure 2b);
- {8, 0, 8, 4}, i.e., 8 transponders are placed in nodes a and c, 4 transponders are placed in node d, and the lightpath uses transponders in the following way <4, 0, 6, 2> (Figure 2c);
- {3, 7, 7, 3}, i.e., 3 transponders are placed in nodes a and d, 7 transponders are placed in nodes b and c, and the lightpath uses transponders in the following way <3, 7, 7, 2> (Figure 2d).

## 4. Algorithms

^{UNI}= ⎿T/│V│⏌.

^{ND}= ⎿T ·nd(v)/∑

_{w}

_{∊V}nd(w)⏌,

^{RO}= ⎿T ·nsp(v)/ ∑

_{w}

_{∊V}nsp(w)⏌,

^{CONF}= ⎿T ·ncsp(v)/ ∑

_{w}

_{∊V}ncsp(w)⏌,

^{COMB}= ⎿0.4·t

^{ND}(v) + 0.4·t

^{ENC}(v) + 0.2·t

^{AD}(v)⏌,

^{ND}(v) = ⎿T ·nd(v)/ ∑

_{w}

_{∊V}nd(w)⏌ denotes the number of transponders assigned to node v according to nodal degree, t

^{ENC}(v) = ⎿T ·enc(v)/ ∑

_{w}

_{∊V}enc(w)⏌ denotes the number of transponders assigned to node v according to number of transponders in the end nodes in the best configuration, and t

^{AD}(v) = ⎿(T ·(1/ad(v))/∑

_{w}

_{∊V}(1/ad(w))⏌ denotes the number of transponders assigned to node v according to number of transponders in the end nodes in the best configuration.

^{SAUR}= ⎿(a(v)·T/∑

_{w}

_{∊V}a(w)⏌,

^{3}) assuming the Floyd–Warshall algorithm. Finally, the time complexity of the two last methods, MSU and SAUR, depend on the execution time of the ARBR algorithm and the size of network traffic to be simulated. However, the final placement of transponders has simple complexity of O(|V|). Thus, the overall complexity of MSU and SAUR can be formulated as O(|V| + time(ARBR)), where time(ARBR) denotes the execution time required to simulate the analyzed traffic with the use of the ARBR method.

## 5. Results

#### 5.1. Simulation Setup

- TP A. The distribution of requests between s–d nodes is uniform, i.e., the source node selection probability is the same for all nodes and the same applies for every node to be chosen as the destination node.
- TP B. The distribution of requests between s–d nodes is inversely proportional to the square root of the distance between node pairs, i.e., the source node selection probability is uniform, but the probability of choosing the destination node is inversely proportional to the square root of the distance between selected source node and each of the remaining nodes.
- TP C. The distribution of requests between s–d nodes is inversely proportional to the distance between node pairs, i.e., the source node selection probability is uniform, but the probability of choosing the destination node is inversely proportional to the distance between selected source node and each of the remaining nodes.
- TP D. The distribution of requests between s–d nodes depends on the square root of two elements: distance between nodes (inversely) and product of population and GDP for given node, i.e., the source node selection probability is proportional to the square root of the product of population and GDP for given node. In turn, the probability of destination node selection is inversely proportional to the square root of the distance between chosen source node and each of the remaining nodes.
- TP E. The distribution of requests between s–d nodes depends on two elements: distance between nodes (inversely) and product of population and GDP for given node, i.e., the source node selection probability is proportional to the product of population and GDP for a given node. In turn, the probability of destination node selection is inversely proportional to the distance between chosen source node and each of the remaining nodes.

#### 5.2. Tuning of the SAUR Algorithm

#### 5.3. Comparison of Algorithms

## 6. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

- Klonidis, D.; Cugini, F.; Gerstel, O.; Jinno, M.; Lopez, V.; Palkopoulou, E. Spectrally and spatially flexible optical network planning and operations. IEEE Commun. Mag.
**2015**, 53, 69–78. [Google Scholar] [CrossRef] - Marom, D.M.; Colbourne, P.D.; D’errico, A.; Fontaine, N.K.; Ikuma, Y.; Proietti, R. Survey of photonic switching architectures and technologies in support of spatially and spectrally flexible optical networking [invited]. IEEE Osa J. Opt. Commun. Netw.
**2017**, 9, 1–26. [Google Scholar] [CrossRef] - Klinkowski, M.; Lechowicz, P.; Walkowiak, K. Survey of resource allocation schemes and algorithms in spectrally-spatially flexible optical networking. Opt. Switch. Netw.
**2018**, 27, 58–78. [Google Scholar] [CrossRef] - Shen, G.; Tucker, R.S. Translucent optical networks: The way forward. IEEE Commun. Mag.
**2007**, 45, 48–54. [Google Scholar] [CrossRef] - Walkowiak, K. Modeling and Optimization of Cloud-Ready and Content-Oriented Networks; Studies in Systems, Decision and Control; Springer: Berlin/Heidelberg, Germany, 2016; Volume 56. [Google Scholar]
- Eira, A.; Santos, J.; Pedro, J.; Pires, J. Multi-objective design of survivable flexible-grid DWDM networks. IEEE Osa J. Opt. Commun. Netw.
**2014**, 6, 326–339. [Google Scholar] [CrossRef] - Fallahpour, A.; Beyranvand, H.; Nezamalhosseini, S.A.; Salehi, J.A. Energy efficient routing and spectrum assignment with regenerator placement in elastic optical networks. J. Lightwave Technol.
**2014**, 32, 2019–2027. [Google Scholar] [CrossRef] - Klinkowski, M.; Walkowiak, K. On performance gains of flexible regeneration and modulation conversion in translucent elastic optical networks with super-channel transmission. J. Lightwave Technol.
**2016**, 34, 5485–5495. [Google Scholar] [CrossRef] - Zami, T.; Morea, A.; Pesic, J. Benefit of progressive deployment of regenerators along with traffic growth in WDM elastic networks. In Proceedings of the Optical Fiber Communication Conference OFC, Tu2F.3, San Diego, CA, USA, 11–15 March 2018. [Google Scholar]
- Morea, A.; Zami, T. Optimized Regenerator Placement in Elastic Optical Networks. In Proceedings of the 2017 European Conference on Optical Communication (ECOC), Gothenburg, Sweden, 17–21 September 2017. [Google Scholar]
- Walkowiak, K.; Lechowicz, P.; Klinkowski, M. Dynamic Routing in Spectrally-Spatially Flexible Optical Networks with Back-to-Back Regeneration. IEEE/Osa J. Opt. Commun. Netw.
**2018**, 10, 523–534. [Google Scholar] [CrossRef] - Walkowiak, K.; Klinkowski, M. Predeployment of Transceivers for Dynamic Lightpath Provisioning in Translucent Flexgrid Optical Networks. In Proceedings of the Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 11–15 March 2018. [Google Scholar]
- Chen, S.; Ljubic, I.; Raghavan, S. The regenerator location problem. Networks
**2010**, 55, 205–220. [Google Scholar] [CrossRef] [Green Version] - Yang, X.; Ramamurthy, B. Sparse regeneration in translucent wavelength-routed optical networks: Architecture, network design and wavelength routing. Photonic Netw. Commun.
**2005**, 10, 39–53. [Google Scholar] [CrossRef] [Green Version] - Garcia-Manrubia, B.; Pavon-Marino, P.; Aparicio-Pardo, R.; Klinkowski, M.; Careglio, D. Offline Impairment-Aware RWA and Regenerator Placement in Translucent Optical Networks. J. Lightwave Technol.
**2011**, 29, 265–277. [Google Scholar] [CrossRef] [Green Version] - Flammini, M.; Marchetti-Spaccamela, A.; Monaco, G.; Moscardelli, L.; Zaks, S. On the Complexity of the Regenerator Placement Problem in Optical Networks. IEEE Acm Trans. Netw.
**2011**, 19, 498–511. [Google Scholar] [CrossRef] - Chaves, D.A.; Carvalho, R.V.; Pereira, H.A.; Bastos-Filho, C.J.; Martins-Filho, J.F. Novel strategies for sparse regenerator placement in translucent optical networks. Photonic Netw. Commun.
**2012**, 24, 237–251. [Google Scholar] [CrossRef] - Pedro, J. Predeployment of regenerators for fast service provisioning in DWDM transport networks. IEEE/Osa J. Opt. Commun. Netw.
**2015**, 7, A190–A199. [Google Scholar] [CrossRef] - Klinkowski, M. On the effect of regenerator placement on spectrum usage in translucent Elastic Optical Networks. In Proceedings of the 14th International Conference on Transparent Optical Networks ICTON, Coventry, UK, 2–5 July 2012; pp. 1–6. [Google Scholar]
- Nag, A.; Tornatore, M.; Mukherjee, B. On the effect of channel spacing, launch power, and regenerator placement on the design of mixed-line-rate optical networks. Opt. Switch. Netw.
**2013**, 10, 301–311. [Google Scholar] [CrossRef] - Aibin, M.; Walkowiak, K. Regenerator placement algorithms for cloud-ready Elastic Optical Networks. In Proceedings of the 17th International Conference on Transparent Optical Networks ICTON, Budapest, Hungary, 5–9 July 2015; pp. 1–4. [Google Scholar]
- Madani, F.M. Scalable Framework for Translucent Elastic Optical Network Planning. J. Lightwave Technol.
**2016**, 34, 1086–1097. [Google Scholar] [CrossRef] - Brasileiro, Í.; Valdemir, J.; Soares, A. Regenerator Assignment with circuit invigorating. Opt. Switch. Netw.
**2019**, 34, 58–66. [Google Scholar] [CrossRef] - Cavalcante, M.A.; Pereira, H.A.; Chaves, D.A.R.; Almeida, R.C., Jr. An auxiliary-graph-based methodology for regenerator assignment problem optimization in translucent elastic optical networks. Opt. Fiber Technol.
**2019**, 53, 102008. [Google Scholar] [CrossRef] - da Silva, E.F.; Almeida, R.C.; Pereira, H.A.; Chaves, D.A. Assessment of novel regenerator assignment strategies in dynamic translucent elastic optical networks. Photonic Netw. Commun.
**2020**, 39, 54–69. [Google Scholar] [CrossRef] - Rottondi, C.; Boffi, P.; Martelli, P.; Tornatore, M. Routing, modulation format, baud rate and spectrum allocation in optical metro rings with flexible grid and few-mode transmission. J. Lightwave Technol.
**2017**, 35, 61–70. [Google Scholar] [CrossRef] [Green Version] - Khodashenas, P.S.; Rivas-Moscoso, J.M.; Siracusa, D.; Pederzolli, F.; Shariati, B.; Klonidis, D. Comparison of spectral and spatial super-channel allocation schemes for SDM networks. J. Lightwave Technol.
**2016**, 34, 2710–2716. [Google Scholar] [CrossRef] - Walkowiak, K.; Klinkowski, M.; Lechowicz, P. Scalability Analysis of Spectrally-Spatially Flexible Optical Networks with Back-to-Back Regeneration. In Proceedings of the 20th International Conference on Transparent Optical Networks ICTON, Bucharest, Romania, 1–5 July 2018. [Google Scholar]
- Christodoulopoulos, K.; Soumplis, P.; Varvarigos, E. Planning flexible optical networks under physical layer constraints. IEEE Osa J. Opt. Commun. Netw.
**2013**, 5, 1296–1312. [Google Scholar] [CrossRef] - Orlowski, S.; Pióro, M.; Tomaszewski, A.; Wessäly, R. SNDlib 1.0—Survivable network design library. Proceedings of the 3rd International Network Optimization Conference INOC 2007. Available online: http://sndlib.zib.de (accessed on 1 February 2019).
- Deore, A.; Turkcu, O.; Ahuja, S.; Hand, S.J.; Melle, S. Total cost of ownership of WDM and switching architectures for next-generation 100Gb/s networks. IEEE Commun. Mag.
**2012**, 50, 179–187. [Google Scholar] [CrossRef]

**Figure 1.**Provisioning of a 200 Gbit/s lightpath without back-to-back (B2B) regeneration (case A) and with B2B regeneration (case B). The following modulation formats are applied: BPSK (Binary Phase Shift Keying), QPSK (Quadrature Phase Shift Keying), and 16-QAM (Quadrature Amplitude Modulation).

**Figure 2.**Example of different transponder placement scenarios for provisioning a request: a) placement of transponders in network nodes: {5, 5, 5, 5}; b) placement of transponders in network nodes: {10, 0, 0, 10}; c) placement of transponders in network nodes: {8, 0, 8, 4}; d) placement of transponders in network nodes: {3, 7, 7, 3}.

**Figure 6.**Tuning of the SAUR algorithm—accepted traffic as a function of tuning parameter β for the US26 network with different traffic profiles: (

**a**) 10,000 transponders, (

**b**) 20,000 transponders.

**Figure 7.**Tuning of the SAUR algorithm—accepted traffic as a function of tuning parameter β for the Euro28 network with different traffic profiles: (

**a**) 10,000 transponders, (

**b**) 20,000 transponders.

**Figure 8.**Placement of transponders in nodes of network US26 for traffic profile TP A as a function of various algorithms.

**Figure 9.**Placement of transponders in nodes of network US26 for traffic profile TP B as a function of various algorithms.

**Figure 10.**Placement of transponders in nodes of network US26 for traffic profile TP C as a function of various algorithms.

**Figure 11.**Utilization of spectrum and transponders and average number of regeneration points for the US26 network and TP A as a function of various algorithms and number of transponders.

**Figure 12.**Utilization of spectrum and transponders and average number of regeneration points for the US26 network and TP B as a function of various algorithms and number of transponders.

**Figure 13.**Utilization of spectrum and transponders and average number of regeneration points for the US26 network and TP C as a function of various algorithms and number of transponders.

**Figure 14.**Box graph with placement of transponders given by: (

**a**) UNI and (

**b**) SAUR algorithms, for the US26 network, TP A, and 15,000 transponders. The dotted line shows the number of transponders in each node according to a particular algorithm. The red line represents the average observed values of transponder usage, while the boxes show data through their quartiles.

**Figure 15.**Box graph with placement of transponders given by: (

**a**) UNI and (

**b**) SAUR algorithms, for the US26 network, TP B, and 15,000 transponders. The dotted line shows the number of transponders in each node according to a particular algorithm. The red line represents the average observed values of transponder usage, while the boxes show data through their quartiles.

**Figure 16.**Box graph with placement of transponders given by: (

**a**) UNI and (

**b**) SAUR algorithms, for the US26 network, TP C, and 15,000 transponders. The dotted line shows the number of transponders in each node according to a particular algorithm. The red line represents the average observed values of transponder usage, while the boxes show data through their quartiles.

**Table 1.**Transmission reaches (km) and supported bit rates (Gb/s) per one transponder for considered modulation formats.

Modulation Format | Reach (km) | Bit Rate Supported by One Transponder (Gb/s) |
---|---|---|

BPSK | 6300 | 50 |

QPSK | 3500 | 100 |

8-QAM | 1200 | 150 |

16-QAM | 600 | 200 |

**Table 2.**Tuning of the SAUR algorithm—values of the scaling parameter yielding the best result as a function of different number of transponders (TRXs) and various traffic profiles (TP)

Number of TRXs | US26 Network | Euro28 Network | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

TP A | TP B | TP C | TP D | TP E | TP A | TP B | TP C | TP D | TP E | |

10,000 | 1.4 | 1.4 | 1.0 | 1.2 | 1.0 | 1.4 | 1.4 | 1.0 | 1.0 | 0.8 |

15,000 | 1.6 | 1.4 | 1.2 | 1.2 | 1.0 | 2.0 | 1.4 | 1.0 | 1.2 | 1.2 |

20,000 | 2 | 1.4 | 1.0 | 1.4 | 0.8 | 2.0 | 1.8 | 1.4 | 1.6 | 0.8 |

Network | US26 | Euro28 | ||||
---|---|---|---|---|---|---|

Number of TRX | 10,000 | 15,000 | 20,000 | 10,000 | 15,000 | 20,000 |

UNI | 2.6 | 3 | 4.2 | 2.2 | 3.6 | 4.8 |

ND | 4.8 | 5 | 4.4 | 5 | 5 | 4 |

RO | 7 | 7 | 7 | 7 | 7 | 7 |

CONF | 6 | 6 | 6 | 6 | 6 | 5.4 |

COMB | 2.8 | 2.6 | 3.2 | 3.2 | 2.8 | 3.8 |

MSU | 3.8 | 3.4 | 2.2 | 3.6 | 2.6 | 2 |

SAUR | 1 | 1 | 1 | 1 | 1 | 1 |

**Table 4.**Comparison of algorithms for various number of transponders and traffic profiles, US26 network in terms of the accepted traffic expressed in NTUs (network traffic units).

TP | Accepted Traffic (NTUs) | Distance to SAUR | |||||
---|---|---|---|---|---|---|---|

UNI | COMB | MSU | SAUR | UNI | COMB | MSU | |

10,000 transponders | |||||||

A | 1149 | 1178 | 927 | 1235 | 6.9% | 4.6% | 24.9% |

B | 1310 | 1322 | 1076 | 1364 | 4.0% | 3.1% | 21.2% |

C | 1429 | 1428 | 1242 | 1482 | 3.6% | 3.7% | 16.2% |

D | 1072 | 1041 | 968 | 1258 | 14.8% | 17.2% | 23.0% |

E | 744 | 732 | 968 | 1230 | 39.6% | 40.5% | 21.3% |

15,000 transponders | |||||||

A | 1411 | 1451 | 1412 | 1559 | 9.6% | 6.9% | 9.5% |

B | 1738 | 1791 | 1715 | 1910 | 9.0% | 6.3% | 10.2% |

C | 2081 | 2158 | 1989 | 2226 | 6.5% | 3.1% | 10.7% |

D | 1636 | 1601 | 1517 | 1824 | 10.3% | 12.2% | 16.8% |

E | 1176 | 1165 | 1533 | 1875 | 37.3% | 37.9% | 18.2% |

20,000 transponders | |||||||

A | 1511 | 1541 | 1585 | 1616 | 6.5% | 4.7% | 1.9% |

B | 1914 | 1941 | 1973 | 2006 | 4.6% | 3.2% | 1.7% |

C | 2418 | 2479 | 2487 | 2499 | 3.2% | 0.8% | 0.5% |

D | 1908 | 1926 | 1921 | 1951 | 2.2% | 1.3% | 1.6% |

E | 1613 | 1610 | 2088 | 2211 | 27.1% | 27.2% | 5.6% |

**Table 5.**Comparison of algorithms for various number of transponders and traffic profiles, Euro28 network.

TP | Accepted Traffic [NTUs] | Distance to SAUR | |||||
---|---|---|---|---|---|---|---|

UNI | COMB | MSU | SAUR | UNI | COMB | MSU | |

10,000 transponders | |||||||

A | 1319 | 1293 | 1075 | 1347 | 2.1% | 4.0% | 20.2% |

B | 1419 | 1377 | 1176 | 1436 | 1.2% | 4.1% | 18.1% |

C | 1476 | 1429 | 1222 | 1491 | 1.0% | 4.2% | 18.0% |

D | 1280 | 1180 | 1129 | 1371 | 6.7% | 14.0% | 17.7% |

E | 1017 | 910 | 1082 | 1377 | 26.1% | 33.9% | 21.4% |

15,000 transponders | |||||||

A | 1500 | 1513 | 1526 | 1554 | 3.5% | 2.6% | 1.8% |

B | 1700 | 1756 | 1749 | 1807 | 5.9% | 2.8% | 3.2% |

C | 1994 | 2068 | 1917 | 2108 | 5.4% | 1.9% | 9.1% |

D | 1648 | 1678 | 1709 | 1780 | 7.4% | 5.7% | 4.0% |

E | 1619 | 1442 | 1754 | 1961 | 17.4% | 26.4% | 10.5% |

20,000 transponders | |||||||

A | 1519 | 1540 | 1567 | 1598 | 4.9% | 3.6% | 1.9% |

B | 1797 | 1806 | 1874 | 1880 | 4.4% | 3.9% | 0.3% |

C | 2216 | 2248 | 2272 | 2332 | 5.0 | 3.6% | 2.6% |

D | 1767 | 1792 | 1822 | 1834 | 3.6% | 2.3% | 0.7% |

E | 2085 | 1996 | 2173 | 2193 | 4.9% | 9.0% | 0.9% |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Walkowiak, K.; Klinkowski, M.; Włodarczyk, A.; Kasprzak, A.
Predeployment of Transponders for Dynamic Lightpath Provisioning in Translucent Spectrally–Spatially Flexible Optical Networks. *Appl. Sci.* **2020**, *10*, 2802.
https://doi.org/10.3390/app10082802

**AMA Style**

Walkowiak K, Klinkowski M, Włodarczyk A, Kasprzak A.
Predeployment of Transponders for Dynamic Lightpath Provisioning in Translucent Spectrally–Spatially Flexible Optical Networks. *Applied Sciences*. 2020; 10(8):2802.
https://doi.org/10.3390/app10082802

**Chicago/Turabian Style**

Walkowiak, Krzysztof, Mirosław Klinkowski, Adam Włodarczyk, and Andrzej Kasprzak.
2020. "Predeployment of Transponders for Dynamic Lightpath Provisioning in Translucent Spectrally–Spatially Flexible Optical Networks" *Applied Sciences* 10, no. 8: 2802.
https://doi.org/10.3390/app10082802