Improving the Efficiency of Online Upstream ... - Semantic Scholar

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Improving the Efficiency of Online Upstream Scheduling and Wavelength Assignment in Hybrid WDM/TDMA EPON Networks Konstantinos Kanonakis, Member, IEEE, and Ioannis Tomkos, Member, IEEE

Abstract—Two general approaches have been followed for solving the problem of upstream grant scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks, i.e. the offline and the online one. The latter boasts significantly lower frame delay performance in all cases. Nevertheless, we show that simplistic online schemes do not utilize wavelength resources as efficiently as possible, especially in the case of large differential distances of ONUs from the OLT. We propose and analyze several low- and higher-complexity solutions to overcome those inefficiencies, leading to improved utilization of network capacity and reduced frame delay. All schemes are evaluated and compared using computer simulations. Index Terms—Ethernet passive optical network (EPON), medium access control (MAC), time division multiple access (TDMA), wavelength division multiplexing (WDM), dynamic bandwidth assignment (DBA), dynamic wavelength assignment.

I. I NTRODUCTION

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AVELENGTH division multiplexed passive optical networks (WDM-PONs) have received a significant amount of attention lately as one of the solutions for boosting the performance of traditional PON networks in terms of scalability, available bandwidth and flexibility. A typical PON network comprises one Optical Line Termination (OLT) located at the Central Office (CO) and a number of Optical Network Units (ONUs). The cost-effectiveness of the PON concept lies in the fact that the longest part of the fiber in the Optical Distribution Network (i.e. from the CO to the users) is shared among ONUs: This common feeder fiber connects the OLT with a passive optical splitter/coupler, usually located close to the ONUs. Hence, the optical signal in the downstream direction is broadcast to all ONUs and each one should select only the data that is destined to them. In the opposite direction, the data sent by all ONUs is combined by the coupler and sent to the OLT. Care should be taken by the OLT, which orchestrates the upstream Time Division Multiple Access (TDMA) operation, to avoid overlapping among ONU transmissions. One of the predominant PON protocols is the EPON, defined by the IEEE [1]. A WDM-EPON adopts essentially the same architecture as a TDMA-EPON, with the difference that the sharing of resources by the ONUs is not achieved solely in the time domain, but also in the wavelength Manuscript received August 13, 2009; revised January 29, 2010. This work has been partly supported by the E.U. FP7 Project SARDANA. Konstantinos Kanonakis and Ioannis Tomkos are with the High-Speed Networks and Optical Communications Group, Athens Information Technology Center, 19.5km Markopoulo Ave., Peania 19002, Athens, Greece (e-mail: {kkan,itom}@ait.edu.gr).

domain. Recently, various architectures have been proposed ([2]–[4]), which extend the scope of the access network to cover a metro area, with multiple PON trees attached to different Remote Nodes (RNs) and managed by only one CO. In the simplest case, no TDMA operation is necessary in any WDM-EPON architecture, as the OLT can statically assign one pair of wavelengths (for downstream/upstream) to each ONU, leading thus to a set of virtual point-to-point connections. In multi-tree architectures where such an approach would require a large amount of wavelengths, a simple solution would be the static assignment of a pair of wavelengths to each PON tree, which can then operate as normal. In these ways, the total capacity of the network is increased using the same fiber infrastructure, while network control and management are largely simplified. Nevertheless, this static assignment of wavelengths does not provide efficient utilization of the resources (i.e. wavelengths), since in the former case each ONU would only consume a small portion of a wavelength, while in the latter case there could be periods of inactivity in some PON trees with simultaneous overload in some others. In addition, it would be beneficial if a single OLT MAC process could control all ONUs in the network. A more advanced approach would hence allow the OLT to independently and dynamically assign each time the wavelength on which each ONU in the network will transmit its upstream data based on channel availability, leading to a hybrid WDM/TDMA way of operation. In that case, significant performance benefits can be achieved due to the statistical multiplexing gain by globally sharing the upstream wavelengths, however efficient algorithms are needed for the assignment of the upstream wavelengths and the scheduling of transmissions within each one of them. There exist two general approaches for handling this issue: The offline and the online one. In the former case, the OLT waits until it has received all the reports from ONUs (or part of them [5], [6]) and then performs some algorithm to find the best scheduling and wavelength assignment scheme for the corresponding grants. In the latter case, upon the arrival and processing of a report from an ONU, the OLT immediately decides on the scheduling and wavelength assignment for the corresponding grant. Although the offline approach allows for scheduling decisions that take into account fairness and QoS issues among different ONUs [7], it is shown [5]–[7] that the online one always outperforms it in terms of frame queuing delay, therefore the motivation of devising algorithms to improve wavelength utilization under the online assumption

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is strong. This work identifies the inefficiency problems that arise in the case of online upstream scheduling and wavelength assignment (online USWA), especially in the case of upcoming next generation long-reach WDM-EPON networks (introducing longer reach and larger number of supported ONUs) and proposes algorithms to minimize them. The main driver for this work (as will also be detailed in Section III) has been the observation that online scheduling inefficiency is strongly affected by the presence of large differential distances of various ONUs from the OLT, which is inevitable in any PON network but even more in metro-scale PON architectures. The paper is structured as follows: Section II presents the WDM-PON architectures that are considered for the rest of the work, as well as the control framework assumed for the bandwidth allocation. In Section III the inefficiencies that arise when adopting simplistic online USWA schemes are identified. Next, in Section IV a variety of online USWA algorithms are described in detail while Section V provides an insightful discussion that includes scheduling theoretic results and a detailed rationale for the chosen solutions. In Section VI the performance of the proposed schemes is evaluated with the help of computer simulations. Finally, in Section VII conclusions are drawn. II. WDM-PON N ETWORK A RCHITECTURE AND C ONTROL O PERATION A. Network Architecture While no standardized architecture for WDM-PON networks has appeared till now, there have been numerous solutions proposed in the literature [8]. As mentioned in Section I, the simplest solution stems directly from a classical tree-shaped PON topology. We will refer to this topology as GENERIC to facilitate discussion. In this case, the downstream signal (including all wavelengths) is broadcast to all ONUs by

means of a passive splitter and then each ONU must extract the specific wavelength assigned to it by the OLT. In the opposite direction, each ONU sends data in a different wavelength and all signals are coupled and received by the OLT. As mentioned above, it is possible to adopt either a pure WDMA approach (by assigning each wavelength to a different ONU) or a hybrid WDM/TDMA one (whereby each wavelength is shared in the time domain by more than one ONU). The second architecture considered (viz. Fig. 1), employs a metro WDM ring which interconnects the CO with several RNs. We will refer to it as RING to distinguish it from the GENERIC topology. RING is very similar to both the SUCCESS [2] and the SARDANA [3], [4] architectures. Each RN uses three 2:1 splitters to drop the WDM signal and then everything operates exactly like in the GENERIC architecture. The maximum OLT-ONU distance can be in the range of 100 km while a reasonable amount of RNs is about 4-5, leading to a maximum total of few hundreds of customers served by a single central office and effectively sharing the same WDM wavelength channels. The work being conducted in the framework of the FP7 ICT Project SARDANA [4] considers remote amplification to solve power budget issues in such architectures. Further solutions (both passive and active) to achieve power budget improvement and/or increase the number of users served, are investigated in [9]. The RING topology combines desired characteristics like long reach, wide user coverage and resilience (in case of a fiber cut in the ring the other direction can still provide connectivity). As it will become more obvious below, it is of special interest in this work due the inherent sparseness of ONUs throughout the whole network. A very important issue in WDM-PON networks is the need for colorless ONUs, i.e. their transmitters/receivers are not tuned to a specific wavelength only. This facilitates a lot the management and distribution of ONU equipment and at the same time allows for dynamic wavelength assignment schemes. Hence, we will hereafter assume that ONUs in both architectures are either colorless or able to operate within a specific wavelength range. Despite the relatively high cost of this feature at present, latest technological advances (e.g. directly modulated lasers - DMLs or arrays of integrated lasers, like VCSELs) indicate that it could become commonplace in the near future. Moreover, it is important to stress that in most cases the cost of the ONU would be shared among many end users: Given the very high data rates potentially offered to the individual ONUs (in the range of multiple hundreds of Mbps), the latter can be considered as endpoints towards enterprise LANs or groups of DSL customers. B. Control Operation The authors in [10] have already proposed modifications to the IPACT protocol of EPONs to support dynamic bandwidth allocation in WDM-EPONs and have named their protocol Simultaneous and Interleaved Polling with Adaptive Cycle Time (SIPACT). A similar scheme has also been proposed in [11]. We will hereafter assume the SIPACT approach for the control operation, as it constitutes a logical and generalized continuation of current EPON bandwidth allocation mechanisms. The

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framework is still based on the concept of the Multi-Point Control Protocol (MPCP) as defined in [1]: There are five types of MPCP control frames: The REGISTER REQ, REGISTER, REGISTER ACK, REPORT and GATE messages. The first three (used for the ONU discovery and registration process) must be modified to include information regarding the supported wavelengths by each ONU. The REPORT and GATE messages are used by the ONUs for reporting their queue status and by the OLT for granting upstream timeslots to the ONUs respectively. The latter must now also convey the upstream wavelength on which the ONU is supposed to send its granted amount of data. For more insight on MPCP modifications required for the WDM-EPON case the reader is referred to [7]. III. P ROBLEM D EFINITION Our work is based on the following observation: In any PON network the need for supporting a large user base, combined with the difficulties of optimal placement of the remote nodes in the field and the targeted long-reach of next generation access networks, will inevitably lead to a considerable spread of round-trip values among the various ONUs, i.e. large differential distances. Such scenarios make even more sense in the case of very sparsely populated or rural areas while the same situation naturally arises in architectures resembling the one in Fig. 1. In any case, the end result is what we refer to as scheduling voids. This will be better explained with the help of the example depicted in Fig. 2(a). Imagine that at some point, due to a previous report not shown in the figure, the OLT sends a GATE frame (G1 in the figure) to the relatively near ON U0 . This grants an amount of bytes that corresponds to

a group of Ethernet frames (shown as E1 in the figure) to be sent in the upstream wavelength λ0 . After some time (and before the reception of the data and report from ON U0 , in line with the SIPACT philosophy), the OLT decides to assign again wavelength λ0 to the distant ON U2 . The reception of the corresponding upstream data frames E4 and report R4 will come much later in time, due to the high round-trip delay for ON U2 . However, existing online USWA schemes will consider λ0 as reserved till the end of the transmission of R4, adopting a “horizon” approach. As a result, G3 to ON U1 assigns λ1 , while the subsequent G4 to ON U0 assigns λ2 , although the upstream transmission of E2 and R2 could in essence be scheduled either in λ0 or λ1 , before the beginning of the already scheduled ones. We refer to the time intervals that can not be utilized (e.g. from the end of R1 till the beginning of E4 at λ0 ) as scheduling voids. Subsequent grants will inevitably have to be scheduled after R4, R3 or R2, leading to increased frame delay, as opposed to a “void filling” scenario [see Fig. 2(b)]. Note that the issue is not present in off-line algorithms since in that case the OLT would normally wait until the REPORT messages from all ONUs have arrived and then try to arrange upstream scheduling in an optimal way (obviously having the opportunity of not leaving any voids, or at least minimizing them to a great extent). The important question then is how large these scheduling voids are expected to be, compared to the amount of data that need to be granted per ONU. In other words, to which extent these scheduling voids can actually affect packet delay and, more importantly, be exploited to achieve improved performance. In the normal case, each user will only require a small fraction of each wavelength, which is translated to smaller chunks of data being sent upstream by each ONU.

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If the expected duration of these chunks is in the same order of magnitude or smaller than the duration of voids (which in turn, as is obvious from the preceding discussion, is directly dependent on the differential round-trip times between ONUs), then we can consider the inefficiency as considerable and the voids as eligible to be used for inserting upstream transmissions. In other words, the problem will arise when differential round-trip delays are large compared to the mean round-trip, while a higher number of ONUs per wavelength will make the situation even worse (hence even traditional TDMA EPONs, where W = 1 are affected as well, especially when their split ratio is high). Finally note that voids can also appear to some extent due to variations in the size of grants as a consequence of temporal variations in the ONU traffic rate. To our knowledge, no work so far has addressed in depth either the issue of inefficiency due to scheduling voids or ways of solving it to improve the performance of online USWA in WDM-EPONs, with the exception of our work presented in [12]. Therein we described the problem in brief and outlined a possible solution based on void filling (First Available Void - FAV). In the present paper we propose and evaluate a much wider range of solutions for online USWA, including on the one hand more sophisticated void filling algorithms (EFT-VF, LFT-VF) and on the other some reducedcomplexity schemes (LFT, DBG) which can under conditions provide satisfactory performance. In addition, we chose EFT for evaluating all other schemes since it is a variation of the most common algorithms found in the literature. Finally, the performance evaluation is extended by also including metroscale architectures (the RING one of Section II) along with typical tree-like ones. IV. O NLINE USWA A LGORITHMS In this section we describe possible online algorithms for the processes of wavelength assignment and grant scheduling. The complete problem of bandwidth allocation in a WDM-EPON consists both by the grant sizing and grant scheduling. The former addresses the issue of how many bytes the OLT will grant to an ONU in the next cycle, given its last queuing report, while the latter defines where (both in time and wavelength domain) this grant will be placed. In order to facilitate the performance comparison of the various proposed algorithms, in this work only grant scheduling will be considered, while sizing is assumed to be based on a simple gated approach. In other words, the OLT grants to an ONU the exact amount of bytes reported in its last REPORT message. Note also that we do not consider downstream transmissions in order to facilitate the isolated evaluation of the solutions proposed. Below we provide the basic notation used: ON Uk , k = 1, ..., N : Each of the N ONUs in the network rttk : Round-trip propagation time between OLT and ON Uk . Dk : Distance between OLT and ON Uk . Wk : Set of upstream wavelengths supported by ON Uk . tc : Time required for the transmission of control frames (GATE or REPORT). Sij : Arrival time at the OLT of the first bit of the j th scheduled

upstream transmission at wavelength i. Fij : Arrival time at the OLT of the last bit of the j th scheduled upstream transmission at wavelength i. Hi : Finish time of the last reservation scheduled within wavelength i up to the present time. We will refer to Hi as the finish time (or horizon) of wavelength i. Using the notation defined above, it holds that: Hi = max Fij

(1)

j

In order to facilitate descriptions in the case when some channel i possesses no reservations, we that o n can consider initially all wavelengths contain one Sij , Fij pair with Si1 = Fi1 = 0. Moreover, for simplicity we will hereafter ignore processing delays at the OLT and the ONUs, as well as possible laser tuning delays. During the descriptions of all algorithms that will follow, we consider the case of a report message from ON Uk arriving at the OLT at time t and reporting G bytes. Any algorithm should n identify for it the set {w, n, Sw , Fwn , d}. We remind that the w value indicates the chosen upstream wavelength, n is the position index of the reservation within this wavelength (if it is inserted in between other reservations, the numbering of n and Fwn are subsequent ones should change appropriately), Sw the start and finish times of the reservation and d denotes a time parameter that will be defined below. This set of values satisfies the following basic constraints: w ∈ Wk

(2)

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(3)

n Sw = max Fwn−1 , t + rttk + tc n Sw = t + rttk + tc + d, d ≥ 0




m n 6 ∃m| (Sw ≤ Fwn ) ∧ (Fwm ≥ Sw )

(4) (5) (6)

(3) stems from the fact that grant sizing is not considered, hence the reserved duration should equal the number of reported bytes plus tc for sending the updated report. (4) implies that the new reservation can be scheduled immediately after the preceding one, as long as this is not earlier than t+rttk +tc . In the latter case, (5) indicates that the GATE message transmission must be sufficiently delayed by a duration d, so that upon its reception and processing by the ONU, the data and REPORT can be immediately sent upstream avoiding collisions. Finally, (6) provides the necessary non-overlapping condition with any other transmission scheduled in the selected wavelength. The following sections will elaborate on how the wavelength assignment [selection of w, of course subject to (2)] and scheduling (selection of n) are performed for each algorithm described. As soon as the {w, n} pair has been decided, then n Sw is calculated based on (4) [which in turn implies a d value satisfying (5)] and Fwn using (3).

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A. The EFT Algorithm The most straightforward and less complex algorithm for online USWA is what we refer to as Earliest Finish Time (EFT): Upon the arrival of a REPORT message from an ONU, the OLT schedules the corresponding grant as follows: w = arg min Hi , i ∈ Wk

(7)

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In other words, no other transmission in the same wavelength should have been programmed after the selected schedule, while the selected wavelength should have the earliest finish time among all channels. The OLT then only needs to keep track of the finish time of each wavelength, and the complexity to schedule a grant using the most straightforward implementation of the algorithm is O(W ). O(log W ) complexity can be achieved if binary search is employed, however this implies using a balanced binary tree for sorting wavelengths based on their horizons after every single reservation [each insertion in the tree needs O(log W ) time]. Variations of the EFT algorithm have appeared in many works, as it is the simplest possible way of achieving dynamic bandwidth allocation in WDM-EPONs. In particular, the NASC algorithm described in [5]–[7], as well as the algorithms proposed in [2], [10], are very similar to EFT, while all DWBA algorithms in [13] also consider a wavelength as free only after the last upstream transmission programmed within it. Notwithstanding its simplicity and multiplexing gain due to the possibility of solving upstream contention in the wavelength domain (compared to a static assignment of wavelengths), the EFT algorithm is suboptimal in the sense that upstream channels are not utilized as efficiently as possible. The reason is that, as explained in Section III, it is expected to lead to the formation of scheduling voids, wasting upstream transmission time and resulting in increased frame queuing delay.

then the wavelength assignment can be described by: ( arg max (Hi |i ∈ Lk ) , Lk 6= ∅ i w= , i ∈ Wk arg min Hi , Lk = ∅

(10)

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Following the descriptions of EFT and LFT we can define the class of horizon-based, non-detaining online USWA scheduling disciplines with immediate dispatching. It includes all algorithms which obey to (8) and also guarantee that, given the past schedule, each new grant is scheduled as early as possible (no additional delay is imposed if it can be avoided) and the decision is taken upon the arrival of the report. Obviously both EFT and LFT belong to this class. Moreover, we can claim that: Theorem 1: LFT is optimal in terms of Report-to-Grant (RTG) delay among all horizon-based, non-detaining online USWA scheduling algorithms with immediate dispatching. Proof: We begin by making the following observations: The minimum possible RTG delay is always rttk + tc and from (5) we see that the only variable delay component is in fact d. With the help of (4),(5) we can calculate the value of d for any horizon-based, non-detaining online USWA scheduling discipline as follows: ( 0, Lk 6= ∅ (11) d= min Hi − (t + rttk + tc ), Lk = ∅ i∈Wk

Therefore, if it is ensured that at any point in time (or in other words after any completed reservation), the term min Hi i∈Wk

is kept minimal for all k, then any new reservation will be scheduled with the minimum possible extra delay. Without loss of generality, consider that at a random point in time ty , a report Ry from ON Uy arrives at the OLT and the corresponding grant Gy is scheduled at wavelength w using LFT. Given the past schedule, the non-detaining property of LFT ensures that Gy creates the minimum possible new horizon when Ly = ∅ while when Ly 6= ∅, (10) ensures that min Hi for any k remains intact if possible. Note though i∈Wk

B. The LFT Algorithm We propose a variation of EFT which we call Latest Finish Time (LFT). It maintains almost the same complexity as EFT, while providing improved channel utilization. The idea is as follows: The constraint that no other transmission in the same wavelength should have been programmed after the selected schedule, described by (8) still holds, however the selected wavelength must now have the latest finish time among all channels, as long as this is not later than t + rttk + tc . The intuitive rationale behind LFT is that voids left before a scheduled upstream transmission are less likely to be used in the future (especially if the current scheduling if for a near ONU), hence they should be minimized as much as possible. Note though that if no channel with finish time less than t + rttk + tc exists, then the algorithm switches to EFT in order to avoid unnecessary delays. If we define the set Lk such that: Lk = {i|Hi ≤ t + rttk + tc } , i ∈ Wk ,

that in the latter case there are probably more than one candidate channels offering the same result. Now consider the subsequent report Ry+1 from ON Uy+1 arriving at ty+1 > ty . We identify two cases: 1) ty+1 + rtty+1 + tc ≥ Hw : In that case no change in the existing scheduling of Gy can affect the horizon produced by Gy+1 . 2) ty+1 + rtty+1 + tc < Hw : If at ty it held that Ly = ∅, then any non-detaining scheme would schedule Gy on w as well. Let us consider the case Ly 6= ∅: Suppose that at a non-detaining scheme other than LFT had scheduled Gy on another wavelength w ´ ∈ Ly , such that Gy+1 would be allowed to create a earlier horizon. This could only possible if at ty it held that Hw < Hw´ . However, since Ly 6= ∅, from (10) we have that Hw = max(Hi |i ∈ Ly ). We have proven therefore that LFT ensures the minimum possible min Hi , for any k, after any two consecutive reseri∈Wk

(9)

vations. Applying this result recursively, beginning from the

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first report (y = 1) we deduce that the same holds after any completed reservation, which completes our proof. Regarding computational complexity, what was mentioned in Section IV-A regarding EFT applies for LFT as well, however the latter has the relative advantage that any empty wavelength can directly be selected since it always fulfils the required criteria. Regarding performance, it is expected that under low loading conditions LFT will outperform EFT, while as loads increases they should tend to demonstrate almost the same behavior, due to the increased probability of all wavelengths being busy before t + rttk + tc .

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In order to make up for the decrease in channel utilization and subsequent increase of frame queuing delay inherent in both aforementioned algorithms, we propose the Earliest Finish Time with Void Filling (EFT-VF) algorithm which works as follows: The OLT keeps track of all scheduling voids in all upstream wavelengths (including the ones defined by the last transmission and the positive infinity) and schedules the upstream transmission for an ONU to take place within the earliest (i.e. the reservation preceding it has the earliest finish time) void which is large enough to contain the granted upstream data plus the accompanying REPORT message. Before formulating the {w, n} selection process, we need to define the set of eligible voids [in order not to violate (6)], or equivalently the set Vk that includes only finish times which precede eligible voids: o  n  Vk = Fij |Sij+1 − max Fij , t + rttk + tc ≥ G + tc , i ∈ Wk (12)

Then, the wavelength assignment and scheduling are described by:   (13) w = arg min Fij |Fij ∈ Vk , i ∈ Wk i
n = arg min Fwj |Fwj ∈ Vk + 1 (14) j

The computational complexity of this algorithm is clearly higher than that of EFT and LFT since the number of voids in the schedule is always higher than the number of wavelengths. It is easy to see though that the maximum amount of voids at any time is upper bounded by W + N , where W is the number of upstream wavelengths, given that at any time there can be at maximum one reservation pending per ONU. Thus, a simple implementation of EFT-VF schedules a single grant in O(W + N ) time, which can be improved to O (log (W + N )) (see IV-A). Moreover, in case some grants are scheduled back-to-back, their intermediate gap is not considered as an eligible void, reducing thus the amount of searches in practice. EFT-VF is expected to always perform better than EFT and LFT in terms of frame delay due to the full exploitation of all possible upstream scheduling opportunities. Of course we could equivalently define the LFT-VF algorithm; however it is expected to exhibit similar performance with EFT-VF. The main reason is that new voids created after performing void filling are too short to be usable in the future, which was also verified by initial simulation results. Therefore we will

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hereafter use only EFT-VF for evaluating the performance of void-filling, non detaining online USWA algorithms with immediate dispatching. Fig. 3 clarifies further the operation of all algorithms described hitherto. Shaded boxes indicate already scheduled upstream transmissions, while white ones represent the current reservation (i.e. for the report that arrived at time t). In Fig. 3(a), the case Lk 6= ∅ is illustrated. It can be seen in the figure that among all three channels which can offer the same delay for the new reservation, EFT and EFT-VF both choose λ0 since it possesses the earliest horizon (the VF variants of course consider the respective reservations as being placed in the voids formed by the horizons of the channels and the positive infinity). On the other hand LFT and LFTVF are scheduled on λ1 , creating as a result the minimum possible void “behind” the new reservation. Fig. 3(b) depicts the behavior of the algorithms when Lk = ∅. In this case, the only option for both EFT and LFT is λ2 since it has the earliest horizon. On the other hand, EFT-VF and LFT-VF can be scheduled earlier and among all 5 eligible voids they choose the ones starting the earliest and latest correspondingly (as long as there are voids starting before t + rttk + tc in the case of LFT-VF). D. The DBG Concept The Distance-Based Grouping (DBG) concept, also introduced in this paper, follows a completely different line compared to EFT-VF. Rather than trying to maximize the utilization of scheduling voids, it instead aims at minimizing the existence of voids in the first place. This is achieved by producing a mapping of ONUs with similar round-trip times to the same set of upstream wavelengths, i.e. by not allowing each ONU to send in any wavelength, even if they are physically capable of doing so. The OLT hence must keep some data structure containing this mapping, which should be updated with every new ONU being registered in the network. Since within each group the differential round-trip delays will now be much lower and the groups operate on

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separate wavelengths, the voids produced are expected to be significantly shorter, leading to higher channel utilization and consequently lower packet delay. In fact, the DBG concept can be employed along with any of the schemes described above, whereby the aforementioned algorithms will be used for the USWA within each individual group. It is obvious that the added complexity of this scheme is very low and consists of the grouping algorithm and the relevant data structure maintenance processes which need to run only during new ONU registrations. In addition, another advantage of DBG is that it could potentially reduce the cost of ONUs by shortening their required wavelength range. Regarding the exact grouping algorithm, for the purposes of this work and just for demonstrating the effectiveness of DBG, we adopt a simple approach (which we call fixed DBG) whereby all groups contain the same (fixed) number of ONUs. If the number of groups is denoted by M , then it should always hold that M ≤ W and M ≤ N . Accordingly, each group contains N/M ONUs (which are neighbors in a list sorted based on round-trip times) and each group operates only within W/M wavelengths (for simplicity we assume that all ONUs support all W wavelengths, N = n · M and W = m · M , where n, m are integers ≥ 1). In reality, a potential disadvantage of all DBG approaches is that since an integer amount of wavelengths has to be assigned to each group proportionally to their cardinalities, it is inevitable that some unfairness will arise (some groups will receive more bandwidth than their actual needs and vice versa - in addition, different ONUs may not have the same contracted rate). The situation is further aggravated in other DBG approaches which result to groups with variable cardinalities. For example, k-means clustering which is a simple and easy to implement algorithm for clustering data sets given the number of clusters that need to be formed [14] was considered as a possible alternative during our preliminary studies. This approach has the potential to form denser groups, however the results we obtained from a large number of topological and traffic scenarios showed that the performance improvement offered compared to the fixed DBG method described above was at best marginal. In addition, as load increased, certain groups (usually ones with lower cardinalities) always tended to starve due to an uneven assignment of wavelengths. One way of solving the aforementioned wavelength assignment issue in DBG is to allow some limited overlapping among wavelength groups so that each group actually gets a “decimal” total amount of wavelengths due to the sharing of some of them. However, the definition of algorithms to perform such assignments is out of the scope of this work but certainly an interesting topic for further study. Moreover, another possible drawback of DBG in general is that the achievable WDM multiplexing gain within each group may be reduced due to the lower amount of wavelengths assigned to each of them. Fig. 4 shows an example of how the two mentioned DBG methods operate for an arbitrary distribution of 32 ONUs at distances between 0 and 25 km. The ONUs are represented as points on an axis based on their rtt values. Shaded boxes represent the four groups formed and also include the number of wavelengths assigned to each of them. It is obvious that the

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mean differential round-trip delays in each group are in both cases lower compared to the mean round-trip calculated across all ONUs. As expected, k-means [Fig. 4(b)] indeed produces denser groups than fixed DBG [Fig. 4(a)], however notice the unfair distribution of wavelengths: Groups 1 and 4 are both assigned 3 wavelengths, although their cardinalities are 5 and 7 respectively. Before proceeding to the evaluation of all aforementioned schemes, the next section discusses the scheduling problem under study from a scheduling theoretic point of view and presents the most important results from the relevant literature. Moreover, it provides the detailed rationale that led to the algorithmic solutions proposed in this work. V. D ISCUSSION A. Scheduling Theoretic Results The corresponding offline scheduling problem can be formulated as a job scheduling problem with m parallel machines, the jobs being the upstream grants and the machines representing the W upstream wavelengths. No preemption is allowed (an upstream grant cannot be interrupted), while jobs have different release dates (rj ), which indicate the time instant when job j becomes available for processing. The release date for a grant to ON Uk is t + rttk + tc if the report arrived at time t. The most common optimality criteria in scheduling problems P are the makespan (Cmax ) and the total completion time ( CjP ), which P j using our notation Fi respectively. It is are equivalent to max Hi and i

j

obvious that by minimizing the total completion time, the average end-to-end delay is also minimized. The corresponding optimization problems are notated as Pm |rj |Cmax and P Pm |rj | Cj . Online scheduling algorithms are commonly described by their competitive ratio ρ. An algorithm is referred to as ρ-competitive if in the worst case performs ρ times worse than the optimal schedule regarding some criterion. In addition, lower performance bounds are commonly sought, which represent the best possible performance an algorithm can achieve compared to the optimal schedule. 1) Pm |rj |Cmax : The offline problem has been proven to be NP-hard. More than 40 years ago Graham proposed the List Scheduling (LS) online algorithm [15] which schedules jobs one by one and assigns them to the next available machine. Therefore, both EFT and NASC [6] algorithms are variations of LS. LS is proven to be (2 − 1/m)-competitive (therefore

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optimal for a single machine and 2-competitive for infinite machines). In [16] it is shown that the on-line LPT algorithm, which schedules the job with the longest processing time in the first available machine, is 1.5-competitive independent of the number of machines. In the same work it is proven that any deterministic online algorithm has a lower performance bound of at least P 1.3473. 2) Pm |rj | Cj : If all release dates are equal, then the optimal offline schedule can be achieved by scheduling the job with the shortest processing time in the first available machine (SPT rule) [16]. However, if release dates are considered, the problem is strongly NP-hard. In [16] it is proven that the lower bound in the performance of any deterministic online algorithm is 1.309, while the lowest currently established competitive ratio is 4 [17]. B. Practical Considerations in a WDM-EPON Context From the above discussion it may seem advantageous to use offline scheduling techniques for grant scheduling, since the performance gap with their online counterparts is considerable, especially regarding the total completion time criterion. However the aforementioned comparisons are misleading, since in the WDM-EPON case the execution of an offline algorithm implies that the OLT must wait until it has received the reports from all ONUs before deciding on the schedule for the next cycle (in the case of non-arriving reports a dedicated timer ensures a maximum cycle time, which is usually in the order of ms). This results in an extra Report-to-Schedule (RTS) delay which does not exist for online algorithms. In [6] the authors provide a plethora of results which reveal that the delay performance of online scheduling - even by employing the simple NASC algorithm - is always by far superior (in some cases the difference approaches one order of magnitude even at moderate system loads) compared to the offline approach. This is the reason for not considering offline scheduling algorithms in this work and focusing on improving the performance of online ones. On the other hand, in Section V-A it was mentioned that the on-line LPT and SPT rules can potentially provide good approximations of the optimal offline schedules. However, the application of those rules in the WDM-EPON context turns out to be problematic, mainly because channel availability actually depends on each individual grant. We will explain this by using an example. Consider that the SPT rule is to be used. This implies that if upon the arrival of a report from ON Uk it holds that Lk = ∅, then the OLT has to delay its decision for a duration equal to d = min Hi −(t + rttk + tc ), i∈Wk

i.e. until the wavelength arg min Hi becomes available [no i∈Wk

extra delay will be imposed to the frame, since the reservation would in any case be delayed by d according to (10)]. Any further reports arriving during this interval should be sorted in increasing order of reported bytes and inserted in a FIFO queue at the OLT. At time t + d the reports will be scheduled in a FIFO order. Note that similar scheduling strategies are proposed in [4] and [6] and referred to as Just in Time (JIT) and online interval scheduling respectively. Suppose now that in the mean time a report from ON Ul with rttl > rttk and

Wl = Wk arrives, for which it holds that Ll 6= ∅ and Gl > Gk (very probable due to the longer rtt). The corresponding grant will be scheduled immediately in wavelength arg min Hi , i∈Wk

violating thus the SPT principle. Such complications, along with the fact that the performance of the online interval scheduler in [6] is shown to be extremely close to NASC, led us to consider only online scheduling algorithms with immediate dispatching. In this work, care was taken to come up with schemes that are tailor-made for real WDM-EPON networks. It is worth stressing again at this point our most important findings from an algorithmic point of view. First of all, we pointed out that the “first available machine” rule, which most online algorithms (e.g. EFT, NASC, online LPT/SPT) adopt regardless of the exact list sorting they perform, is not efficient in the considered environment. The reason is the following: The implicit assumption that timing relationships among grant release dates are defined by the arrival order of the corresponding reports (i.e. when the decisions take place) does not hold, since a report from ON Uk arriving later in time may have a smaller t + rttk + tc value than previously arrived ones, it the rttk is sufficiently smaller. As a consequence, in contrast to the proposed LFT scheme, the aforementioned algorithms would essentially consider all available wavelengths as equally good when Lk 6= ∅ (since they assume that voids left behind cannot be used by upcoming grants). Moreover, even more significant is the fact that for the first time to our knowledge the notion of “channel availability” in WDM-EPONs is extended (in the VF schemes) to include voids instead of only horizons. VI. P ERFORMANCE E VALUATION A. Introduction In order to evaluate the performance of the proposed schemes, a custom simulation model was developed with the help of the OPNET Modeler tool. Both GENERIC and RING topologies were considered in different scenarios. The performance metrics of interest were the average end-to-end frame delay (i.e. the time from the generation of a frame at the ONU till its reception at the OLT), as well as the average upstream channel utilization achieved by each scheme. The latter was measured at each wavelength as the total duration of scheduled grants divided by the finish time of the last grant. Performance was measured against various network parameters, namely the absolute and differential distances between the OLT and the N ONUs, the number of ONUs, the number of available upstream wavelengths and of course the offered network load. The latter will always be provided in Erlangs per wavelength so that it scales with the overall available capacity. For example, if L = 0.5, W = 4 and the capacity of each λ is 1 Gbps, then the average offered load is 2 Gbps. In that respect, any difference in performance when comparing scenarios with different numbers of available wavelengths at the same load is not due to the different overall capacity but rather due to the achieved WDM multiplexing gain. Moreover, note that for the calculation of the offered load L the original user-generated traffic was assumed to be 8b/10b encoded (including EPON headers), while control packets

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were not considered. In order to simulate the self-similar nature of network traffic flows, Ethernet frames in our model were generated at each ONU by aggregating multiple ON/OFF sources with Pareto-distributed ON and OFF periods [18] and E[tON ]/(E[tON ] + E[tOF F ]) = 1/10. The Hurst Parameter was equal to 0.8, while frame sizes were uniformly distributed between 64 and 1518 Bytes. We assumed a guard band of 5 µs between upstream transmissions by different ONUs (large enough to accommodate possible laser tuning delays [8]) and an inter-packet gap (IPG) of 96 ns [1] between consecutive EPON frames transmitted by the same ONU. Results were extracted for all reasonable load values (ranging between 0.1 and 0.9). Each wavelength had a capacity of 1 Gbps and each ONU was connected to the PON network via a Gigabit Ethernet interface. For simplicity we assume that all ONUs support all W upstream wavelengths available in the network (unless of course if DBG is employed). Regarding DBG, the fixed approach was considered. B. Numerical Results For the first set of simulation scenarios, we used the GENERIC topology with 32 ONUs. The latter were located

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at random distances Dk chosen using a uniform probability distribution function within certain lower and upper bounds. Since EFT, due to its simplicity, will serve as the baseline scheme for the performance evaluation it is insightful to begin by depicting its overall behavior; Thus in Fig. 5 we plot the average EFT end-to-end frame delay versus the offered load for W = 1, 2, 4. It can be observed that at most load regions, delay is significantly decreased as the number of wavelengths increases. As described before, this is expected because of the higher multiplexing gain achieved due to the sharing of a higher amount of channels by the ONUs. [Even higher W values for the same number of ONUs would actually lead to the reverse effect at very high loads: Since load is measured in Erlangs per wavelength, the same load value implies that ONUs produce traffic at higher rates when there are more wavelengths in the network. Subsequently, when both load and W are high, the traffic rate of each ONU tends to be comparable to its interface capacity (1 Gbps), inevitably leading to poor performance]. Next, Fig. 6 compares the performance of all mentioned algorithms (namely EFT, LFT, EFT-VF and DBG, the latter applied using EFT and 2 Groups of 16 ONUs and 2 wave-

10 2 EFT LFT EFT-VF EFT DBG - 2 Groups EFT DBG - 4 Groups EFT DBG - 8 Groups

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lengths each) when W = 4. It is evident that the worst performance is offered by EFT while best results are at any load achieved by employing EFT-VF. The effectiveness of LFT against EFT is also clear, although it diminishes at higher loads as was pointed out in the relevant discussion of section IV-B. Moreover, notice that when DBG is used, EFT almost always outperforms LFT. This reveals the great effect that differential distances among ONUs have on performance and verifies that DBG can be a low-complexity alternative to EFT-VF. Fig. 7 shows how the average upstream wavelength utilization is affected by each algorithm. EFT-VF manages to significantly increase utilization compared to EFT, with the improvement ranging from almost 100% at low loads to 10% at moderate loads. Regarding all other schemes, the differences are not as clearly discernible as in Fig. 6, however a closer inspection reveals that, as expected, higher utilization implies lower delay. The effect of differential distances is more clearly depicted in Fig. 8. Here EFT-VF is compared with EFT in various scenarios (again for W = 4), whereby the average OLTONU distance is always kept at 12.5 km but the distances of individual ONUs are spread in different degrees. The greatest delay reduction of EFT-VF compared to EFT (or equivalently the greatest inefficiency of the latter) is observed when Dk is allowed to take any possible value between 0 and 25 km. In the highly improbable case when all ONUs are located at exactly 12.5 km from the OLT, the performance of both schemes is essentially identical, as the effect of scheduling voids is almost negligible. It is also worth discussing the nonmonotonic behavior of the curves in Fig. 8 (and Fig. 11). We could give the following intuitive explanation: As load increases, so does the size of reports (and grants). In EFT, this is bound to cause an increase in the horizons and to the delay of subsequent reservations [they will often have no other option but to be delayed by a d value as dictated by (11)]. On the contrary, the delay of EFT-VF is not affected as long as there are eligible voids to select from. Hence, the improvement offered by EFT-VF is expected to rise with load. However, as very high load values are reached, the voids left in between upstream grants will tend to be much smaller due to the extremely increased grant sizes, causing EFT-VF to operate similarly to EFT (i.e. schedule grants in a horizonbased manner, since voids will be mostly unusable). The second set of simulation scenarios utilized the RING topology as depicted in Fig. 1. This time the number of upstream wavelengths was 8. The network comprised 4 RNs, located at distances of 12.5, 37.5, 62.5 and 87.5 km from the OLT, with equal amounts of ONUs attached to each RN. ONUs were randomly distanced between 0 and 12.5 km from their corresponding RN, hence Dk could take any value between 0 and 100 km. Note that the long reach of this network implies that the minimization of frame delay using USWA algorithms is even more imperative. Fig. 9 depicts the performance of all algorithms under study when each RN supports 32 ONUs, i.e. N = 128. As expected, EFT-VF and EFT offer the worst and the best performance respectively. In particular, the use of void filling can result to an end-to-end delay reduction of up to 35% as it can also be seen clearly in Fig. 11 for N = 128. This reduction is actually

EFT-VF EFT DBG - 2 Groups EFT DBG - 4 Groups EFT DBG - 8 Groups EFT-VF DBG - 2 Groups EFT-VF DBG - 4 Groups EFT-VF DBG - 8 Groups

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translated to more than 0.5 ms (see Fig. 9) and its significance is obvious considering that in [19] for example the requirement for the access delay is set to 1.5 ms (which EFT already trespasses at a load of 0.3 Erlangs per λ). LFT performs fairly well (given its simplicity) at light load conditions but, as explained above, tends to behave like EFT when load increases. In Fig. 9 we also plot the delay performance of EFT with DBG for three different grouping cases. It is evident from the results that a larger number of wavelength groups (the maximum number of groups is obviously limited by the number of upstream wavelengths in the system, 8 in this case) results in improved performance at most load values. However, for very heavy load (e.g. after 0.8 for the 8-group case and after 0.85 for the 4-group one) we notice the trade-off mentioned in Section IV-D: The decreased WDM multiplexing gain for lower numbers of wavelengths per group (i.e. more groups) counterbalances the improvement offered by the decreased differential round-trip delays, causing the queues to collapse earlier. In Fig. 10, results are provided for the case when fixed DBG is used in conjunction with EFT-VF. As expected, EFT-VF reduces the delay of DBG for any number of groups. What is more interesting though is that EFT-VF always performs better when used without DBG (or equivalently with one

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group only). This suggests first of all that there is no serious motivation for sacrificing the main advantage of DBG (which is its reduced complexity) by using it along with EFT-VF. In addition, it reveals that (in contrast to EFT) EFT-VF benefits much more by an increased number of available channels than by reduced differential round-trip delays. The same conclusion can be reached by inspecting the EFT-VF DBG curves for 2, 4 and 8 groups in Fig. 10: It is remarkable that their delay performance is completely reversed compared to the respective EFT DBG ones. For example, in the 8-group case performance remains almost unaffected, especially as load increases, while for 2 groups the improvement is significant. Finally, Fig. 11 apart from the effectiveness of EFT-VF also exposes another very important aspect of this scheme, which is its scalability: It is demonstrated there that the higher the number of ONUs in the PON, the larger the delay reduction achieved. As mentioned in Section III, this can be attributed to the fact that when more ONUs share the same number of wavelengths, it is easier for voids to be utilized (the chunks of data produced by each ONU are relatively shorter compared to voids). VII. C ONCLUSION We have shown that simplistic online upstream scheduling and wavelength assignment algorithms (e.g. EFT) do not provide satisfactory utilization of the wavelength channels available in hybrid WDM/TDMA PONs. Accordingly, we have proposed three schemes that attempt to improve performance; a modified version of EFT, i.e. the LFT algorithm, manages to reduce frame delay significantly, though only at low or moderate network load. Variants of both EFT and LFT which adopt void filling (VF) exhibit vast delay reduction and increased wavelength utilization under all loading conditions but at the same time imply increased algorithmic complexity. Moreover, the results demonstrate that the performance of VF scales very well with the number of ONUs in the network. Finally, the DBG scheme, by leveraging the knowledge of the OLT regarding network topology, resulted in performance improvement which in some cases approached that of VF, while in essence maintaining the simplicity of EFT.

[1] IEEE Draft P802.3ah, IEEE Standard, 2004. [2] F. T. An et al., “SUCCESS: a next-generation hybrid WDM/TDM optical access network architecture,” J. Lightw. Technol., vol. 22, no. 11, pp. 2557–2569, Nov. 2004. [3] C. Bock, J. L´azaro, and J. Prat, “Extension of TDM-PON standards to a single-fiber ring access network featuring resilience and service overlay,” J. Lightw. Technol., vol. 25, no. 6, pp. 1416–1421, Jun. 2007. [4] J. Prat et al., “A long-reach resilient passive optical network for scalable access,” in Proc. ICT Mobile Summit, Santander, Spain, Jun. 2009. [5] M. P. McGarry et al., “Just-in-time scheduling for multichannel EPONs,” J. Lightw. Technol., vol. 26, no. 10, pp. 1204–1216, May 2008. [6] M. P. McGarry, M. Reisslein, M. Maier, and A. Keha, “Bandwidth management for WDM EPONs,” Journal of Optical Networking, vol. 5, no. 9, pp. 637–654, Sep. 2006. [7] M. P. McGarry, M. Reisslein, and M. Maier, “WDM ethernet passive optical networks,” IEEE Commun. Mag., vol. 44, no. 2, pp. 15–22, Feb. 2006. [8] A. Banerjee et al., “Wavelength-division-multiplexed passive optical network (WDM-PON) technologies for broadband access: a review [Invited],” Journal of Optical Networking, vol. 4, no. 11, pp. 737–758, Nov. 2005. [9] F. Saliou et al., “Reach extension strategies for passive optical networks [Invited],” IEEE/OSA J. Opt. Commun. Networking, vol. 1, no. 4, pp. C51–C60, Aug. 2009. [10] F. Clarke, S. Sarkar, and B. Mukherjee, “Simultaneous and interleaved polling: an upstream protocol for WDM-PON,” in Proc. OFC, Anaheim, CA, USA, Mar. 2006. [11] K. Kwong, D. Harle, and I. Andonovic, “Dynamic bandwidth allocation algorithm for differentiated services over WDM EPONs,” in Proc. 9th Int. Conf. Communications Systems, Sep. 2004, pp. 116–120. [12] K. Kanonakis and I. Tomkos, “Online upstream scheduling and wavelength assignment algorithms for WDM-EPON networks,” in Proc. European Conference on Optical Communications (ECOC), Vienna, Austria, Sep. 2009. [13] A. Dhaini, C. Assi, M. Maier, and A. Shami, “Dynamic wavelength and bandwidth allocation in hybrid TDM/WDM EPON networks,” J. Lightw. Technol., vol. 25, no. 1, pp. 277–286, Jan. 2007. [14] R. Xu and D. Wunsch, “Survey of clustering algorithms,” IEEE Trans. Neural Netw., vol. 16, no. 3, pp. 645–678, May 2005. [15] R. L. Graham, “Bounds for certain multiprocessing anomalies,” Bell Syst. Tech. Jour, vol. 45, no. 9, pp. 1563–1581, 1966. [16] A. P. A. Vestjens, “On-line machine scheduling,” Ph.D Thesis, Eindhoven University of Technology, Netherlands, 1997. [17] S. Chakrabarti et al., “Improved scheduling algorithms for minsum criteria,” in Proc. of the 23rd International Colloquium on Automata, Languages and Programming, 1996, pp. 646–657. [18] M. S. Taqqu, W. Willinger, and R. Sherman, “Proof of a fundamental result in self-similar traffic modeling,” ACM/SIGCOMM Computer Communication Review, vol. 27, pp. 5–23, 1997. [19] ITU-T Rec. G.114, “One-way transmission time,” May 2004. Konstantinos Kanonakis was awarded his PhD and Dipl.-Ing degrees in 2007 and 2004 respectively, both from the National Technical University of Athens (NTUA), Greece. His main research interests are in the area of architectures and control protocols for broadband access and optical core networks. He has co-authored more than 30 papers that appeared in international peer-reviewed journals and conferences and has participated in several EU-funded projects.

Ioannis Tomkos has co-authored about 300 peerreviewed archival articles (over 160 IEEE sponsored), including about 100 Journal/Magazine/Book publications. His work focuses on optical networking and techno-economic studies of broadband networks. Dr. Tomkos has received the prestigious title of “Distinguished Lecturer” of the IEEE Communications Society in the topic of transparent optical networking.