Nejm Eddine Frigui
email: nejm.frigui@orange.com

Tayeb Lemlouma
email: tayeb.lemlouma@irisa.fr

Stéphane Gosselin
email: stephane.gosselin@orange.com

⇤ Benoit

Renaud Le Meur
email: renaud.lemeur@orange.com

Jean-Marie Bonnin
email: jm.bonnin@imt-atlantique.fr

Optimization of the Upstream Bandwidth Allocation in Passive Optical Networks Using Internet Users' Behavior Forecast

Keywords: Passive Optical Network (PON), Clustering Analysis, Service Level Agreement (SLA), Grey Model GM(1, 1)

The application of classification techniques based on machine learning approaches to analyze the behavior of network users has interested many researchers in the last years. In a recent work, we have proposed an architecture for optimizing the upstream bandwidth allocation in Passive Optical Network (PON) based on the traffic pattern of each user. Clustering analysis was used in association with an assignment index calculation in order to specify for PON users their upstream data transmission tendency. A dynamic adjustment of Service Level Agreement (SLA) parameters is then performed to maximize the overall customers' satisfaction with the network. In this work, we extend the proposed architecture by adding a prediction module as a complementary to the first classification phase. Grey Model GM(1,1) is used in this context to learn more about the traffic trend of users and improve their assignment. An experimental study is conducted to show the impact of the forecaster and how it can overcome the limits of the initial model.

I. INTRODUCTION

In the recent years, a change of paradigm in fixed access networks has been experienced. The fast emergence of Passive Optical Networks (PONs) allowed to carry huge amounts of traffic and to offer high bandwidth services to operators' customers. However, the continuous exponential growth of data traffic in the next years as well as the expected widespread integration of Internet of Things, 5G networks, and highspeed services may impact the efficiency of the bandwidth allocation process. Dynamic Bandwidth Allocation (DBA) is currently the mechanism responsible for allocating the upstream resources in PONs. To optimize the DBA performance, two approaches can be distinguished. The first consists in modifying the way in which the DBA works by acting on the algorithm itself and trying to invent a new mechanism that can overcome the limits of the existing one. The second relies on managing the external parameters of the DBA in a different way without modifying the DBA control algorithm itself at the Optical Line Terminal (OLT) level. The main difficulty of the first approach is the inability to be directly implementable from the operator perspective. Indeed, the DBA as a closed control protocol in the PON network cannot be modified by the network operator who doesn't have the total control of this mechanism due to equipment supplier dependency. In this regard, the second approach looks more suitable in a context of network resources optimization under the control of the network administrator.

In a recent work [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF], we have proposed an architecture for optimizing the upstream bandwidth allocation in PON based on the dynamic adjustment of Service Level Agreement (SLA) parameters. The latter represent the input parameters of the DBA algorithm that can be managed by the operator. The idea was to efficiently exploit the bandwidth available in the network by adjusting dynamically the SLA parameters based on the estimation of users' traffic patterns linked to daily life. Clustering analysis was used to identify heavy and light users based on their mean upstream bitrates for a specific time interval (e.g., 5 minutes). Then, an Assignment Index Calculator module was proposed to assign each user to a particular class (heavy, light, or flexible) for all the time series possessed by the network operator. The combination of the clustering analysis and the assignment index calculation allows to have an overall vision of the traffic profile of each user and makes it possible to estimate the possible behavior of a specific user at a specific time. In this case, the reallocation of the SLA parameters can be very useful and advantageous in the context of optimizing PON upstream resources for a specific day period. The evaluation phase that we have conducted in [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF] was limited to the analysis of the clustering module in order to select which algorithm gives a better distribution of users. In this work, we continue the evaluation of the model that we have proposed in [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF] by analysing the assignment index module and its impact on the user classification phase. Then, we extend the proposed architecture by adding a forecasting module as a part of a second user classification step that we suggest to be an improvement of the first classification method.

The paper is structured as follows. Section II presents some work related to the DBA mechanism optimization, a summary of the initial model that we have proposed in a previous 978-3-903176-07-2 © 2018 IFIP work, its limits, and the need for a forecasting approach to deal with network users' traffic behavior. Section III presents the enhanced version of the initial model using a forecasting module based on the GM(1,1) model. In section IV, we present simulations used to evaluate the classification techniques as well as the obtained experimental results and their analysis. Finally, we conclude our work in section V.

II. RELATED WORK

The dynamicity of users' traffic patterns lets always network operators thinking about new ideas to make the upstream bandwidth allocation mechanism more efficient. In the research world, many works [2]- [START_REF] Assi | Dynamic bandwidth allocation for quality-of-service over Ethernet PONs[END_REF] have been proposed in this context with the aim of enhancing the DBA overall operation. Despite their contribution at the optimization level, the majority of these works remain theoretical proposals that a network operator cannot directly integrate in its equipment due to the implementation nature of the DBA (a closed control protocol) and the dependency on a specific vendor.

With the trend of using machine learning in the last few years, thoughts are directed towards approaches that have the character of being able to be managed and capable of learning over time. In this context, we have proposed in [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF] a new model (Fig. 1) for the optimization of PON upstream resources which stems from a very simple idea: analyzing the past customers' behavior based on their historical data to estimate and reallocate their upstream bitrates in the future. Indeed, in daily life, traffic patterns of different users may change several times per day. In this case, it is highly possible to have some customers who consume more bandwidth than others for a specific day period. The current DBA allows allocation of PON resources, depending on the instantaneous demand of each Optical Network Unit (ONU). However, each user is limited by predefined Peak Information Rate, which represents one of the SLA parameters which defines the maximum bitrate that a user might benefit from. In this case, when the extra available bandwidth resulting from the presence of light ONUs is greater than the maximum bandwidth authorized to be allocated to heavy users, a part of the extra bandwidth will be lost and not exploited. For this, the idea was to try to exploit this extra bandwidth theoretically untapped by the DBA in order to share it among heavy users without being limited by the constraints of the SLA parameters. As the goal is to propose an implementable approach by the operator in which the DBA algorihm should not be touched, the challenge is then to be able to model the functioning of the DBA while using the historical data provided by the operator and acting only on the DBA externally manageable parameters i.e., SLA parameters.

By analogy with the DBA process, four main components were proposed. The Monitored Data Collector gathers the traffic data for each ONU by requesting the Management Information Base (MIB) at regular intervals. This module connects also to the network operator in order to store the historical transmission data. As the DBA refers to the paquet queue status of each ONU to know its needs, two complementary modules responsible for the classification of different users depending on their historical transmission data were proposed. The clustering module classifies users into 3 classes: heavy, light, and flexible. Depending on the chosen algorithm, the results may vary. In [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF], two well known clustering algorithms namely, K-Means [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF] and DBSCAN [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] were evaluated. The results have shown that K-Means using a log 10 (Bitrate) metric outperforms DBSCAN in terms of a more balanced customer distribution. The clustering module is supposed to be applied per time interval (e.g., 5 minutes). To be able to classify all users based on the entire time series, a second module called Assignment Index Calculator was proposed. This module aims to provide the probability for each user to be either heavy, light or flexible. For each day and for each time interval, it analyzes the clustering results. If the user belongs to the heavy class in a given time interval, his probability to be a heavy will increase and likewise for the light class. Then, a calculation process of the average of all probabilities associated to a standard deviation calculation (for validation) is assured to finally assign each user to a specific class. The final users' classification will be used then by the Reallocation of SLA Parameters module to define for each heavy user new temporary upstream bitrate allocation in a specific day period.

The purpose of using clustering analysis associated with an assignment index calculation process is to classify PON users depending on their traffic patterns. Although this approach is characterized by its high accuracy in the assignment of a PON user to a certain traffic class, it can lead to an unbalanced user distribution where the majority of ONUs will be assigned to the flexible users class. This may be an impediment to the overall objective which consists in maximizing as much as possible the satisfaction for the majority of customers. In this case, it is preferable to have a significant ratio of heavy and light users in order to maximize the efficiency of the bandwidth usage in the network. To resolve this issue, reference can be made to forecasting-based approaches that deal with the analysis and the prediction of network users' traffic behavior in order to have an idea about the possible future trend of flexible users (whether heavy or light ). [START_REF] Cortez | Multi-scale internet traffic forecasting using neural networks and time series methods[END_REF]- [START_REF] Alarcon-Aquino | Multiresolution fir neural-networkbased learning algorithm applied to network traffic prediction[END_REF] represent some works related to the network traffic behavior forecasting in several types of networks. In general, we can distinguish two main techniques for forecasting models: qualitative and quantitative approaches. The first technique relies on the knowledge and the experience of the forecaster who will take the final decision about the expected trend of data. The second one aims to identify the data patterns from the historical dataset in order to predict the future values [START_REF] Yi | Research on forecasting and early-warning methods[END_REF] [START_REF] Uysal | An overview of approaches used to forecast tourism demand[END_REF]. Quantitative approaches may be also classified into causal relationship methods and time series ones. While the first category tries to make a relationship between many factors in order to generate the forecasted values, the second is limited to the statistical data that was observed and collected over regular time intervals such as hourly, daily, weekly, monthly, etc [START_REF] Jouini | Employing grey model forecasting gm(1,1) to historical medical sensor data towards system preventive in smart home e-health for elderly person[END_REF].

Since the historical data required by the network operator to forceast users' traffic behavior can be easily obtained and processed with the aim to classify the different customers, the focus will be on time series methods and especially on two major forecasting models, respectively Artificial Neural Networks and Grey theory. Artificial neural network (ANN) represents one of the most popular forecasting paradigms [START_REF] Milojkovi | Ann versus grey theory based forecasting methods implemented on short time series[END_REF]. Classified as a machine learning approach, ANN has the ability to learn from complicated data and deduce its pattern and tendency. It can be very appropriate in the context of a knowledge-based learning mechanism that is difficult to specify [START_REF] Zhang | Forecasting with artificial neural networks:: The state of the art[END_REF]. By analogy to the human brain, ANN ensure the information process through the interaction of artificial neurons and can interpret the future behavior of a dataset despite the existence of noisy information [START_REF] Yi | Research on forecasting and early-warning methods[END_REF] [START_REF] Zhang | Forecasting with artificial neural networks:: The state of the art[END_REF]. As for Grey forecasting theory [START_REF] Deng | Introduction to grey system theory[END_REF], it was proposed for the first time in 1982. Thanks to its ability to estimate the possible data behavior based only on a few information samples even if they are incomplete, Grey theory becomes one of the most popular prediction approaches used in the research world [START_REF] Wang | Grey system theory based prediction for topic trend on internet[END_REF]. The core and the most commonly used model of Grey is known as GM(1,1) [START_REF] Jouini | Employing grey model forecasting gm(1,1) to historical medical sensor data towards system preventive in smart home e-health for elderly person[END_REF]. The main task of this model is to identify the mathematical relationship between different points to learn about the behavior of the dataset and to make the right decision about the future trend [START_REF] Yi | Research on forecasting and early-warning methods[END_REF].

In relation with our recent work [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF], ANN and Grey model allow both to achieve our main goal concerning the forecasting of customers' traffic behavior. However, we expect that only the Grey Model GM(1,1) remains for the moment the most appropriate for our usecase. This is due to the fact that the dataset we have is limited, which does not represent a problem for Grey systems which can even work with incomplete data. However, neural networks require a very large amount of data to ensure that the forecasted values are statistically accurate, which makes the learning speed slower [START_REF] Yi | Research on forecasting and early-warning methods[END_REF] [START_REF] Cannady | Artificial neural networks for misuse detection[END_REF].

III. ENHANCED MODEL USING A FORECASTING MODULE

In this section, we propose the design of the enhanced model inspired by the first model [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF] while the main novelty introduced lies in the integration of a forecasting module based on the GM(1,1) model. Fig. 2 shows the architecture of the new proposed model.

We expect that the forecasting module will be considered as a second step of the users classification phase as it depends Fig. 2. Enhanced model using a forecasting module on the results of the clustering analysis and assignment index calculator modules. This new module will be applied particularly to the assignment indexes of flexible users while heavy and light ones will not be involved. Indeed, in our approach, a user can be flexible only if the averages of his assignment indexes to heavy and light users over the supervised days are smaller than 0.5 (the selected threshold). That is, the user does not tend to be neither heavy nor light. Since the index is calculated on the basis of historical data, cases like missing data or the lack of a vision on the traffic trend of users in the future will be often encountered. This can impact the calculation of the assignment index and subsequently the classification of users. In this context, the enhancement of the initial model by using a forecasting approach can be beneficial to have a more reliable and useful approach where a part of flexible users can be assigned to one of the other two classes. Accordingly, the extra bandwidth estimated and the number of beneficiary heavy users will increase automatically. Unlike the initial model where PON users are classified based on the whole set of supervised days, we propose in this work to classify customers per weekdays (from Monday to Friday) and per weekends (Saturday and Sunday). This aims to determine whether the online behavior of PON users is the same for weekdays as it is for weekends.

The mathematical formulation of the Grey forecasting Model GM(1,1) is illustrated below. We assume the initial data series with n (n 4) non-negative values as follows:

x (0) = (x (0) (1), x (0) (2), ..., x (0) (n)) (1)
The Accumulated Generating Operation (AGO) is then applied since the initial data series may change randomly while there is a need to know its regular pattern [START_REF] Deng | Introduction to grey system theory[END_REF]:

x (1) = (x (1) (1), x (1) (2), ..., x (1) (n))

Where

x (1) (k) = P k m=1 x (0) (m), k 2 [1, n]
The original form of the GM(1,1) model is:

x (0) (k) + ax (1) (k) = b ( 3
)
Where a is the developing coefficient and b is the grey input according to the Grey theory. x (1) (k) can be replaced then by the average of two consecutive neighbours x (1) (k) and x (1) (k 1):

x (0) (k) + az (1) (k) = b, k 2 [2, n] (4)
Where z (1) (k) = 0, 5(x (1) (k) + x (1) (k 1)) According to the least square method, a and b can be identified as follow:

A =  a b = (B T B) 1 B T Y (5)
Where:

B = 2 6 6 6 6 6 6 4
z (1) (2) 1 z (1) (3) 1 . . . z (1) (n) 1 x (0) (2)

x (0) (3) . . . x (0) (n) 3 7 7 7 7 7 7 5
By regarding the following differential equation as a shadow of Eq. ( 4):

dx (1) (k) dk + ax (1) (k) = b (6)
The GM(1,1) can be therefore established:

b x (1) (k + 1) = (x (1) (1) b a )e ak + b a (7)
As we have applied the AGO in the equation 2, we apply the inverse (IAGO) to obtain the forecasted value of the original data x (0) : b x (0) (k + 1) = (1 e a )(x (1) (1) b a )e ak (8)

IV. EXPERIMENTATION AND RESULTS

In this section, we proceed to an evaluation of the user classification modules proposed in the initial model [START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF] and the enhanced one proposed in this work. The objective is to demonstrate that adding a forecasting module can give a more balanced distribution and consequently provide top customers satisfaction. The reference dataset used in this work relies on a real traffic traces collected within the Orange France network. The data collection was ensured by the use of a probe called OTARIE and equipped with a DAG (Data Acquisition and Generation) traffic capture card which has an Application Programming Interface (API) that allows reading the packets as they arrive on the network interface. 3447 ONUs belonging to the same OLT were supervised over a period of one month between the 2nd of November and the 3rd of December 2016. Given that the traffic traces do not cover the whole day, the day period theoretically qualified as the busiest which is between 9p.m and 12a.m was selected in order to analyze the behavior of the majority of subscribers.

As the customer traffic pattern is linked to daily life where the online behavior in the weekends may not be the same as the other weekdays, we decide to classify customers per weekday and per weekend. For display reasons, we decide to show the results for a list of Wednesdays as a weekday and a list of Saturdays as day of the weekend. The accomplishment of the experiment relies on the use of Python scripts to evaluate the different algorithms and Matplotlib and Seaborn libraries to plot the different results in the most convenient way. Fig. 3 and Fig. 4 show the users rate for each class (heavy, light, and flexible) for Wednesdays and Saturdays of the supervised period. These rates are calculated for each day based on the assignment index of each user to the heavy or light classes, calculated once the clustering process based on the K-Means algorithm is finished. This index has been fixed at 0.5 and represents the probability of belonging to a specific class of users. The selected threshold 0.5 is the minimum value that must be chosen to remove any ambiguity concerning the classification step. Indeed, the sum of the assignment indexes to the heavy and light classes is always lower than 1. If we choose a threshold lower than 0.5, we may have cases where both indexes are above the selected threshold and therefore, users will be assigned to both classes at the same time. The analysis of the resulting user rates shows an absolute majority of flexible users compared to light and heavy ones as it was expected. This is confirmed for Wednesdays as well as Saturdays. To be able to show the impact of using our forecasting module on the users' rate, we choose to work on a specific OLT PON Port instead of working on the whole OLT. This choice is more appropriate since our optimization approach is supposed to be applied per PON port. As for the whole OLT, Fig. 5 and Fig. 6 show the users distribution for a PON port that connects 32 subscribers. Fig. 7 presents the final distribution of the PON port users based on the average of their assignment indexes over all supervised days. As mentioned in section III, the Grey forecasting model takes into account the different user distributions resulted from the combination of clustering analysis and assignment index calculation. While the heavy and light users are already selected with high precision, the flexible ones which represent the majority may tend to one of the other classes if we extend the dataset and generate more indexes. This can influence the final users distribution and consequently the extra bandwidth that will be estimated to be shared among heavy customers. Fig. 8 and Table II highlight for a flexible user, the real values of the assignment index to the heavy class for all Wednesdays in the supervised period, and the forecasted values while extending the dataset by 4 weeks. We evaluated our forecasting module based on GM(1,1) using the metrics presented in Table I. The results demonstrate that the average of the assignment indexes to the heavy class for this flexible user increases from 0.4828 (using real values for the supervised days) to 0.505 (using real values for the supervised days and forecasted ones for the next 4 weeks), which qualifies it as a heavy user instead of a flexible one. The different metrics used to evaluate the GM(1,1) show high performances of this model with a good forecast accuracy (the minimum obtained is 80,155 %) and a low Mean Absolute Deviation. The Tracking Signal is generally used to decide if the forecasting model need or not to be reviewed. The low value that we have obtained for this parameter brings confirmation of the good quality of the GM(1,1) model. We performed the same approach for all flexible users belonging to the same PON port. The new users classification is shown in Fig. 9. Whereas before using the forecasting model, the rate of flexible users was 87,5% for Wednesdays and 96,87 % for Saturdays, the application of the GM(1,1) shows a more balanced distribution where the flexible users rate decreases to 68,75% for Wednesdays and 75% for Saturdays. The fact that a part of flexible users tends to be heavy more than light for Wednesdays whereas it's the opposite for Saturdays can be explained by making the analogy with the daily life of connected people where the most of them tend to go out on weekends more than weekdays. By looking to the new users' distribution resulted from the application of the Grey model, it's clear that the additional bandwidth that can be estimated will be greater since the number of light users has increased whether for Wednesdays or Saturdays.

TABLE I MATHEMATICAL FORMULAS OF FORECASTING METRICS

Additionally, the number of users who will benefit from the bandwidth supplement i.e., heavy users, has also increased, which asserts that the use of the GM(1,1) looks essential and advantageous in a context of satisfying the majority of customers in our approach.

V. CONCLUSIONS AND FUTURE WORK A new approach for enhancing PON users classification based on their traffic patterns has been proposed in this paper. In a previous work, we have proposed a mechanism for reallocating SLA parameters in a PON network based on their online behavior. This mechanism has as objective to optimize the upstream bandwidth allocation process without modifying the DBA itself. The idea was to classify PON users into 3 classes, heavy, light, and flexible and then, try to add an extra bandwidth to heavy users for a specific day period. The classification mechanism was designed based on clustering analysis and an assignment index calculation method. This mechanism is limited by the fact that the majority of users were assigned to the flexible class, which looks like an obstacle in our optimization approach. In this work, we referred to the Grey forecasting theory in order to predict the possible traffic behavior of flexible users in the future with the aim to have a more balanced distribution. Results have shown clearly the advantage of using this predictive approach to improve the final users distribution which impacts directly the extra bandwidth estimation and the number of beneficiary customers. In a future work, we expect to proceed to the whole evaluation of the proposed model taking into account several QoS parameters. We also plan to have a third version of our model based on the self management aspect where our optimization mechanism will be integrated in a real platform and managed by the network itself without any human intervention.

Fig. 1 .

 1 Fig.1. The proposed model for optimizing PON upstream resources[START_REF] Frigui | Dynamic reallocation of SLA parameters in passive optical network based on clustering analysis[END_REF]

Fig. 3 .

 3 Fig. 3. OLT user distribution for Wednesdays

Fig. 5 .

 5 Fig. 5. A PON port user distribution for Wednesdays

(Fig. 8 .

 8 Fig. 8. Forecasted and real assignment indexes of a flexible user to the heavy users class for Wednesdays using GM(1,1)

Fig. 9 .

 9 Fig. 9. A PON port user distribution for Wednesdays And Saturdays Using GM(1,1)

TABLE II ASSIGNMENT

 II INDEX (AI) OF A FLEXIBLE USER TO THE HEAVY CLASS:

		REAL AND FORECASTED VALUES
	Day	AI to Heavy Users Real Value	AI to Heavy Users Forecasted Value	Residual	Forecast Error (%) Accuracy (%) Forecast
	02-11-2016	0,583	0,583	0	0	100
	09-11-2016	0,444	0,432	0,012	2,702	97,298
	16-11-2016	0,472	0,448	0,024	5,084	94,916
	23-11-2016	0,388	0,465	-0,077	19,845	80,155
	30-11-2016	0,527	0,483	0,044	8,349	91,651
	07-12-2016	-	0,502	-	-	-
	14-12-2016	-	0,522	-	-	-
	21-12-2016	-	0,542	-	-	-
	28-12-2016	-	0,563	-	-	-
			Mean Forecast Error (MFE) :	0,0006
			Mean Absolute Deviation (MAD) :	0,0314
			Tracking Signal (TS) :	0,095


Nejm Eddine Frigui
email: nejm.frigui@orange.com

Tayeb Lemlouma
email: tayeb.lemlouma@irisa.fr

Stéphane Gosselin
email: stephane.gosselin@orange.com

Benoit Radier
email: benoit.radier@orange.com

Renaud Le Meur
email: renaud.lemeur@orange.com

Jean-Marie Bonnin
email: jm.bonnin@imt-atlantique.fr

Dynamic Reallocation of SLA Parameters in Passive Optical Network Based on Clustering Analysis

Keywords: Passive Optical Network (PON), Clustering Analysis, Service Level Agreement (SLA)

The introduction of new services as well as the growth in the number of communication terminals in the last years has led to an exponential growth of data traffic in both fixed and mobile networks. Passive Optical Networks (PONs) offer high bandwidth services to service providers customers. However, due to the dynamicity of users traffic patterns, PONs need to rely on an efficient upstream bandwidth allocation mechanism to define for each customer the amount of data that needs to be transmitted at a specific time. This mechanism is currently limited by the static nature of Service Level Agreement (SLA) parameters which can lead to an unoptimized bandwidth allocation in the network. In this paper, we propose a novel mechanism for optimizing the allocation of upstream Gigabit-capable Passive Optical Networks (GPON) resources based on the dynamic adjustment of some SLA parameters according to customer's estimated traffic patterns. Clustering analysis is used to differentiate customers according to their bandwidth utilization based on real-time and historical data. Three user classes are taken into account: heavy, light and flexible. Our work considers two fundamental clustering algorithms, namely K-means, a very well-known partitioning method and DBSCAN, one of the most common density-based clustering algorithms. An experimental study is conducted to evaluate the two algorithms and select which one can be the most suitable for the differentiation of user classes.

I. INTRODUCTION

In the last years, the development of telecommunications networks and information technology has become increasingly fast. At the horizon 2020, we expect an exponential growth of data traffic in both fixed and mobile networks. This is mainly due to the widespread integration of Internet of Things, 5G networks, and the usage of high-speed services such as VoD, IPTV, video conferencing, and Ultra High Definition video services. Passive Optical Networks (PONs) offer high bandwidth services to operators' customers. The well known generation of ITU-T PON standards is the Gigabit-capable Passive Optical Networks (GPON) [START_REF]Gigabit-capable Passive Optical Networks (G-PON): General characteristics[END_REF]. It was standardized for the first time in 2003 and provides 2.5 Gbit/s downstream and 1.25 Gbit/s upstream capacities while these rates can be shared up to 64 users depending on the splitter options used. As the demand for higher data speeds is increasing over the years, the control of the bandwidth allocation mechanism will be a key task in the network the capacity of which needs to be continiously utilized in a more efficient manner.

In our work, we propose a novel mechanism for optimizing the allocation of upstream GPON resources based on customer's estimated traffic patterns. Accordingly, we propose to dynamically adjust the Service Level Agreement (SLA) parameters as the only upstream resources allocation mechanism inputs that are allowed to be modified by the operator while maintaining the overall customer satisfaction. Traffic patterns will be identified through the use of clustering techniques based on real-time and historical data. We evaluate different clustering techniques in order to choose which one is more efficient for our case.

The paper is structured as follows. Section II describes the upstream bandwidth allocation mechanism in GPON. Section III presents some works related to the Dynamic Bandwidth allocation (DBA) mechanism. Section IV introduces the problem that needs to be adressed. In section V, we present our proposed model for optimizing the GPON upstream bandwidth allocation based on the dynamic adjustment of SLA parameters. In section VI, we present the clustering module in details as well as Python simulations to evaluate different clustering techniques applied to a real traffic trace captured on an operational FTTH network of Orange France. The obtained experimental results are then reported and analysed. Finally, we conclude our work in section VII.

II. UPSTREAM BANDWIDTH ALLOACTION MECHANISM

In PON networks, upstream bandwidth allocation is a control mechansim ensured by the Optical Line Terminal (OLT) which defines for each Optical Network Unit (ONU) the length and the time of transmission of each upstream burst. This mechanism can be also performed by the ONUs, socalled distributed bandwidth allocation. However, it is rarely known and not very common compared to the other one. The upstream bandwidth allocation can be achieved either in a static or dynamic way. Fig. 1 shows the concepts of both Static Bandwidth Allocation (SBA) and Dynamic Bandwidth Allocation (DBA).

SBA has the advantage of being simple to implement at the OLT level. However, the risk of congestion or bottleneck in the network is high due to the possibility to have idle time slots that occupy the network. This can result in a degradation of the overall network performance and a customer dissatisfaction towards his service provider [START_REF] Haran | The importance of dynamic bandwidth allocation in GPON networks[END_REF]. SBA can be classified as a QoS-unaware allocation mechanism and can be optimal only in the case where all network services require a constant bitrate. It should not be considered in the case of a shared-medium transmission system such as GPON.

As service providers need to adapt their network performances based on the dynamicity of users traffic patterns, a DBA mechanism is needed in order to make the best use of the unallocated bandwidth. DBA allows the bandwidth which is not consumed by some ONUs to be assigned to the other ones, resulting in a more flexible, efficient, and fair bandwidth allocation mechanism. ONUs can send their pending data only within the limits of the allocated grants which are specified in the Upstream Bandwidth Map (US-BWmap) field. These grants are transmitted by the OLT to the different ONUs in the downstream traffic frames [START_REF] Feknous | Status reporting versus non status reporting dynamic bandwidth allocation[END_REF]. They are updated regularly in each DBA cycle which represents the duration that covers all transmissions from all ONUs and may vary depending on the state of the ONUs packet queues [START_REF] Haran | The importance of dynamic bandwidth allocation in GPON networks[END_REF]. GPON supports a mixture of services (e.g. VoIP, internet browsing, business services...) which do not have the same bandwidth requirements in the upstream (e.g. VoIP requires a constant bitrate). Thus, the DBA needs to take this into account in order to satisfy all customer needs. In this context, ONUs may support multiple classes of services. Each class has its own buffer with a specific quality of service (QoS) [START_REF] Walid | Self-adaptive dynamic bandwidth allocation for GPON[END_REF]. Therefore, the bandwidth allocation is no longer assured per ONU but rather per ONU per service. To guarantee the different QoS levels, GPON uses the Transmission Container (T-CONT) mechanism which allows different ONU's GPON Encapsulation Method (GEM) flows to be gathered in the same class of service [START_REF]Gigabit-capable Passive Optical Networks (G-PON): Transmission convergence layer specification[END_REF][6] [START_REF] Ozimkiewiez | Dynamic bandwidth allocation in GPON networks[END_REF]. Table I shows the five containers that can be assigned to one ONU depending on which services the latter had requested [8][9]. The activity status of each container can be obtained either through a status or non-status reporting mechanism. Fig. 2 provides a simplified schematic of the Status Reporting (SR-DBA) mode [3][9]. In the Non-Status Reporting (NSR-DBA) mode, the ONUs data queue occupancy information is not provided to the OLT. The latter should hinge on the actual transmission in the previous cycle and the information given by the GEM headers to estimate the ONUs queue status. In fact, when the ONU does not have data to send, idle frames are generated and sent during the allocation interval. These frames are observed by the OLT which understands that there is no transmission for the corresponding ONU and automatically decreases its bandwidth allocation in the following cycle [START_REF] Haran | The importance of dynamic bandwidth allocation in GPON networks[END_REF][3] [START_REF] Bang | Dynamic bandwidth allocation method for high link utilization to support NSR ONUs in GPON[END_REF]. The SR-DBA based algorithms are widely implemented in OLTs compared to the NSR-DBA ones. Thanks to their ability to reduce the latency (traffic can be granted for transmission once reported) and to avoid the overestimation or the underestimation of data queues, we will only consider the SR-DBA mechanism in the following. SR-DBA algorithms are based on the combination of the queue occupancy information transmitted from each T-CONT depending on its activity status and the provisioned SLA of each T-CONT [START_REF] Bang | Dynamic bandwidth allocation method for high link utilization to support NSR ONUs in GPON[END_REF]. SLA parameters are defined in a service contract which represents a formal commitment between the provider and the subscriber. They define the specific objectives expected and the QoS that a client wishes to obtain from the service provider. The main parameters specified in the customer SLA are respectively the Committed Information Rate (CIR), the Excess Information Rate (EIR), and the Peak Information Rate (PIR) [START_REF] Feknous | Status reporting versus non status reporting dynamic bandwidth allocation[END_REF]. The CIR defines the guaranteed bandwidth provided by the network when delivering the data frames. The EIR specifies the additional bandwidth above that of the CIR that a subscriber may use if available. The PIR represents the maximum bandwidth that can be provided. More details about SLA parameters are given in table II [START_REF]Gigabit-capable Passive Optical Networks (G-PON): Transmission convergence layer specification[END_REF][8] [START_REF] Loumiotis | Optimal Backhaul Resource Management in Wireless-Optical Converged Networks[END_REF]. III. RELATED WORK TO DBA ALGORITHMS As the DBA directly affects the performance of the network in the upstream, many works [START_REF] Nowak | Bandwidth allocation for service level agreement aware Ethernet passive optical networks[END_REF]- [START_REF] Assi | Dynamic bandwidth allocation for quality-of-service over Ethernet PONs[END_REF] have been proposed in the literature with the objective to enhance its operation. These works can be classified according to their ability to take or not into consideration the constraints agreed in the SLA contract, i.e. SLA awareness. In this paper, only the enhanced DBA proposals which respect the minimum and the maximum of bandwidth that must be provided to subscribers according to their SLA parameters are taken into account.

TABLE I: T-CONT Types

In [START_REF] Nowak | Bandwidth allocation for service level agreement aware Ethernet passive optical networks[END_REF], an SLA aware dynamic bandwidth allocation algorithm (SLA-DBA) was presented. In this algorithm, the OLT allocates in a first stage a number of bytes to an ONU queue depending on its bandwidth report. Then taking into account the SLA constraints, an adjustment will be performed in such a way that the number of assigned bytes never exceeds the maximum guaranteed rate provided by the SLA.

In [START_REF] Choi | SLA-Aware Dynamic Bandwidth Allocation for QoS in EPONs[END_REF], the proposal introduces an approach called cyclicpolling-based dynamic bandwidth allocation with service level agreements (CPBA-SLA) based on a two-layer allocation scheme: SLA-layer and ONU-layer. In the SLA-layer allocation, ONUs are distributed on two or more groups based on their SLA parameters. Then, the OLT assigns the bandwidth for each class of service in each group in a way that high-priority traffic can be served earlier. In the ONU-layer allocation, bandwidth is assigned to ONUs which belong to the same group where a group can be defined as a set of ONUs that require the same average packet delay of a specific class of service (e.g. high-priority, delay-sensitive traffic, etc.) for a specific cycle time.

Authors in [START_REF] Merayo | Fair bandwidth allocation algorithm for PONS based on network utility maximization[END_REF] propose a fair bandwidth allocation algorithm based on network utility maximization. In addition to the requested bandwidth by each ONU in its report message and the guaranteed bandwidth coming from the SLA contract, the algorithm takes into account an additional factor that corresponds to the importance of an ONU regarding the conditions specified in its QoS requirements. Then, it distributes the extra bandwidth available in the network in a fair manner according to the definition of fairness in the network utility maximization model.

Although the majority of these works contributes to the optimization of the DBA mechanism, they do not take into account the fact that the DBA is a closed control protocol between the OLT and the ONUs in the GPON network [START_REF] Dai | Towards SDN for optical access networks[END_REF] [START_REF] Woesner | SDN and OpenFlow for converged access/aggregation networks[END_REF]. Thus, modifying its operation is a hard task for an operator or a service provider who doesn't have the total control of this mechanism due to the dependency on a specific vendor. To resolve this issue and allow operators to optimize their networks without being bound to the constraints of specific vendor, it's recommended to focus only on the input parameters of the DBA algorithm which can be managed by the operator, i.e. SLA parameters. The idea is so, to try to optimize the management of these parameters in order to exploit in a more efficient manner the bandwidth available in the network, without modifying the implementation of the DBA mechanism itself as it was done in the majority of the reviewed works.

IV. PROBLEM STATEMENT

In our work, we propose a novel management procedure for optimizing the allocation of GPON resources based on the dynamic adjustment of the SLA parameters according to estimated customer traffic patterns. The latter will be identified through the use of clustering techniques based on real-time and historical data. The idea came from the fact that during the day, customers are not connected to the network in the same way. There are times when some of them need more than their PIRs, but they can not afford an extra bandwidth by the DBA due to the SLA parameters constraints. Thus, adjusting dynamically these parameters during the day can improve the QoS and maximize the overall satisfaction of users. To summarize, the problem can be formulated as follows:

• Given: The initial SLA parameters and the activity status of each ONU based on real-time and historical transmission data • Objective: Optimize the upstream resource allocation by adjusting the SLA parameters depending on the customer bandwidth usage • Output: New SLA parameters for each ONU at a specific period of time

V. THE PROPOSED MODEL

To achieve the main objective introduced in the previous section, we present a new architecture for optimizing the upstream bandwidth allocation in Fig. 3. To the best of our knowledge, this is the first time, an optimization approach based on the dynamic adjustment of SLA parameters and the customer traffic behaviour during the day is applied to PON networks. The proposed architecture consists of four main modules: Monitored Data Collector, Clustering Module, Assignment Index Calculator, and a mechanism for Reallocating SLA Parameters. The operation of each module is explained in the following.

A. Monitored Data Collector

In this module, the Initial SLA parameters are retrieved from the Management Information Base (MIB) only once for each ONU and then stored in a specific table. Monitored traffic data Fig. 3: Proposed architecture for the dynamic adjustment of SLA parameters for each ONU is collected from the MIB at regular intervals that can be parameterized by the network operator. It will be then stored as well as the historical transmission data which will be recovered from the network operator side.

B. Clustering Module

As the traffic utilization of GPON users may change several times per day since traffic patterns are linked to daily life, defining different time periods of the day when users have a similar traffic utilization can be very useful in the optimization of PON resources allocation. In this case we will refer to a clustering module to classify subscribers according to their online behaviour during the day. The main objective is to identify which users consume a lot of bandwidth (heavy users) and try to maximize their satisfaction in terms of QoS by giving them a surplus of bitrate on their EIRs. Consequently, for all day periods, the clustering will identify clusters of heavy users with a high upstream transmission bitrate and clusters which contain light users with a low upstream bitrate. The input of this module is the historical transmission data collected over some time horizon. The collection is achieved using a time series format with the average bitrates for each ONU over a parameterizable monitoring interval (e.g. 5min). The clustering process will be executed for the whole OLT in order to have as many as possible of data points. Table III presents an example of decomposing each day into four time slots, in each time slot, three classes of users can be distinguished: heavy, light, and flexible users.

C. Assignment Index Calculator

As the results of the clustering module are provided according to the chosen monitored time interval, we introduce an Assignment Index (AI) to classify the user's traffic by day period. This index ranges from 0 to 1 and represents the degree of attachment of one ONU to a certain traffic class in a specific day period. For instance, if during a day period, a user has been classified as heavy 5 times over 10 time intervals, then its AI to the heavy users class will be 0.5. The mathematical formulation for this calculation process is detailed in Algorithm 1 while the notations are provided in Table IV. The average of the extra bandwidth by day period for a specific day Algorithm 1 Assignment Index Calculation for j in DP do 3:

for each Ui do

4:

nbItr ← 0 # nbItr: number of time intervals in a day period j 5:

x ← 0 # x: number of times the Ui was considered as heavy 6:

y ← 0 # y: number of times the Ui was considered as light 7:

for t in j do 8:

if Ui ∈ Ct H then 9:

x ← x + 1 end for 20: end for In a first phase, the AI is computed upon the results of the clustering analysis. The latter is performed on the historical data provided by the service provider over a specified time horizon. To get a more accurate index, it is preferable to have a longer monitoring period as well as time intervals with smaller steps in a day period. As the index is calculated per day and per day period, we calculate the average of all daily AIs per day period for each user:

     AI avg C j H (U i ) = d∈Days AI d C j H (Ui) D ∀j ∈ DP, ∀i ∈ [1, n] AI avg C j L (U i ) = d∈Days AI d C j L (Ui) D ∀j ∈ DP, ∀i ∈ [1, n]
Since the AI avg C j H (U i ) and AI avg C j L (U i ) may not be too meaningful in the case where the different indexes are very dispersed, an additional step consisting in calculating the standard deviation will be strongly recommended to decide whether or not the mean value can be taken into account:

           AI sd C j H (U i ) = 1 D d∈Days (AI d C j H (U i ) -AI avg C j H (U i )) 2 AI sd C j L (U i ) = 1 D d∈Days (AI d C j L (U i ) -AI avg C j L (U i )) 2 ∀j ∈ DP, ∀i ∈ [1, n]
We propose that once the AI sd C j H (U i ) and AI sd C j L (U i ) reach a certain threshold AI sd T H , the AI avg C j H (U i ) and AI avg C j L (U i ) will not be taken into account and hence the U i will be assigned to flexible user clusters (i.e. C j F ). The AI sd T H value should be as close as possible to 0 to assert that the calculated averages are significant. Hence, the assignment index of a user during a long period of time can be a good criterion to classify it as heavy or light for a specific day period. Finally, to decide to which cluster the user belongs based on its mean AI, we suppose that:

   U i ∈ C j H if AI avg C j H (U i ) ≥ 0.75 ∀j ∈ DP, ∀i ∈ [1, n] U i ∈ C j L if AI avg C j L (U i ) ≥ 0.75 ∀j ∈ DP, ∀i ∈ [1, n] U i ∈ C j F Otherwise ∀j ∈ DP, ∀i ∈ [1, n]
To improve the accuracy of the AI process, we continuously consider the results of the clustering module. This is achieved based on the new data collected by the Monitored Data Collector module which is regularly updated. As a first step, we consider a weekly update. The AI is used as a reference in the reallocation of the SLA parameters in the network and the determination of the additional bandwidth that can be provided to heavy users.

D. Reallocation of SLA Parameters

The main objective of the reallocation of SLA parameters in the network is to try to maximize as well as possible the satisfaction of all users in a specific day period. Ordinarily, the DBA assigns to each ONU the amount of data to be transferred regarding its packet queue status and the whole state of the network. The problem is when there is a majority of light or offline users in the PON, the excess available bandwidth to be assigned by the DBA to heavy users (i.e. to their EIRs) may exceed their PIRs. Thus, heavy users do not take advantage of a part of the additional bandwidth due to their SLA parameters constraints. The idea is therefore to extend the EIRs for this class of users in such a way they can benefit from a bandwidth supplement whenever possible. We propose a calculation process of this extra bandwidth in Algorithm 2. This algorithm is performed by PON port, i.e. the considered users (whether light or heavy) are all part of the same PON port. We consider that offline users are part of light users cluster. Notations are provided in Table IV for j in DP do 3:

Sum L EIR T ← 0, ExBw ← 0 4:
for Ui in Cj L do 5:

Sum L EIR T ← Sum L EIR T + EIR(Ui) 6:
end for 7:

nbItr ← 0 # nbItr: number of time intervals in a day period j 8:

for t in j do end for 20: end for 21: for j in DP do The resulted extra bandwidth ExBw avg j is calculated by day period and represents the average of all extra bandwidths over a specific number of days. It will be shared between the heavy users according two possible options: either a fair sharing where the additional bandwidth is added to all ONUs in the same way, or a prioritization of some ONUs on others. In this work, we apply a fair sharing where all heavy users will have the same amount of ExBw avg j in a specified day period and so, the share of each user will be added to its EIR parameter. The new configuration of the SLA parameters will be then planned to be executed at a specific time. The Monitored DATA Collector is informed by the new SLA parameters and stored them in the same table as the initial parameters. In the event that a problem has occurred, a rapid return to the initial configuration can be performed. In the remainder of this paper, we will focus on the clustering module. The objective is to study and evaluate the different clustering mechanisms that exist in the literature in order to select which one can be the most suitable for our usecase.

VI. CLUSTERING MODULE

The easiest way to classify subscribers according to their online traffic behaviour over a time period is to look at the differences between the traffic data of each user in order to create common groups based on the traffic similarity. If we specify for heavy and light users the minimum (or maximum) threshold that each subscriber shall reach to be assigned to a specific class, then this approach can be the most suitable to be adopted. However, in PON networks, the usage segments can be very varied since all heavy or light users do not have the same behavior in terms of upstream data bitrate. Thus, there is no exact definition for these two classes of users. To overcome these limitations, we will refer to the clustering analysis approach which identifies the attachement of a user to a specific group without any prior assumption. Clustering analysis is a very common approach in the field of data analysis and related disciplines and can be very useful in the case of grouping customers into different classes regarding their traffic data. Given a specific data set, the objective of clustering is to find segments where objects are similar based on a measure of similarity (e.g. size, density, shape, etc.) [START_REF] Jain | Data clustering: 50 years beyond K-means[END_REF].

A. Clustering Algorithms

As many clustering algorithms exist in the literature and several categorization criteria can be taken into account, it is difficult to consider all of them in this work. For this, we will focus on two major fundamental clustering approaches that can be applied in our usecase which are respectively, partitioning methods and density-based ones [START_REF] Han | Data mining: concepts and techniques[END_REF]- [START_REF] Venkatkumar | Comparative study of data mining clustering algorithms[END_REF].

1) Partitioning Methods: Partitioning methods represent the most simplest and fundamental way to group points in clustering analysis. They take a set of n data points and try to construct k clusters (k ≤ n) while each data point belongs to exactly one cluster. The metric used to differentiate clusters in most of partitioning methods is the distance between the objects. Therefore, objects that belong to the same cluster are probably close [START_REF] Han | Data mining: concepts and techniques[END_REF]. The most well-known partitioning algorithm in the literature is the K-means. Even if it was proposed a long time ago, K-means [START_REF] Macqueen | Some methods for classification and analysis of multivariate observations[END_REF] remains one of the most used partitioning algorithms by researchers thanks to its simplicity and ease of implementation. The K-means algorithm performs as follows. Given a data set D containing n objects and k the number of clusters, the algorithm selects arbitrarily k points from D called cluster centroids. Then, each remaining point in D will be assigned to one of the k clusters in such a way that the Euclidean Distance between the points and the centroids is minimized. This process will be repeated for several times and in each time, the centroids values will be updated based on the objects that belong to the corresponding cluster. Then, all objects will be re-assigned taken into account the new cluster centers. Once the centroids values and the objects assignments are immutable, the algorithm process is stopped and clusters are formed [START_REF] Jain | Data clustering: 50 years beyond K-means[END_REF].

2) Density-Based Methods: Density based methods represent clustering approaches that divide a set of data points into dense regions separated by scattered ones. The capacity of a given cluster continues to increase as long as the number of objects, i.e. density, in the "neighborhood" reachs some threshold [START_REF] Han | Data mining: concepts and techniques[END_REF]. One of the most common and cited densitybased clustering algorithms is DBSCAN (Density Based Spatial Clustering of Applications with Noise). It was proposed for the first time in 1996 [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF]. The idea of DBSCAN is to find core data points which have dense neighborhoods in order to connect them and form the corresponding clusters. Unlike partitioning algorithms, DBSCAN does not require any specification regarding the number of clusters. Only two parameters need to be taken into account: the maximum radius of each cluster " " and the smallest number of cluster points "M inP ts" which represents the density threshold of a dense region [START_REF] Lu | Data mining applied to oil well using K-Means and DBSCAN[END_REF]. The process of the DBSCAN algorithm is as follows. Given a data set D, and M inP ts, all points are marked as unvisited. The algorithm selects a randomly unvisited point P and marks it as visited. Then it calculates the number of points within the -neighborhood of P ( -neighborhood = {Q ∈ D/dist(P, Q) ≤ }). If the number of points is larger than M inP ts, a new cluster is created containing all identified points. Else, P is considered as noise point and does not belong to any cluster. The same process will be repeated until all points are assigned to a cluster or considered as noise [START_REF] Ester | A density-based algorithm for discovering clusters in large spatial databases with noise[END_REF] [START_REF] Anikin | Privacy preserving DBSCAN clustering algorithm for vertically partitioned data in distributed systems[END_REF].

B. Experimental Results

In order to analyse and evaluate the clustering algorithms presented in section VI and choose which one is more suitable for our use case, we rely on a real traffic trace collected based on a tool developed within Orange France called OTARIE. This probe is based on a software written in C that works on various PC-based hardware architectures equipped with a DAG (Data Acquisition and Generation) traffic capture card which has an API that allows to read the packets as they arrive on the network interface. The traffic traces that we dispose are collected for 3447 ONUs belonging to the same OLT equipment over a period of two weeks between the 7th and the 20th of November 2016. However, they do not cover the whole day. For this, we have chosen to work on a specific period of the day between 9p.m and 12a.m with a 5 minutes interval since the clustering approach becomes very advantageous in the case of busy hours when a significant number of subscribers are online. Due to space constraints, we present the results only for the day of November 14, 2016. Fig. 4 shows the distribution of the different users by common slice of mean upstream bitrate. For a better representation, we limited the time axis scale between 9:05p.m and 10:05p.m. In the following subsections, the results of the application of the K-means and DBSCAN algorithms to our dataset are presented. The accomplishment of the experiment relies on the use of the sklearn library [START_REF] Pedregosa | Scikit-learn: Machine learning in Python[END_REF] provided for Python developers. Matplotlib and seaborn modules have been used for plotting the different points and clusters in the most convenient way.

1) K-means: As mentionned in section VI-A1, the K-means algorithm takes as input the number of possible clusters k. In our dataset, k represents the number of user classes per a parameterized interval of time t (see Table IV). We would expect that for each time interval t, a maximum of 3 user classes may exist: heavy, light and the rest of users. Therefore, we evaluated the K-means algorithm with k = 3 for each time interval. Two metrics were used to calculate the Euclidean Distance used by K-means to differentiate user classes: the first consists in directly calculating the difference between two ONUs mean upstream bitrates. The second applies the decimal logarithm on the ONUs mean upstream bitrates. The results are presented respectively in Fig. 5 and Fig. 6. In all intervals, the three requested clusters are visualized. In Fig. 5, the K-means algorithm has assigned the majority of users with a very low mean upstream bitrate to the same cluster. In Fig. 6, the use of the decimal logarithm metric allows to have a more balanced distribution between the different clusters. 2) DBSCAN: Unlike K-means, DBSCAN does not have any requirements regarding the specification of the number of clusters before analyzing the dataset. However, the most difficult task lies in how to choose the and M inP ts parameters discussed in section VI-A2. We assume that a user class can contain at least one user (heavy or light), that is, even if only one user has been assigned to a group, the DBSCAN algorithm must take it into account and not consider it as noise. It is possible to have a minority of users who are online during a day period. If we add that the final assignment of a user to a specific cluster depends on the calculation of his AI (i.e. the M inP ts value does not reflect the final percentage of heavy or light users), we can propose as a first hypothesis that M inP ts=1. Regarding , we tried to vary it in order to choose which value can produce the best clustering results. In our case, can be understood as the gap between two user classes. Thus, the wider the gap, the easier the interpretation of the clusters. The tested values range from 0.1 Mbit/s to 20 Mbit/s. When the value decreases, more clusters are formed by the DBSCAN algorithm. The number of resulted clusters is a very important criterion to take into consideration in traffic patterns classification. Indeed, the higher it is, the more complicated the interpretation will be. Between the different evaluated values, we have chosen to show the results for =10 Mbit/s (see Fig. 7) since the number of the identified clusters is the same as the number of clusters initialized to K-means (i.e. k = 3).

C. Discussion

The evaluation of the K-means and DBSCAN algorithms allows us to visualize and differentiate users according to their traffic patterns. DBSCAN, thanks to its concept based on the differentiation of points according to their density, makes it possible to determine heavy and light user classes. However, it has a strong tendency to identify only a very small number of heavy users compared to the number of light ones using a 5 minutes time interval. This may seem as a major drawback for this algorithm in a policy of maximizing satisfaction for all network users. The other problem with DBSCAN is that we can fall in a case where one of the identified clusters contains heavy and light users in the same time. This case can occur when there are no differences between the densities of points in one time interval in such a way that the epsilon parameter has no effect (e.g. the interval of 10:05 pm in Fig. 7). Concerning K-Means, this algorithm gives a much more balanced distribution in terms of users number between heavy and light. The use of the decimal logarithm metric allowed to have a better classification results compared to the other metric. Nonetheless, K-means has the disadvantage of depending on the initial positions of different centroids and the need to specify for it the possible number of clusters before each process.

VII. CONCLUSION AND FUTURE WORK

A new mechanism for reallocating SLA parameters based on users traffic patterns in a PON network has been proposed in this paper. A particular attention has been granted to the clustering module which allows to classify subscribers according to their hourly online behaviour during the day in order to have clusters that contain heavy users who have a high usptream transmission bitrate and clusters which contain light users with a low transmission upstream bitrate. Two clustering approaches have been evaluated in this paper, namely K-means and DBSCAN algorithms. The analysis that we have conducted is based on the ability of each algorithm to differentiate or not the PON users according to their mean upstream bitrates by time interval in a day period. The results showed that the two algorithms can meet this requirement. However, K-means based on the decimal logarithm metric shows a better classification results compared to DBSCAN in terms of equitable distribution between heavy and light users. This can be an important point in terms of maximizing the satisfaction of all users. In a future work, we expect to continue the investigations on the presented and the other clustering algorithms (e.g., hierarchical clustering) in order to select the most efficient tool for classifying PON users. Given that the traffic traces that we dispose are collected over a limited period of two weeks, we plan to complete the analysis of our approach using a network simulator. This will allow us to have more visibility and to evaluate the whole mechanism while taking into account several QoS parameters.

Fig. 1 :

 1 Fig. 1: Static Bandwidth Allocation (SBA) and Dynamic Bandwidth Allocation (DBA) mechanisms

Fig. 2 :

 2 Fig. 2: Status Reporting (SR-DBA) mode

1 :

 1 for d in Days do 2:

Fig. 4 :

 4 Fig. 4: Distribution of users per mean upstream bitrate slices

Fig. 5 :

 5 Fig. 5: K-means results (k=3, metric: ONUs mean upstream bitrates)

Fig. 7 :

 7 Fig. 7: DBSCAN results ( =10, M inP ts = 1)

TABLE II

 II

			: SLA Parameters
		SLA Parameters		Significance
		Committed	Fixed Information Rate	* Fixed bandwidth allocated to T-CONT type 1
	Peak Information Rate	Information Rate	(FIR)	* Untouchable parameter * Reserved cyclically regard-
				less of demand
	(PIR)	(CIR)	Assured Information Rate	* Assured bandwidth allocated to T-CONTs type 2 and 3
	PIR = CIR + EIR	CIR = FIR + AIR	(AIR)	* Not given without demand
		Excess Information Rate (EIR)	* Allocated to T-CONTs type 3
				and 4

TABLE III :

 III Clustering Explanation

	Day Period	Time Slot	User Traffic Classes	Cluster Index
	Morning	6 a.m. to 12 p.m.	Heavy Users Light Users	C M H C M L
			Flexible Users	C M F
	Afternoon	12 p.m. to 6 p.m.	Heavy Users Light Users	C A H C A L
			Flexible Users	C A F
	Evening	6 p.m. to 11 p.m.	Heavy Users Light Users	C E H C E L
			Flexible Users	C E F
	Night	11 p.m. to 6 a.m.	Heavy Users Light Users	C N H C N L
			Flexible Users	C N F

TABLE IV :

 IV Table of Notations

	Notation	Meaning
	U Sum L EIRT	The sum of theoretical EIRs of light users
	Sum H EIRP ExBw avg j-d	The sum of provided EIRs to heavy users

i User index, i ∈ [1, n], with n:total number of users t Interval of time in a day period, e.g. with a 5 minutes step D Number of supervised days Days The set of supervised days DP The set of day periods (e.g. morning, afternoon, evening, and night) C t H The cluster which contains heavy users for a specific interval t C t L The cluster which contains light users for a specific interval t AI d Cj H (U i ) AI of U i to the heavy users cluster in the day period j of the day d AI d Cj L (U i ) AI of U i to the light users cluster in the day period j of the day d CIR(U i ) Committed Information Rate of U i EIR(U i ) Excess Information Rate of U i BR avg t (U i ) Mean upstream bitrate of U i over a specific interval t

  .

	Algorithm 2 Extra Bandwidth Calculation

1: for d in Days do 2: