# A QoS-Aware Dynamic Bandwidth Allocation Algorithm for Passive Optical Networks with Non-Zero Laser Tuning Time

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. PON Standards

#### 2.2. Laser Tuning Time

#### 2.3. DBAs for TWDM-PONs

## 3. The Proposed Algorithm

_{i}has length L

_{i}and several wavelengths ω, our objective is to achieve the earliest possible time required to schedule all jobs in J on ω wavelengths such that none overlaps. Since there is a large number of requests coming from the ONUs to be transmitted on the four wavelengths in real-time, heuristic approaches are most suitable in achieving near-optimal scheduling efficiency [19].

_{1}(i), J

_{2}(i)…J

_{M}(i), according to the length of time needed for them to be processed such that L

_{r}(i) ≥ L

_{s}(i) ≥ …≥ L

_{m}(i) being r, s, and m ≤ M. LPT has the advantage of scheduling almost equal loads on the wavelengths and avoiding situations where some wavelengths will be idle. The upper limit of LPT, $\frac{{C}_{max}\left(LPT\right)}{{C}_{max}\left(OPT\right)}$, has the approximation ratio shown in (1) where ${C}_{max}\left(LPT\right)$ is the maximum makespan of LPT heuristic, and ${C}_{max}\left(OPT\right)$ is the maximum makespan of an optimal scheduler [47].

_{m}) are sorted in descending order. The ONUs are then assigned to the respective available wavelengths ω such that ONU m with job J

_{m}(i) with the longest processing time L

_{m}(i) is processed first and followed by the next one, assigned to the minimally loaded channel. If ${{\displaystyle \sum}}_{0}^{M}{L}_{m}\le {\delta}_{max},$ the requested time is granted for the connected ONUs in a cycle ($i$), else ${\delta}_{max}$ will be granted and certain jobs with lower lengths have to wait for the cycle ($i+1$). The aforementioned parameters are summarized in Table 2, and the pseudocode is provided in Algorithm 1.

_{1}, $\alpha $

_{2}, ..., $\alpha $

_{m}with ONUs 1, 2, ..., m, which reflect their relative resource share. The resources are allocated to the ONUs in increasing order of their requests, normalized by their weights, with the small requests being fully granted first. In this case, the ONU with the lowest demand is maximized, if satisfied, only then the ONU with the second-lowest demand will be maximized. After the ONU with the second-lowest is satisfied, only then the ONU with the third-lowest demand will be maximized, and so on. Therefore, no ONU gets more than its demand, and the ONUs whose demands are not met get a fair share of the resources in proportion to their weights. This also avoids the situation where the resources will be monopolized by ONUs with bigger requests and consequently eliminating network congestion to some extent. We combine the WFQ principle with the LPT algorithm to give us WFQLPT, a hybrid algorithm that provides inherent QoS with the minimal makespan associated with LPT.

Algorithm 1. Pseudocode for LPT executed at the OLT for each cycle i. |

Pseudocode of the LPT Heuristic Non-Preemptive Scheduler |

for m = 1:M if (ONU_{m} is connected && Queue$\ne 0$)Consider ONU; k = Connected_ONUs++; end ifend forform = 1: ksort${J}_{m}$in descending order based on their length; ${L}_{r}\ge {L}_{s}\ge {L}_{t}\ge \dots \ge {L}_{m}$ end for${{\displaystyle \sum}}_{0}^{k}{L}_{m}\ge {\delta}_{max}$)if (${\delta}_{max}isgranted$ in cycle i; ${J}_{m}thatarenotassignedwillbeprocessedfirstincyclei+1$ end if |

Algorithm 2. Pseudocode for WFQ executed at the OLT for each cycle i. |

Pseudocode of the Max-Min weighted fair-share queuing |

for m = 1:Mif (ONU_{m} is connected && Queue$\ne 0$)Consider ONU; k = Connected_ONUs++; end ifend forform = 1:kSearch for the smallest weight (${\alpha}_{m}$) among the connected ONUs ${\alpha}_{min}=1;$ Normalize the remaining weights (${\alpha}_{m})$ of remaining connected ONUs based on $\alpha ratioofnormalization;$ end forfor m = 1:k $\gamma $ = ${{\displaystyle \sum}}_{1}^{k}{\alpha}_{m}$ end for$\rho ={\delta}_{max}/\gamma $ for m = 1:k${\beta}_{m}=\rho .{\alpha}_{m}$ end forfor m = 1:k${\beta}_{m}\ge {L}_{m})$if (Remaining += (${\beta}_{m}-{L}_{m})$ Distribute the Remaining among unserved ONUs end if if (ONU_{m} is not served)$\gamma $ = ${{\displaystyle \sum}}_{1}^{k}{\alpha}_{m}$ $\rho ={\delta}_{remaining}/\gamma $ ${\beta}_{m}^{\prime}=\rho .{\alpha}_{m}$ $\beta {\u2019}_{m}+={\beta}_{m}$ if (${{\displaystyle \sum}}_{1}^{k}\beta {\u2019}_{m}\le {\delta}_{max}$)grant all Jobs end ifelse The remaining jobs wait for the next cycle end elseend ifend forif (${{\displaystyle \sum}}_{1}^{k}{\beta}_{m}\le {\delta}_{max}$)grant all Jobs end ifelseThe remaining jobs wait for the next cycle end else |

Algorithm 3. Pseudocode for NASC with LTT executed at the OLT for each cycle i. |

Pseudocode of the Wavelength Assignment-NASC with LTT |

if $({\omega}_{i}={\omega}_{i-1})$No tuning $\tau isnotconsidered$ queue_delay +=$\theta \left(\omega ,i\right)$ end ifelseif$({\omega}_{i}\ne {\omega}_{i-1})$ if($\tau \ge \theta \left(\omega ,i-1\right))$No tuning $\tau isnotconsidered$ $({\omega}_{i}={\omega}_{i-1})$ queue_delay +=$\theta \left(\omega ,i\right)$ end ifend ifelse$Lasertunes$ $\tau isconsidered$ queue_delay +=$\tau $ end elseend else |

## 4. Performance Evaluation

#### 4.1. Simulation Model

_{max}) is 1 ms, and the sources generate self-similar traffic [43,50] with Hurst parameter H = 0.75 and a mean packet rate that is adjusted according to varying offered load. The frame size follows a uniform distribution with a lower limit of 512 bits and an upper limit of 12,144 bits, thus realistically modeling Ethernet traffic [43].

- Set 1.
- IPACT with four wavelengths at LTT = 0 and 10 µs.
- Set 2.
- LPT over IPACT with four wavelengths at LTT = 0 and 10 µs.
- Set 3.
- WFQ with four wavelengths at LTT = 0 and 10 µs.
- Set 4.
- LPT over WFQ (WFQLPT) with four wavelengths at LTT = 0 and 10 µs

#### 4.2. Results

#### 4.2.1. Throughput

#### 4.2.2. Queue Delay

#### 4.3. Discussion of the Results

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Taylor, R.; Baron, D.; Schmidt, D. The world in 2025—Predictions for the next ten years. In Proceedings of the 10th International Microsystems, Packaging, Assembly and Circuits Technology Conference (IMPACT), Taipei, Taiwan, 21–23 October 2015; pp. 192–195. [Google Scholar]
- Hadi, M.; Bhar, C.; Agrell, E. General QoS-aware scheduling procedure for passive optical networks. J. Opt. Commun. Netw.
**2020**, 12, 217–226. [Google Scholar] [CrossRef] - Pizzinat, A.; Chanclou, P.; Saliou, F.; Diallo, T. Things You Should Know About Fronthaul. J. Light. Technol.
**2015**, 33, 1077–1083. [Google Scholar] [CrossRef] - Nakayama, Y.; Hisano, D. Wavelength and Bandwidth Allocation for Mobile Fronthaul in TWDM-PON. IEEE Trans. Commun.
**2019**, 67, 7642–7655. [Google Scholar] [CrossRef] - Kondepu, K.; Valcarenghi, L.; Castoldi, P. Balancing the impact of ONU tuning overhead in reconfigurable TWDM-PONs: An FPGA-based evaluation. In Proceedings of the IEEE Global Communications Conference (GLOBECOM), San Diego, CA, USA, 6–10 December 2015; pp. 1–6. [Google Scholar]
- Memon, K.A.; Mohammadani, K.H.; Shaikh, A.; Ullah, S.; Zhang, Q.; Das, B.; Ullah, R.; Tian, F.; Xin, X. Demand forecasting DBA algorithm for reducing packet delay with efficient bandwidth allocation in XG-PO. Electronics
**2019**, 8, 147. [Google Scholar] [CrossRef] [Green Version] - Ruffini, M.; Achouche, M.; Arbelaez, A.; Bonk, R.; Di Giglio, A.; Doran, N.J.; Furdek, M.; Jensen, R.; Montalvo, J.; Parsons, N.; et al. Access and Metro Network Convergence for Flexible End-to-End Network Design. J. Opt. Commun. Netw.
**2017**, 9, 524–535. [Google Scholar] [CrossRef] [Green Version] - Rafiq, A.; Hayat, M.F. QoS-Based DWBA Algorithm for NG-EPON. Electronics
**2019**, 8, 230. [Google Scholar] [CrossRef] [Green Version] - Liu, X.; Deng, N.; Zhou, M.; Wang, Y.; Tao, M.; Zhou, L.; Li, S.; Zeng, H.; Megeed, S.; Shen, A.; et al. Enabling Technologies for 5G-Oriented Optical Networks. In Proceedings of the Optical Fiber Communications Conference and Exhibition (OFC), San Diego, CA, USA, 3–7 March 2019; pp. 1–3. [Google Scholar]
- Afraz, N.; Slyne, F.; Gill, H.; Ruffini, M. Evolution of Access Network Sharing and Its Role in 5G Networks. Appl. Sci.
**2019**, 9, 4566. [Google Scholar] [CrossRef] [Green Version] - Nakayama, Y.; Uzawa, H.; Hisano, D.; Ujikawa, H.; Nakamura, H.; Terada, J.; Otaka, A. Efficient DWBA Algorithm for TWDM-PON with Mobile Fronthaul in 5G Networks. In Proceedings of the IEEE Global Communications Conference (GLOBECOM), Singapore, 4–8 December 2017; pp. 1–6. [Google Scholar]
- Dixit, A.; Lannoo, B.; Colle, D.; Pickavet, M.; Demeester, P. Dynamic bandwidth allocation with optimal wavelength switching in TWDM-PONs. In Proceedings of the 15th International Conference on Transparent Optical Networks (ICTON), Cartagena, Spain, 23–27 June 2013; pp. 1–4. [Google Scholar]
- Park, C.; Min, J.; Kim, S. Semi-passive optical front-haul supporting channel monitoring and link protection for the cloud radio access network. IET Commun.
**2019**, 13, 442–448. [Google Scholar] [CrossRef] - Xue, L.; Yi, L.; Ji, H.; Li, P.; Hu, W. Symmetric 100-Gb/s TWDM-PON in O-Band Based on 10G-Class Optical Devices Enabled by Dispersion-Supported Equalization. J. Light. Technol.
**2017**, 36, 580–586. [Google Scholar] [CrossRef] - Jaffer, S.S.; Hussain, A.; Qureshi, M.A.; Khawaja, W.S. Towards the Shifting of 5G Front Haul Traffic on Passive Optical Network. Wirel. Pers. Commun.
**2020**, 112, 1549–1568. [Google Scholar] [CrossRef] - Liem, A.T.; Hwang, I.-S.; Nikoukar, A.; Pakpahan, A.F. SD-Enabled Mobile Fronthaul Dynamic Bandwidth and Wave-length Allocation (DBWA) Mechanism in Converged TWDM-EPON Architecture. In Proceedings of the 6th International Conference on Cyber and IT Service Management (CITSM), Parapat, Indonesia, 7–9 August 2018; pp. 1–6. [Google Scholar]
- Zhang, J.; Ansari, N. Scheduling Hybrid WDM/TDM Passive Optical Networks with Nonzero Laser Tuning Time. IEEE/ACM Trans. Netw.
**2010**, 19, 1014–1027. [Google Scholar] [CrossRef] - Buttaboni, A.; de Andrade, M.; Tornatore, M.; Pattavina, A. Dynamic bandwidth and wavelength allocation with coexist-ing transceiver technology in WDM/TDM PONs. Opt. Switch. Netw.
**2016**, 21, 31–42. [Google Scholar] [CrossRef] - Ojeyinka, T.O. Bin packing algorithms with applications to passenger bus loading and multiprocessor scheduling problems. Commun. Appl. Electron.
**2015**, 2, 38–44. [Google Scholar] - Marbach, P. Priority service and max-min fairness. In Proceedings of the Twenty-First Annual Joint Conference of the IEEE Computer and Communications Societies, New York, NY, USA, 23–27 June 2002; Volume 1, pp. 266–275. [Google Scholar]
- Kramer, G.; Mukherjee, B.; Pesavento, G. Interleaved Polling with Adaptive Cycle Time (IPACT): A Dynamic Bandwidth Distribution Scheme in an Optical Access Network. Photon. Netw. Commun.
**2002**, 4, 89–107. [Google Scholar] [CrossRef] - Horvath, T.; Munster, P.; Vojtech, J. Deployment of PON in Europe and Deep Data Analysis of GPON. Telecommun. Syst. Princ. Appl. Wirel. Opt. Technol.
**2019**, 56–76. [Google Scholar] [CrossRef] [Green Version] - Law, D.; Dove, D.; D’Ambrosia, J.; Hajduczenia, M.; Laubach, M.; Carlson, S. Evolution of ethernet standards in the IEEE 802.3 working group. IEEE Commun. Mag.
**2013**, 51, 88–96. [Google Scholar] [CrossRef] - IEEE Standards Association. IEEE Standard for Ethernet, IEEE Std 802.3-2018 (Revision of IEEE Std 802.3-2015), IEEE. 31 August 2018. Available online: https://ieeexplore.ieee.org/document/8457469 (accessed on 29 April 2021).
- ITU-T Recommendation, G.9807.1, 10-Gigabit-Capable Symmetric Passive Optical Network (XGS-PON), International Tele-communications Union. 1 June 2016. Available online: https://www.itu.int/rec/T-REC-G.9807.1/en (accessed on 29 April 2021).
- IEEE Standards Association, 802.3ca-2020 Approved Draft Standard for Ethernet Amendment, IEEE. June 2020. Available online: https://standards.ieee.org/standard/802_3ca-2020.html (accessed on 24 June 2020).
- ITU-T Recommendation, G.989.2, 40-Gigabit-Capable Passive Optical Networks 2 (NG-PON2): Physical Media Dependent (PMD) Layer Specification, International Telecommunications Union. February 2019. Available online: https://www.itu.int/rec/T-REC-G.989.2 (accessed on 29 April 2021).
- Wey, J.S.; Nesset, D.; Valvo, M.; Grobe, K.; Roberts, H.; Luo, Y.; Smith, J. Physical layer aspects of NG-PON2 standards—Part 1: Optical link design. IEEE/OSA J. Opt. Commun. Netw.
**2016**, 8, 33–42. [Google Scholar] [CrossRef] - ITU-T Recommendation G.984.6, Gigabit-Capable Passive Optical Networks (GPON): Reach Extension, International Telecom-munications Union. March 2008. Available online: https://www.itu.int/rec/T-REC-G.984.6-200803-I/en (accessed on 29 April 2021).
- ITU-T Recommendation G.9807.2, 10 Gigabit-Capable Passive Optical Networks (XG(S)-PON): Reach Extension, International Telecommunications Union. August 2017. Available online: https://www.itu.int/rec/T-REC-G.9807.2/en (accessed on 29 April 2021).
- ITU-T Work Programme, Work Item G.9807.3 (ex G.SuperPON). Available online: https://www.itu.int/ITU-T/workprog/wp_item.aspx?isnD15208 (accessed on 29 April 2021).
- DeSanti, C.; Du, L.; Guarin, J.; Bone, J.; Lam, C. Super-PON: An evolution of access networks. Opt. Commun. Netw.
**2020**, 12, D66–D76. [Google Scholar] [CrossRef] - McGarry, M.P.; Reisslein, M.; Colbourn, C.J.; Maier, M.; Aurzada, F.; Scheutzow, M. Just-in-time scheduling for multichan-nel EPON. Lightwave Technol.
**2008**, 26, 1204–1216. [Google Scholar] [CrossRef] - Dixit, A.; Lannoo, B.; Colle, D.; Pickavet, M.; Demeester, P.; Abhishek, D. Energy efficient DBA algorithms for TWDM-PONs. In Proceedings of the 17th International Conference on Transparent Optical Networks (ICTON), Budapest, Hungary, 5–9 July 2015; pp. 1–5. [Google Scholar]
- Kanonakis, K.; Tomkos, I. Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks. IEEE J. Sel. Areas Commun.
**2010**, 28, 838–848. [Google Scholar] [CrossRef] - Dixit, A.; Colle, D.; Lannoo, B.; Demeester, P.; Pickavet, M. Novel DBA algorithm for energy efficiency in TWDM-PONs. In Proceedings of the 9th European Conference and Exhibition on Optical Communication (ECOC), London, UK, 22–26 September 2013; pp. 1–3. [Google Scholar]
- Wang, W.; Guo, W.; Hu, W. Adaptive wavelength allocation pattern for an online DWBA in the NG-EPON. OSA Contin.
**2018**, 1, 690–702. [Google Scholar] [CrossRef] - Zaouga, A.; De Sousa, A.; Najja, M.; Monteiro, P. Low Latency Dynamic Bandwidth Allocation Algorithms for NG-PON2 to Support 5G Fronthaul and Data Services. In Proceedings of the 21st International Conference on Transparent Optical Networks (ICTON), Angers, France, 9–13 July 2019; pp. 1–4. [Google Scholar]
- Wang, H.; Su, S.; Gu, R.; Ji, Y. A minimum wavelength tuning scheme for dynamic wavelength assignment in TWDM-PON. In Proceedings of the 7th IEEE International Conference on Software Engineering and Service Science (ICSESS), Beijing, China, 26–28 August 2016; pp. 1–3. [Google Scholar]
- Zhang, H.; Zhang, M.; Liu, X.; Wang, D.; Jiang, L. A Multi-OLTs and Virtual Passive Optical Network for Hybrid Net-work. In Proceedings of the 7th IEEE International Conference on Software Engineering and Service Science (ICSESS), Beijing, China, 26–28 August 2016; pp. 1009–1012. [Google Scholar]
- Zhang, L.; Qi, J.; Wei, K.; Zhang, W.; Feng, Y.; Hou, W. High-priority first dynamic wavelength and bandwidth allocation algorithm in TWDM-PON. Opt. Fiber Technol.
**2019**, 48, 165–172. [Google Scholar] [CrossRef] - Gravalos, I.; Yiannopoulos, K.; Papadimitriou, G.; Varvarigos, E.A. A modified max-min fair dynamic bandwidth alloca-tion algorithm for XG-PONs. In Proceedings of the 19th European Conference on Networks and Optical Communications (NOC), Milan, Italy, 4–6 June 2014; pp. 57–62. [Google Scholar]
- Navarro, M.C. Study and Implementation of New DBA for WDM-PON. Master’s Thesis, Universitat Politècnica de Cata-Lunya (UPC), Barcelona, Spain, 2010. [Google Scholar]
- Agrawal, T.K.; Sahu, A.; Ghose, M.; Sharma, R. Scheduling chained multiprocessor tasks onto large multiprocessor system. Computing
**2017**, 99, 1007–1028. [Google Scholar] [CrossRef] [Green Version] - Grigoriu, L. Approximation for Scheduling on Parallel Machines with Fixed Jobs or Unavailability Periods. Sched. Probl. New Appl. Trends
**2020**, 1–17. [Google Scholar] [CrossRef] [Green Version] - Lee, C.-Y.; Massey, J.D. Multiprocessor scheduling: Combining LPT and MULTIFIT. Discret. Appl. Math.
**1988**, 20, 233–242. [Google Scholar] [CrossRef] [Green Version] - Pinedo, M.; Hadavi, K. Scheduling: Theory, Algorithms and Systems Development. In Operations Research Proceedings 1991; Springer: Berlin/Heidelberg, Germany, 1992; pp. 35–42. [Google Scholar]
- Li, G.; Qian, Y.; Yang, Y.R. On max-min fair allocation for multi-source transmission. ACM Sigcomm Comput. Commun. Rev.
**2019**, 48, 2–8. [Google Scholar] [CrossRef] - Alkallak, I.N. A Modified for Largest Processing Time Scheduling Algorithm in Multiprocessor. Tikrit J. Pure Sci.
**2011**, 16, 280–283. [Google Scholar] - Melo, E.F.; de Oliveira, H.M. An Overview of Self-Similar Traffic: Its Implications in the Network Design. Rev. Tecnol. Inf. E Comun.
**2020**, 9, 38–46. [Google Scholar] - Kramer, G. How Efficient Is EPON? White Paper. Available online: https://www.ieee802.org/3/efm/public/p2mp_email/pdf00001.pdf (accessed on 29 April 2021).
- Parvez, I.; Rahmati, A.; Guvenc, I.; Sarwat, A.I.; Dai, H. A Survey on Low Latency Towards 5G: RAN, Core Network and Caching Solutions. IEEE Commun. Surv. Tutor.
**2018**, 20, 3098–3130. [Google Scholar] [CrossRef] - Khalili, H.; Rincón, D.; Sallent, S.; Piney, J.R. An Energy-Efficient Distributed Dynamic Bandwidth Allocation Algorithm for Passive Optical Access Networks. Sustainability
**2020**, 12, 2264. [Google Scholar] [CrossRef] [Green Version] - Zehri, M.; Haastrup, A.; Rincón, D.; Piney, J.R.; Sallent, S.; Bazzi, A. Leveraging SDN-Based Management for Improved Traffic Scheduling in PONs. In Proceedings of the 22nd International Conference on Transparent Optical Networks (ICTON), Bari, Italy, 19–23 July 2020; pp. 1–4. [Google Scholar]

**Figure 2.**Throughput for all 16 ONUs at LTT = 0 µs; IPACT vs. LPT (

**left**) and WFQ vs. WFQLPT (

**right**).

**Figure 3.**Throughput for ONU 1 at both LTT = 0 µs and LTT = 10 µs in a 16-ONU scenario; IPACT and LPT (

**left**); and WFQ and WFQLPT (

**right**).

**Figure 4.**Throughput of all ONUs at LTT = 10 µs for 16 ONUs vs. 8 ONUs; LPT (

**left**) and IPACT (

**right**).

**Figure 5.**Throughput for all ONUs at LTT = 10 µs for a range of 18–20 km vs. 2–20 km for LPT (

**left**) and for IPACT (

**right**).

**Figure 6.**CDF of the throughput for ONU 1 and 4 at LTT = 0 µs; IPACT vs. LPT at low load (

**left**) and heavy load (

**right**).

**Figure 8.**Queue delay for ONU 1 at both LTT = 0 µs and LTT = 10 µs; IPACT and LPT (

**left**); and WFQ and WFQLPT (

**right**).

**Figure 9.**Average queue delay for all ONUs at LTT = 10 µs for 64 ONUs, 16 ONUs and 8 ONUs; LPT (

**left**) and IPACT (

**right**).

**Figure 10.**Queue delay for a 16-ONU system with a distance range of 2–20 km vs. 18–20 km at LTT = 10 µs; LPT (

**left**) and IPACT (

**right**).

**Figure 11.**CDF of the queue delay for ONU 1 and ONU 4 under the IPACT and LPT algorithms for LTT = 10 µs at offered loads of 37.5 Mbps (

**left**) and 150 Mbps (

**right**).

**Table 1.**Classes of Laser Tuning Time, according to ITU-T [23].

Class | Laser Tuning Time |
---|---|

Class 1 | <10 μs |

Class 2 | 10 μs to 25 ms |

Class 3 | 25 ms to 1 s |

Parameter | Description |
---|---|

M | Total number of ONUs |

Ω | Assigned wavelength, 0 ≤ ω ≤ 3 |

i | Cycle number i, 0 < i < ∞ |

J_{m}(i) | The job requested by ONU m at cycle i, 1 < m < M |

L_{m}(i) | Length of job J_{m}(i) requested by ONU m at cycle i |

Τ | Laser tuning time |

ω_{i} | The wavelength assigned for ONU m during cycle i |

θ(ω, i) | Waiting time for a job J_{m}(i) on a wavelength ω during cycle i |

δ_{max} | Maximum allowed cycle length in bytes |

φ_{ω} | The completion time of the last job on wavelength ω |

α_{m} | Weight of the ONU m |

α_{min} | The smallest weight among ONUs |

Γ | The summation of the normalized weights |

Ρ | Weighted base resource share for an ONU |

k | Number of connected ONUs in cycle i |

β_{m} | Resource share based on the weight of each user |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Zehri, M.; Haastrup, A.; Rincón, D.; Piney, J.R.; Sallent, S.; Bazzi, A.
A QoS-Aware Dynamic Bandwidth Allocation Algorithm for Passive Optical Networks with Non-Zero Laser Tuning Time. *Photonics* **2021**, *8*, 159.
https://doi.org/10.3390/photonics8050159

**AMA Style**

Zehri M, Haastrup A, Rincón D, Piney JR, Sallent S, Bazzi A.
A QoS-Aware Dynamic Bandwidth Allocation Algorithm for Passive Optical Networks with Non-Zero Laser Tuning Time. *Photonics*. 2021; 8(5):159.
https://doi.org/10.3390/photonics8050159

**Chicago/Turabian Style**

Zehri, Mohammad, Adebanjo Haastrup, David Rincón, José Ramón Piney, Sebastià Sallent, and Ali Bazzi.
2021. "A QoS-Aware Dynamic Bandwidth Allocation Algorithm for Passive Optical Networks with Non-Zero Laser Tuning Time" *Photonics* 8, no. 5: 159.
https://doi.org/10.3390/photonics8050159