Network coding based joint signaling and dynamic bandwidth allocation scheme for inter optical network unit communication in passive optical networks

Optical Fiber Technology 20 (2014) 280–293

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Optical Fiber Technology www.elsevier.com/locate/yofte

Network coding based joint signaling and dynamic bandwidth allocation scheme for inter optical network unit communication in passive optical networks Pei Wei, Rentao Gu, Yuefeng Ji ⇑ State Key Laboratory of Information Photonics and Optical Communications, School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, P.O. Box 90, 100876 Beijing, PR China

a r t i c l e

i n f o

Article history: Received 16 December 2013 Revised 15 February 2014 Available online 27 March 2014 Keywords: Passive optical networks (PON) Network coding (NC) Signaling Dynamic bandwidth allocation (DBA)

a b s t r a c t As an innovative and promising technology, network coding has been introduced to passive optical networks (PON) in recent years to support inter optical network unit (ONU) communication, yet the signaling process and dynamic bandwidth allocation (DBA) in PON with network coding (NC-PON) still need further study. Thus, we propose a joint signaling and DBA scheme for efficiently supporting differentiated services of inter ONU communication in NC-PON. In the proposed joint scheme, the signaling process lays the foundation to fulfill network coding in PON, and it can not only avoid the potential threat to downstream security in previous schemes but also be suitable for the proposed hybrid dynamic bandwidth allocation (HDBA) scheme. In HDBA, a DBA cycle is divided into two sub-cycles for applying different coding, scheduling and bandwidth allocation strategies to differentiated classes of services. Besides, as network traffic load varies, the entire upstream transmission window for all REPORT messages slides accordingly, leaving the transmission time of one or two sub-cycles to overlap with the bandwidth allocation calculation time at the optical line terminal (the OLT), so that the upstream idle time can be efficiently eliminated. Performance evaluation results validate that compared with the existing two DBA algorithms deployed in NC-PON, HDBA demonstrates the best quality of service (QoS) support in terms of delay for all classes of services, especially guarantees the end-to-end delay bound of high class services. Specifically, HDBA can eliminate queuing delay and scheduling delay of high class services, reduce those of lower class services by at least 20%, and reduce the average end-to-end delay of all services over 50%. Moreover, HDBA also achieves the maximum delay fairness between coded and uncoded lower class services, and medium delay fairness for high class services. Ó 2014 Elsevier Inc. All rights reserved.

1. Introduction Nowadays, passive optical networks (PON) have been a popular and reliable solution to access network, and there is fast growing trend of replacing the conventional copper networks with PON. Meanwhile, the demands for inter-optical network unit (ONU) communication in PON have been increasing with the rapid growth of peer-to-peer (P2P) communications, such as P2P file dissemination, online interactive game, audio/video conferencing, future cellar networks, data exchange in smart grid, and virtual private network (VPN) communication [1–5]. As a respond to these urgent demands, the next generation passive optical networks has been developed for years, and they can provide lots of ⇑ Corresponding author. E-mail addresses: [email protected] (P. Wei), [email protected] (R. Gu), [email protected] (Y. Ji). http://dx.doi.org/10.1016/j.yofte.2014.02.013 1068-5200/Ó 2014 Elsevier Inc. All rights reserved.

opportunities for applying novel technologies to cope with the emerging challenges. One of these novel technologies is network coding (NC), which was firstly proposed by Ahlswede et al. [6]. Network coding refers to combining different incoming packet flows into one encoded packet flow without loss of information, rather than simple storing-and-forwarding or routing at network nodes. As innovative and promising technology, network coding is shown to improve throughput, simplify routing, and provide robustness against transmission errors and failures in various packet networks [2], and it has been introduced to PON only in recent years to support inter-ONU communication. Previous studies have proved that network coding technology in PON is capable to support secure VPN [5], reduce the packet loss and queuing delay in case of congestion [7], enable the OLT to save up to 50% on energy consumption by reducing the packet transmitting time [1,8], and increase downlink throughput by up to 50% in

P. Wei et al. / Optical Fiber Technology 20 (2014) 280–293

inter-ONU communication without changing the PON hardware [3]. Thus, PON with network coding (NC-PON), which needs only software upgrade at a low cost and complexity, can not only achieve significant performance improvements but also be attractive to network operators. Signaling process plays an important role in any kinds of communication networks, and also lays the foundation to fulfill network coding in PON. For the first time, Liu et al. in [1] proposed an NC signaling process to make the study on the implementation of NC-PON more complete. However, the signaling process scheme proposed in [1] requires that a source ONU is able to determine the destination ONU of each packet it sends upstream, which is similar to that in previous study [3]. Thus, a list of internet protocol (IP) or media access control (MAC) address to LLID mappings should be maintained by each ONU, so that the determination process of destination ONU can be implemented. Note that those mappings are created/updated whenever an ONU overhears a downstream frame that contains an IP datagram [3]. However, such a mapping list can be a threat to downstream security in PON, because an ONU may overhear packets belonging to other ONUs by faking a legal receiver with the help of the awareness of all LLIDs in PON. Thus, it is inappropriate for ONUs to maintain such a list, and a new signaling process is needed to guarantee both feasibility and security in NCPON. Moreover, as a key technology in NC-PON, dynamic bandwidth allocation (DBA) is worth studying. As yet, only a few efforts have been devoted to this issue. Miller et al. [3] and Fouli et al. [2] implemented their simulations in ethernet passive optical networks (EPON) integrated with network coding, using the classic interleaved polling with adaptive cycle time (IPACT) DBA algorithm proposed in [9]. IPACT can provide statistical multiplexing and efficient channel utilization. Thus, it works efficiently in traditional EPON. However, the IPACT in NC-PON cannot contribute to the reduction of additional queuing delay at the optical line terminal (the OLT) caused by network coding, not to mention the latency fairness between coded and uncoded inter-ONU flows. Kubo et al. [4] firstly focused on these problems in NC-PON, and proposed an adaptive priority scheduling (APS) algorithm to reduce the additional queuing delay at the OLT and improve the latency fairness among coded and uncoded inter-ONU flows. The main difference between APS and IPACT in NC-PON lies in the scheduling scheme. In APS, all the GATE messages are transmitted to ONUs in the next polling cycle only after all the REPORT messages are received by the OLT in previous polling cycle. Then, packets of each ONU can be allowed to transmit in the next polling cycle after the GATE message is received. Therefore, bidirectional inter-ONU flows in APS would experience a large end-to-end delay, for these flows had to wait at least two DBA cycles from the moment they arrived at the corresponding ONUs to the moment they were being transmitted to the OLT. This delay may be acceptable to the data exchanged among ONUs for smart grid applications, but may be unacceptable to some delay sensitive services of other common applications, such as voice and streaming multimedia data. Moreover, different delay, jitter and bandwidth requirements of differentiated classes of services had not been considered in APS, whereas queuing delay at the OLT and different polling orders in different DBA cycles would have negative impacts on those jitter sensitive services in APS. Hence, it is necessary to propose an efficient dynamic bandwidth allocation algorithm which can offer solutions to the above drawbacks of the existing DBA algorithms in NC-PON. Toward those ends mentioned above, we propose a joint signaling and dynamic bandwidth allocation scheme in NC-PON. Note that both the signaling process and DBA scheme are based on multi-point control protocol (MPCP) arbitration mechanism, thus they are proposed jointly. Specifically, the signaling process is a founda-

281

tional part of our proposed joint scheme. In the signaling process, destination address information of packet flows in ONU queues is included in REPORT messages by using the pad fields, and these destination address information provides the basis to the inter ONU communication detection at the OLT. In addition, the proposed signaling process can not only avoid the potential threat to downstream security in previous schemes [1,3], but also be suitable for the proposed hybrid dynamic bandwidth allocation (HDBA) scheme. In HDBA, a DBA cycle is divided into two sub-cycles for applying different coding, scheduling and bandwidth allocation strategies to differentiated classes of services, thus quality of services (QoS) requirements in NC-PON can be supported. Furthermore, as network traffic load varies, the entire upstream transmission window for all REPORT messages slides accordingly, leaving the transmission time of one or two sub-cycles to overlap with the bandwidth allocation calculation time at the optical line terminal (the OLT), so that the upstream idle time can be efficiently eliminated. The remainder of the paper is organized as follows: The rationale and the proposed signaling process for NC-PON are described in the following section. Section 3 presents the HDBA algorithm in NC-PON, including the proposed scheduling and bandwidth allocation schemes. Numerical analyses and simulations for performance evaluation are shown and discussed in Section 4. Finally, we conclude the paper in Section 5.

2. The rationale and the proposed signaling process for NC-PON In this section, we first introduce the rationale for NC-PON, and then we propose a signaling process to help fulfilling network coding in PON.

2.1. The rationale for NC-PON The rationale for NC-PON is illustrated in Fig. 1, which was firstly proposed in [7]. There are two packets (p1 and p2) to be exchanged between ONU 1 and ONU 2. As a result of the directional properties of the splitter/combiner, direct traffic between ONUs is not feasible. Any packet exchanged between ONUs is first transmitted to the OLT and then forwarded to the destination. Therefore, for PON without network coding as illustrated in Fig. 2(a), the two packets are first transmitted to the OLT and then broadcast by the OLT sequentially, which means two downstream transmissions are needed. However, if PON is integrated with network coding as illustrated in Fig. 2(b), the OLT will store the first transmitted packet p1 in its local buffer while not broadcast it downstream immediately. After the latter transmitted packet p2 is received, the OLT encodes p1 and p2 usually using a simple coding operation, such as bitwise exclusive-OR (XOR) operation (denoted by ), and then broadcast the single coded packet to the destination ONU 1 and ONU 2 by setting the logic link identifier (LLID) for multicast. After receiving the coded packet, ONU 1(ONU 2) decodes this packet in the same XOR operation by using the ever transmitted packet p1 (p2) copy in its local buffer, and finally get the corresponding packet p2 (p1) with the packet p1 (p2) copy cleared up from its local buffer afterwards. Note that before p1 is transmitted upstream, the OLT should have had the knowledge of bidirectional communication between ONU 1 and 2, and these ONUs should have been informed which packets to be stored in local buffer when transmitting. Network coding can also be applied to cyclic inter-ONU flows scenarios with no direct communication or bidirectional flows between any ONU pair [3]. For simplicity, we assume network coding is carried out only when an ONU group including bidirectional

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Fig. 1. Illustration of network coding in PON.

Fig. 2. Illustration of signaling process in NC-PON.

inter-ONU flows between any ONU pair is detected during a DBA polling cycle, and the ONU group is called NC group. 2.2. The proposed signaling process for NC-PON Obviously, both upstream and downstream rules in NC-PON have changed to some extent as compared to those in traditional PON. Packets transmitted by ONUs in NC group should be stored in their local buffer for the latter decoding operation. Besides, those packets which belong to ONUs in NC group and arrive at the OLT first will not be forwarded by the OLT immediately as usual, while they will be stored in the local buffer of the OLT until the arrival of packets which belong to the ONU with the last upstream transmission in NC group during a DBA polling cycle. Moreover, copies of packets that have taken part in the coding operation should be cleared up in the buffer of the OLT in time, and so do those copies of packets in the buffer of ONUs which have finished the decoding operation. Therefore, an additional signaling process is required to

help fulfilling the application of network coding in PON, and a new signaling process is proposed as follow and illustrated in Fig. 2. In our scheme, the destination address information (e.g. IP address) of packet flows in ONU queues is included in REPORT messages by using the pad fields, as illustrated in Fig. 3. This is a key factor to avoid the potential threat to downstream security in previous studies, since each ONU does not need to maintain a list of IP/ MAC address to LLID mappings or charge the detection of intraPON traffic. Therefore, if the OLT detects bidirectional inter-ONU flows based on the destination information of all the received REPORT messages in one DBA cycle, it executes DBA and then sends bandwidth grants along with the network coding notification information to the corresponding ONUs through GATE messages, in which network coding notification information is included also by using the pad fields of GATE messages as illustrated in Fig. 4. Note that the OLT can easily maintain a list of IP or MAC address to LLID mappings, which is essential to the detection of

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283

Fig. 3. Illustration of REPORT message in NC-PON.

Fig. 4. Illustration of GATE message in NC-PON.

bidirectional inter-ONU flows. In addition, the destination information of bidirectional inter-ONU packet flows, which is carried by the REPORT message, can be used as network coding notification information in the GATE message, with which ONUs are informed which packets in their queues should be stored in buffer when transmitting upstream. Notably, both the length of REPORT and GATE messages are fixed to 64 bytes [10], and payloads in REPORT and GATE messages may occupy the whole packet size so that there will be no extra fields to carry the destination information. Thus, in order to provide enough fields to carry all the destination information of packets in ONU queues, the length of REPORT and GATE messages in NC-PON are allowed to exceeded 64 bytes but within 1518 bytes, which is the maximum length of an Ethernet frame. The signaling process is a foundational part of our proposed joint scheme, and more important, it is not only compliant with the IEEE 802.3 ah multi-point control MPCP arbitration mechanism except some minor extensions to the REPORT and GATE messages, but also suitable for the proposed HDBA scheme for NC-PON in the following section.

Table 1 Parameters definitions. Parameter

Description

w R N Tcycle Tguard Tidle TDBAcal TDBAnc

The number of total ONUs in NC group Upstream link rate (in bps) Number of total ONUs in NC-PON The maximum length of a DBA cycle Guard time between any two consecutive upstream slots Idle time in upstream transmission The OLT DBA calculation time The length of DBA polling cycle with network coding The minimum guaranteed bandwidth for ONU i

Bmin i Bex k Bexd k

Total excessive bandwidth in Cycle k Total excessive bandwidth demands in Cycle k

GEF iðkÞ

The bandwidth for EF services in Cycle k pre-allocated to ONU i

GAF iðkÞ

The bandwidth for AF services in Cycle k allocated to ONU i

GAF iðkÞp

The bandwidth for AF services in Cycle k pre-allocated to ONU i

GBE iðkÞ

The bandwidth for BE services in Cycle k allocated to ONU i

GBE iðkÞp

The bandwidth of BE services in Cycle k pre-allocated to ONU i

REF ik

The bandwidth requests of EF service in ONU i reported to the OLT in Cycle k The bandwidth requests of AF service in ONU i reported to the OLT in Cycle k The bandwidth requests of BE service in ONU i reported to the OLT in Cycle k The extra bandwidth needed for complete idle time elimination The set of underload ONUs The set of overload ONUs The EF service transmission start time of the ith ONU in the kth DBA polling cycle The AF&BE service transmission start time of the ith ONU in the kth DBA polling cycle The average EF service rate for the kth prediction

RAF ik

3. HDBA scheme for NC-PON For formularization of HDBA, some necessary parameters are defined in Table 1. 3.1. Seamless scheduling scheme with QoS support for HDBA in NC-PON The proposed seamless scheduling scheme with QoS support in NC-PON is illustrated in Fig. 5. First and foremost, the scheduling scheme is based on a ‘‘two sub-cycles division’’ strategy. Specifically, as illustrated in Fig. 5(a), one DBA polling cycle is divided into two sub-cycles, which is ‘‘uncoded sub-cycle’’ for the highest class services of each ONU, following with ‘‘coded sub-cycle’’ for lower class services of each ONU. All of the highest class services of a single ONU are transmitted in one upstream slot of the uncoded subcycle, with a guard time between every two neighboring slots, so are the lower class services in the coded sub-cycle. Additionally, we classify the expedited forwarding (EF) services into the highest class, where EF class is defined in [11] for bounded delay and jitter sensitive services (such as constant bit rate (CBR) voice). Correspondingly, the lower class services include the assured forwarding (AF) services that are not delay sensitive but requiring bandwidth guarantee (such as variable bit rate (VBR) video stream) and the best effort (BE) services that are neither delay sensitive nor requir-

RBE ik Bex idle U O testart ik tabstart ik AEF ik

ing bandwidth guarantee (such as e-mail and web browsing applications) [11]. Bidirectional inter-ONU flows among ONUs in NC group usually last for multiple DBA cycles, and all the bidirectional inter-ONU flows, which arrive at the OLT ahead of the flow belongs to the last ONU in NC group, have to experience queuing delay at the OLT to execute network coding operation. Obviously, queuing delay at the OLT would enlarge the total end-to-end delay of delay sensitive services, and different polling orders in different DBA cycles would have negative impacts on jitter sensitive services, since different polling orders may lead to different delays of these services. Thus, EF services will always be kept uncoded and a fixed polling order in every uncoded sub-cycle, while AF and BE services will be allowed to participate the network coding process in the coded sub-cycle.

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Fig. 5. Illustration of HDBA in NC-PON.

Besides, we define AF and BE services that participate network coding process as coded AF and BE services. On the contrary, AF and BE services that do not participate network coding processes are defined as uncoded AF and BE services. In order to minimize the queuing delay of AF and BE service flows, ONUs in one NC group should be assigned with consecutive upstream slots in the coded

sub-cycle of the following DBA polling cycle (Cycle k) once NC group is detected in one DBA polling cycle (Cycle (k  1)), as illustrated in Fig. 5(b). Furthermore, it is necessary to determine the transmission orders between coded and uncoded AF and BE service flows in the coded sub-cycle, and the latency fairness between coded and uncoded flows can be a key factor in the determination

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process. Thus, the NC group with consecutive upstream slots should be forwarded in advance of the nth slot among all N upstream slots in the coded sub-cycle as illustrated in Fig. 5(b). In other words, w ONUs in NC group can be allocated with arbitrary w consecutive upstream slots among the first n slots of all N slots in the coded sub-cycle, then the maximum latency fairness between coded and uncoded AF and BE service flows can be achieved [4]. The value of n is given by (24), which can make the latency fairness index defined by (23) equal to its maximum value, one, and this is a part of our previous research in [11]. As mentioned above, the OLT should have a global view of the entire network to rearrange the transmission order of ONUs in and outside of NC group. Thus, grant for each ONU can be calculated and sent only after all ONU REPORT messages are received by the OLT. In addition, different grant strategies are applied to differentiated classes of services in the proposed scheduling scheme. On one hand, the ‘‘grant-before-report’’ strategy is applied to EF services because of their CBR and deterministic nature [13]. This means the OLT can grant EF services via a predictive strategy, and the GATE messages include the pre-allocated bandwidth for the expected EF services that will arrive before the next transmission start time of the service generating ONU. On the other hand, in contrast with the predictive strategy to EF services, the conventional ‘‘grant-after-report’’ strategy is applied to AF and BE services because of their inherently bursty and nondeterministic nature. This means the OLT can only grant AF and BE services via the GATE messages after receiving the corresponding REPORT messages. Therefore, once an uncoded sub-cycle for AF and BE services is allocated, the following coded sub-cycle for EF service is pre-allocated, not only for the delay reduction to EF services but also for the elimination to idle time in upstream transmission, which is called ‘‘upstream idle time’’ problem. Specifically, idle time in upstream transmission is caused by the DBA calculation and round trip time (RTT) delay of REPORT and GATE messages, and can be formulated as

T idle ¼ RTT þ T DBAcal :

ð1Þ

Note that during the first time of bandwidth allocation, the uncoded and coded sub-cycle of Cycle 1 along with the uncoded sub-cycle of Cycle 2 should be allocated after the auto discovery process in the initial window as illustrated in Fig. 5(a), which is the only exception in all bandwidth allocation operations. Since AF and BE services are bursty, the length of coded sub-cycle is variable, which leads to variable length of the pre-allocated uncoded sub-cycle. Then, the pre-allocated uncoded sub-cycle may not be sufficient to eliminate the idle time in upstream transmission completely. To achieve high upstream bandwidth utilization, the entire upstream transmission window for all REPORT messages in our scheme is slidable for complete idle time elimination, and it is called ‘‘slidable REPORT window’’, which makes the upstream transmissions of every two DBA cycles are seamless. Specifically, the slidable REPORT window is determined as the following three cases. CASE 1: The length of pre-allocated uncoded sub-cycle in Cycle (k + 1) is larger than the idle time when the total traffic load is high enough. This case can be formulated as: N X GEF jðkþ1Þ þ ðN þ 1Þ  T guard P T idle :

ð2Þ

j¼1

to eliminate the idle time. Specifically, the value of ni is determined when the length of these (N  ni) slots are equal to or just larger than the idle time, which can be formulated as: N X

GEF jðkþ1Þ þ ðN  nd þ 1Þ  T guard P T idle and ni ¼ max½nd ;

ð3Þ

j¼ðnd þ1Þ

where max[nd] denotes the maximum value of nd and ðN  1Þ P nd P 1. CASE 2: The length of pre-allocated uncoded sub-cycle is not large enough to eliminate the idle time completely when the total network load is lower, but the length of the pre-allocated uncoded sub-cycle along with the coded sub-cycle is larger than or equal to the idle time. This case can be formulated as: N X GEF jðkþ1Þ þ ðN þ 1Þ  T guard < T idle j¼1

6

N   X AF BE GEF jðkþ1Þ þ GjðkÞ þ GjðkÞ þ ð2N þ 1Þ  T guard :

ð4Þ

j¼1

The slidable REPORT window in CASE 2 is determined as follows. As illustrated in Fig. 5(d), the REPORT window slides back towards the DBA cycle before the pre-allocated uncoded sub-cycle in Cycle (k + 1), leaving the rest (N  ni) slots in the coded sub-cycle along with the total N slots in the pre-allocated uncoded sub-cycle just large enough to eliminate the idle time, which can be formulated as: N  X

N  X BE GAF GEF jðkÞ þ GjðkÞ þ jðkþ1Þ þ ð2N  nd þ 1Þ  T guard

j¼ðnd þ1Þ

j¼1

P T idle and ni ¼ max½nd ;

ð5Þ

where ni is also determined. CASE 3: The length of the pre-allocated uncoded sub-cycle in Cycle (k + 1) along with the coded sub-cycle in Cycle k is smaller than the idle time when the total network load is extremely low. This case can be formulated as:

T idle >

N   X AF BE GEF jðkþ1Þ þ GjðkÞ þ GjðkÞ þ ð2N þ 1Þ  T guard :

ð6Þ

j¼1

The slidable REPORT window in CASE 3 is determined as follows. As illustrated in Fig. 5(e), the REPORT window overlaps with the uncoded sub-cycle in Cycle k, while the following coded subcycle in Cycle k along with the pre-allocated uncoded sub-cycle in Cycle (k + 1) are still not large enough to eliminate the idle time. Then, a pre-allocated slot (slot N0 ) of the coded sub-cycle in Cycle (k + 1) is attached to the last slot (slot N) of the pre-allocated uncoded sub-cycle in Cycle (k + 1) without guard time between them. This slot N0 of ONU N is the pre-allocated bandwidth that can make the length of the coded sub-cycle in Cycle k along with the preallocated uncoded sub-cycle and slot N0 in Cycle (k + 1) equal to the idle time, And it is for the expected AF and BE services of ONU N, which will arrive before the start of the unallocated coded sub-cycle in Cycle (k + 1). Then, the idle time can be eliminated completely. Note that ONU N corresponds to the ONU in slot N of the pre-allocated uncoded sub-cycle in Cycle (k + 1). Thus, the solution to this case can be formulated as follows: N   X AF BE AF BE GEF jðkþ1Þ þ GjðkÞ þ GjðkÞ þ GNðkþ1Þp þ GNðkþ1Þp þ ð2N þ 1Þ j¼1

The slidable REPORT window in CASE 1 is determined as follows. As illustrated in Fig. 5(c), the REPORT window can span across the coded sub-cycle in Cycle k and the pre-allocated uncoded sub-cycle in Cycle (k + 1) when the pre-allocated uncoded sub-cycle is large enough to eliminate the idle time, and the last (N  ni) slots in the pre-allocated uncoded sub-cycle are arranged

 T guard ¼ T idle :

ð7Þ

In order to sustain the consecutive upstream order of ONUs in NC group, slots for these ONUs in the unallocated coded sub-cycle of Cycle (k + 1) will be scheduled to follow the slot N0 , in case ONU N belongs to NC group.

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bandwidth limit of each ONU. Then, the remaining available bandwidth of this ONU is firstly allocated to the medium class AF services, with the bandwidth request of the lowest class BE services considered finally. Therefore, the corresponding bandwidth allocation scheme to the scheduling scheme is described as follows. The flowchart of the HDBA scheme is illustrated in Fig. 6. First, in order to achieve both bandwidth guarantee and allocation fairness [13,14], the minimum guaranteed bandwidth for ONU i is

Bmin ¼ i

  r T cycle  2N  T guard ; N

ð8Þ

assuming all ONUs are equally weighted in service level agreement (SLA). Due to the bursty nature of AF and BE services, some ONUs might request less bandwidth than Bmin while some ONUs might i request more. In order to achieve sufficient utilization of the available bandwidth in a DBA cycle, it is necessary to reallocate the excessive bandwidth of underload ONUs to overloaded ONUs, according to the bandwidth requests of differentiated classes of services. The total excessive bandwidth in Cycle k (Bex k ) and total excessive bandwidth demands in Cycle k (Bexd k ) are given by

Bex k ¼

X

 AF BE Bmin  GEF jðkÞ  Rjðk1Þ  Rjðk1Þ ; j

j2U



Bexd ¼ k

 AF BE U : Bmin > GEF j jðkÞ þ Rjðk1Þ þ Rjðk1Þ ;

ð9Þ

 X EF BE min GlðkÞ þ RAF ; lðk1Þ þ Rlðk1Þ  Bl l2O

  AF BE < GEF O : Bmin l lðkÞ þ Rlðk1Þ þ Rlðk1Þ :

ð10Þ

In addition, bandwidth allocation among EF, AF and BE services should take their classes and bandwidth guarantee requirements into consideration. According to the aforementioned scheduling scheme, the bandwidth for the coded sub-cycle of lower class AF&BE services in Cycle k is allocated before pre-allocating the bandwidth for the uncoded sub-cycle of high class EF services in Cycle (k + 1). Thus, when the total traffic load is high as illustrated in Fig. 5(c), we can give the bandwidth allocated to ONU i for AF and BE services in the coded sub-cycle of Cycle k as the following scheme, which is corresponding to CASE 1: When ni < i 6 N, then Fig. 6. The flowchart of the HDBA scheme.

GAF iðkÞ

¼

3.2. Corresponding bandwidth allocation scheme to the scheduling scheme According to the aforementioned scheduling scheme, the GATE messages except those in the initial window include two grant sections: one for the coded sub-cycle of the current DBA cycle and the other for the uncoded sub-cycle of the next DBA cycle. All the grants to ONUs are calculated according to both scheduling scheme and bandwidth allocation scheme. In the proposed bandwidth allocation scheme, both bandwidth allocation fairness among all ONUs is taken into the first consideration. Besides, excessive bandwidth of overloaded ONUs is reallocated to underload ONUs for sufficient bandwidth utilization. Furthermore, for bandwidth requests of different services in each ONU, priority and bandwidth guarantee requirement of a certain service determine the bandwidth allocated to this service. Specifically, bandwidth request of the highest class EF services is firstly satisfied within the minimum guaranteed

8 AF < Riðk1Þ ;

min ex exd RAF  GEF iðkÞ or Bk P Bk iðk1Þ 6 Bi RAF

ex P iðk1Þ : Bmin  GEF AF iðkÞ þ Bk i R

otherwise

;

ð11Þ

;

j2U jðk1Þ

GBE iðkÞ

¼

8 BE < Riðk1Þ ;

AF min ex exd RBE  GEF iðk1Þ 6 Bi iðkÞ  GiðkÞ or Bk P Bk ; RBE

AF ex P iðk1Þ : Bmin  GEF BE iðkÞ  GiðkÞ þ Bk R

;

otherwise

:

ð12Þ

j2U jðk1Þ

When 1 6 i 6 ni , then

GAF iðkÞ

¼

8 AF < RiðkÞ ;

min ex exd RAF  GEF iðkÞ or Bk P Bk iðkÞ 6 Bi RAF

ex P iðkÞ : Bmin  GEF ; iðkÞ þ Bk i RAF

otherwise

ð13Þ

;

j2U jðkÞ

GBE iðkÞ

¼

8 BE < RiðkÞ ;

AF min ex exd RBE  GEF iðkÞ 6 Bi iðkÞ  GiðkÞ or Bk P Bk RBE

AF ex P iðkÞ : Bmin  GEF ; iðkÞ  GiðkÞ þ Bk RBE j2U jðkÞ

otherwise;

;

ð14Þ

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where ni mentioned above is determined by (3).When the traffic load is low as illustrated in Fig. 5(d) and (e) or presented in CASE 2 and 3, we can give the bandwidth allocated to ONU i for AF and BE services in the coded sub-cycle of Cycle k as (11) and (12) correspondingly, where 1 6 i 6 N. Furthermore, once a coded sub-cycle of AF and BE services in Cycle k is determined, the following uncoded sub-cycle of EF services in Cycle (k + 1) can be determined, as EF services are always generated in a CBR fashion and not considered bursty. Thus, the bandwidth of ONU i in the pre-allocated uncoded sub-cycle of Cycle (k + 1) is for its EF service traffic arriving between its last transmission start in Cycle k and its next transmission start in Cycle (k + 1). This part of bandwidth for EF services pre-allocated to ONU i can take a prediction scheme as follows:

h  i min estart estart GEF ; AEF ; iðkþ1Þ ¼ min Bi ik  t iðkþ1Þ  t ik

ð15Þ

where min[x] denotes the minimum value of x and the average EF service rate for the kth prediction is given by

AEF ik ¼

EF EF REF iðk1Þ  Riðk2Þ þ Giðk1Þ abstart t abstart iðk1Þ  t iðk2Þ

N  X

Sc : Su ¼ b;

:

 AF BE GEF jðkþ1Þ þ GjðkÞ þ GjðkÞ  ð2N þ 1Þ  T guard :

ð16Þ ¼

GAF Nðkþ1Þp ¼ min

h

 i ex Bmin  GEF Nðkþ1Þ ; Bidle : i

ð17Þ

ð18Þ

Then, the bandwidth for BE services in the coded sub-cycle of Cycle (k + 1) pre-allocated to ONU i is given by

GBE Nðkþ1Þp

h

 i AF ¼ max 0; Bex : idle  GNðkþ1Þp

nwþ1 X 1 ½ðt  1ÞSu þ ðw  1ÞSc  n  w þ 1 t¼1

T AF&BE ðn þ 2wb  w  2bÞ ; 2ðN þ wb  wÞ

¼

T AF&BE ½NðN þ 2bw  2w  1Þ þ wð1  bnÞ þ ð1  bÞw2  : 2ðN  wÞðN þ wb  wÞ ð22Þ

For the evaluation of scheduling delay fairness between coded and uncoded service flows, the latency fairness index is calculated as

LFI ¼

N X i¼1

ð19Þ

4. Performance evaluation In this section, we present the performance evaluation on different DBA schemes deployed in NC-PON, including IPACT, APS and HDBA. We performed both numerical analyses and simulations in 10G EPON via Matlab. Since APS algorithm has not specified the bandwidth allocation schemes for differentiated classes of services, we classify all the services into two basic classes in the following studies for simplicity: the highest class EF services and the lower class AF&BE services. For the determination of value n in the proposed scheduling scheme, we introduce the definitions of queuing delay and scheduling delay of coded ONU flows in [4]. As illustrated in Fig. 7, Queuing delay dq at the OLT is the total slot intervals between the start of an arbitrary network coding slot and the start of the last network coding slot in the coded sub-cycle. Scheduling delay ds at the OLT is the total slot intervals between the start of the last network coding slot and the start of the first slot in the coded sub-cycle. To simplify the problem, it is assumed that bidirectional flows among w ONUs are generated synchronously with the DBA polling cycle, and only one NC group is considered in the following performance evaluations. In other words, the data flows exchanged among ONUs in a

ð21Þ

where TAF&BE is the length of coded sub-cycle for AF&BE services. n is calculated by (24). Similarly, the expected value of scheduling delay ds0 for uncoded AF&BE service flows in HDBA is given by   1 ðn  wÞðbw þ n  w  1ÞSu ðN  2w þ 2bw þ n  1ÞðN  nÞSu E½ds0  ¼ þ 2 2 Nw

j¼1

Therefore, the bandwidth for AF services in the coded sub-cycle of Cycle (k + 1) pre-allocated to ONU i is given by

ð20Þ

where b is the ratio of the slot interval for any of ONUs in NC group and the slot interval for any of ONUs outside NC group in the coded sub-cycle. According to the aforementioned definition, the expected values of scheduling delay ds for coded bidirectional AF&BE service flows in HDBA are given by

E½ds  ¼

Finally, when the total traffic load is low as illustrated in Fig. 5(e) or presented in CASE 3, we can give the bandwidth preallocated to ONU i for AF and BE services in the coded sub-cycle of Cycle (k + 1) as the following scheme. According to (7), the extra bandwidth needed for complete idle time elimination in Cycle (k + 1) is

Bex idle ¼ T idle 

NC group are generated at intervals that are integral multiples of the DBA polling cycle as illustrated in Fig. 5. For comprehensive analyses, we assume that traffic amounts or bandwidth requests of ONUs in NC group might be different from those of ONUs outside NC group, whereas traffic amounts or bandwidth requests of ONUs in NC group are the same with each other, and so are ONUs outside NC group [12]. Therefore, the length of slot interval for ONUs in NC group, Sc, might be different from the length of slot interval for ONUs outside NC group, Su, as illustrated in Fig. 5. Then we can define

!2 , ds; i

N

N X

! ds; i

2

;

ð23Þ

i¼1

where ds, i is the scheduling delay of service flow coming from ONU i and 1 6 i 6 N. If LFI is equal to one, the scheduling delay fairness between coded and uncoded service flows is maximized. Thus, when the following condition, (24), is satisfied, the expected values of scheduling delay of coded and uncoded AF&BE service flows yield the same value and the latency fairness between these flows is maximized.

n¼

" # 2 N2 þ ð2b  1  wÞN þ ð1  2bÞw þ bw þ 0:5 ; N  w þ bw

ð24Þ

where [x] denotes the integer part of x. For comparing the queuing delay and scheduling delay of EF, AF&BE service flows in HDBA, APS and IPACT, the DBA polling cycle with network coding, TDBAnc, is fixed to 2 ms for simplicity, and the guard time, Tguard, is set to 1 ls. In addition, extensive studies suggest the traffic profile as follows: 20% of the total generated traffic is allocated for narrowband EF service, and the remaining 80% is for AF and BE services [13,14], which is adopted in the following numerical analysis. Firstly, mean queuing delay and mean scheduling delay of coded services in IPACT, APS and HDBA were compared while the number of ONUs in NC group, w, varied from 2 to N (N = 16, 32, 64), and each ONU was assigned with the same size slot (b = 1). The comparison results are shown in Figs. 8 and 9.

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Fig. 7. Definition of delay parameters in NC-PON.

Fig. 8. Mean queuing delay of services of coded ONUs.

Fig. 9. Mean scheduling delay of coded ONU services.

As illustrated in Figs. 8 and 9, both the mean queuing delay and mean scheduling delay belonging to all classes of services in HDBA are the smallest as compared with those of APS and IPACT, because the ‘‘two sub-cycles division’’ and its corresponding scheduling scheme are deployed in HDBA for reducing the delay caused by network coding. Particularly, the mean queuing delay and mean scheduling delay of EF services in HDBA always stay zero no matter

the number of ONUs in NC group, w, or the number of total ONUs, N, varies. These are because EF services in HDBA are never scheduled to take part in the network coding process. In contrast, both the mean queuing delay and mean scheduling delay of coded EF services in IPACT are the largest, while those in APS achieve the medium performance, since APS efficiently rearranges the scheduling order of coded EF service flows for better delay performance as

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Fig. 10. Mean queuing delay of services of coded ONUs (N = 32).

Fig. 11. Mean scheduling delay of coded ONU services (N = 32).

compared with IPACT. However, both the mean queuing delay and mean scheduling delay of AF&BE services in HDBA have been reduced by 20% as compared to those in APS, which is the first DBA algorithm proposed in NC-PON. Moreover, larger w leads to larger mean queuing/scheduling delays of all classes of services in three algorithms (except EF services in HDBA), because that more ONUs in NC group means the afore transmitted service flows have to experience larger queuing delay at the OLT to wait the last transmitted service flow in NC group, and then the scheduling delays of the last coded service flows also increase. Secondly, mean queuing delay and mean scheduling delay of coded services in IPACT, APS and HDBA were further compared under each of three conditions: CASE 1 (b = 1:2), CASE 2 (b = 1:1) and CASE 3 (b = 2:1), while the number of coded ONUs, w, varied from 2 to N (N = 32). Comparison results are shown in Figs. 10 and 11. As the results illustrated in Figs. 10 and 11, no matter how the ratio of slots assigned to ONUs in and outside NC group, b, varies, the mean queuing delay and mean scheduling delay belonging to all classes of services in HDBA are also the smallest as compared with those of APS and IPACT. The reasons for these are familiar to those we have analyzed for all classes of services in HDBA above. Besides, larger ratio between slots assigned to ONUs in and outside NC group (i.e. larger b), also leads to larger mean queuing and scheduling delay of EF services in APS and IPACT, so are AF&BE services in all three algorithms. The reason for these are that larger slots of ONUs in NC group increase the queuing delay of the

afore-transmitted service flows at the OLT, and then the scheduling delay of the last coded service flows in NC group also increases. Note that lager b means lager slots of ONUs in NC group. Finally, we focused on the latency fairness index LFI of scheduling delay in different DBA algorithms. Thus, we analyzed mean scheduling delay of coded and uncoded AF&BE services and the corresponding latency fairness index LFI. N varies from 16 to 32, and w, is set to 6. Each ONU is assigned with the same size slot (b = 1). Since EF services in HDBA are always uncoded, only AF&BE services in different DBA algorithms are analyzed. The comparison results are shown in Fig. 12. As illustrated in Fig. 12(a), the differences of mean scheduling delay between coded and uncoded AF&BE services in both HDBA and APS are smaller than that in IPACT. Correspondingly in Fig. 12(b), the LFI of HDBA and APS always stay a high level (approximately one) as the number of total ONUs, N, varies. These are because the scheduling order of coded and uncoded AF&BE services in both HDBA and APS are properly arranged for maximum latency fairness. By contrast, as illustrated in Fig. 12(b), the LFI of IPACT is the smallest as compared with other two algorithms, because IPACT schedules coded and uncoded AF&BE services always in a fixed polling order without caring about the latency fairness between these services. Therefore, based on all the numerical analyses above, it is confirmed that HDBA can decrease the mean queuing delay and mean scheduling delay of coded and uncoded AF&BE services than APS and IPACT, and eliminate the queuing delay and scheduling delay

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Fig. 12. Mean scheduling delay of coded and uncoded AF&BE services and fairness.

Table 2 Parameters for simulation. Number of ONUs Upstream/downstream link capacity User Network Interface (UNI) rate The OLT–ONU distance (uniform) Round trip time (RTT) Maximum DBA cycle time Guard time

16 10 Gbps 1 Gbps 20 km 200 ls 2 ms 1 ls

of EF services. Moreover, the latency fairness of the scheduling delay of coded and uncoded AF&BE services in HDBA can also be improved as compared to that of the conventional IPACT algorithm. For further analysis and comparison to end-to-end delay performance and fairness of differentiated classes of services in IPACT, APS and HDBA in NC-PON, we performed our simulations in a symmetrical 10G EPON system developed in Matlab, using Simulink packet. Specifically, the 10G EPON consists of one OLT and 16 ONUs in total. Maximum DBA cycle time is 2 ms and guard time is set to 1 ls. The downstream and upstream channels are both 10 Gbps, and the UNI rate of each ONU is set to 1 Gbps. Highest class EF service traffic was modeled using Poisson distribution with packet size was fixed to 70 bytes [11,14]. Lower class AF&BE service traffic were modeled by the Pareto distribution, which has been widely used to model self-similarity and long-range dependence (LRD) traffic [15]. Packet sizes for AF&BE services were uniformly distributed between 64 and 1518 bytes. In addition, when an ONU sends out a bandwidth request, additional overhead including 8 bytes frame preamble and 12 bytes interframe gap (IFG) between consecutive frames must be taken into account. The traffic profile is as follows: 20% of the total generated traffic is allocated for narrowband EF service, and the remaining 80% is equally distributed between AF and BE services [13,14]. Moreover, the distance between the OLT and ONUs were uniformly set to 20 km, thus the RTT between the OLT and ONU is 200 ls. For reasons of simplicity, bidirectional flows among w ONUs were still assumed to be generated synchronously with the DBA polling cycle as illustrated in Fig. 4. Specifically in our simulation, bidirectional inter-ONU flows are generated at an interval of one DBA cycle. Moreover, the total network load was assumed to be evenly distributed amongst all ONUs, and all ONUs were assumed to be equally weighted. Key parameters for simulation are summarized in Table 2. Outcomes of multiple repeated simulation are averaged for all results. Firstly, the average end-to-end delays de of coded and uncoded ONU flows were assessed while the total traffic load varied from

0.1 to 1. Note that de indicates the delay from the moment that service flows arrive at ONU to the moment that they arrive at the OLT. The simulation was performed for 60 s with 10 ONUs generating bidirectional inter-ONU flows. For comparison, besides coded flows, we only analyzed the end-to-end delay of uncoded ONU flows which generated at the same time with coded flows. To evaluate the end-to-end delay fairness among different algorithms, the end-to-end delay fairness index (EEFI) is calculated as

EEFI ¼

!2 , ! N N X X 2 de; i N de; i ; i¼1

ð25Þ

i¼1

where de, i denotes the end-to-end delay of service flow coming from ONU i [12]. The EEFI of coded and uncoded services in different algorithms were also assessed while the total traffic load varied. Simulation results are compared in Figs. 13 and 14. As illustrated in Fig. 13, simulation results show that the average end-to-end delays of EF services belonging to coded and uncoded ONUs in HDBA can achieve the best performance, and both of them are the smallest as compared with those in APS and IPACT. So are coded and uncoded AF&BE services in HDBA. Furthermore, as compared to the average end-to-end delay of coded and uncoded EF services in APS, those in HDBA have been reduced by 97.763% at most and 87.83% at least. Correspondingly, the average end-to-end delay of coded and uncoded AF&BE services in HDBA have been reduced by 96.428% at most and 56.87% at least. The above results are mainly due to the proper scheduling and bandwidth allocation schemes applied to all classes of services in HDBA, which aims to decrease the delays introduced by the network coding process and to eliminate the ‘‘upstream idle time’’ problem. Besides, since the ‘‘grant-before-report’’ strategy is applied to EF services in HDBA, the average end-to-end delays of EF services in coded and uncoded ONUs are smaller than those of coded and uncoded AF&BE services in HDBA. On the contrary, though the mean queuing delay and scheduling delay in APS are smaller than those in IPACT, the average end-to-end delays of coded EF, AF&BE services in APS are the largest in three algorithms, because all classes of services in APS are always granted to transmit two DBA cycles later after they arrive at ONUs. Moreover, in Fig. 13, it is important to note that when the traffic load is high, both the average end-toend delays of coded and uncoded EF services in APS and IPACT exceed the delay-bound requirement of 1.5 ms for voice traffic in the access network, which is specified in ITU-T Recommendation G.114 [16]. The reason for this is that the basic delay requirement of coded EF services has not been cared in both APS and IPACT, thus

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Fig. 13. Average end-to-end delay of services in coded and uncoded ONUs (load varies).

Fig. 14. EEFI of services between coded and uncoded ONUs (load varies).

high class EF services in these algorithms have to face the high delay penalty introduced by network coding. Therefore, it is confirmed that high class EF services are not suitable to join the network coding process, especially when the ONU traffic load is high. Though the dissociation of narrow band EF services from the network coding traffic may lead to the slight reduction of downstream throughput gain, the delay guarantee of EF services should be of the primary concern. As illustrated in Fig. 14, simulation results show that the endto-end delay fairness of the coded and uncoded AF&BE services in HDBA always keeps a high level and is approximately one as the traffic load varies. This is because the coded and uncoded AF&BE services in HDBA are properly scheduled for maximum delay fairness. Notably, the same results can be obtained for all classes of coded and uncoded services in APS. Correspondingly in Fig. 13, especially as illustrated in the zoomed insets, the average end-to-end delays of coded and uncoded AF&BE services in HDBA are approximately equal to each other. So are those in APS. By contrast, all classes of coded and uncoded services in IPACT are scheduled in a fixed polling order and the delay fairness issue has not been concerned, thus the end-to-end delay fairness of these services in IPACT basically decreases as the traffic load increases, and is smaller than that in APS. So are the coded and uncoded EF services in HDBA. Therefore, in order to achieve better and acceptable end-to-end delay performance of EF services at all

loads, end-to-end delay fairness of EF services between coded and uncoded ONUs in HDBA degrades for compromise, though the end-to-end delay fairness between these services in HDBA is larger than that in IPACT except under the maximum load. Secondly, the average end-to-end delay de for coded bidirectional inter-ONU flows and uncoded ONU flows were assessed as the number of coded ONUs, w, varies from 2 to 8, and the total traffic load was set to 0.7. The end-to-end delay fairness between coded and uncoded services in different algorithms was also assessed under the same settings. Simulation results were compared in Figs. 15 and 16. In Fig. 15, compared with APS and IPACT, the average end-toend delays of EF services in coded and uncoded ONUs in HDBA are also the smallest as the number of coded ONUs varies, and so are coded and uncoded AF&BE services in HDBA. Note that the average end-to-end delays of EF services in coded and uncoded ONUs are still within the delay-bound requirement of 1.5 ms as the number of coded ONUs varies. In addition, as the number of coded ONUs varies, the average end-to-end delays of all classes of coded and uncoded services in IPACT are smaller than those in APS. The reason for this is also because all classes of services in APS are always granted to transmit two DBA cycles later after they arrive at ONUs. In Fig. 16, the EEFI of all classes of services in APS also demonstrates the maximum value as the number of coded ONUs varies,

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Fig. 15. Average end-to-end delay of services in coded and uncoded ONUs (w varies).

Fig. 16. EEFI of services between coded and uncoded ONUs (w varies).

Table 3 Comparison between analytical and simulation results of average queuing delay of AF&BE services.

Analytical results Simulation results Difference

IPACT (ms)

APS (ms)

HDBA (ms)

0.7589 0.7607 0.0018

0.3125 0.3134 0.0009

0.25 0.2517 0.0017

which is similar to the results of EEFI versus varying loads in Fig. 14. Besides, the EEFI of coded and uncoded AF&BE services in HDBA also keeps a high level above 0.98, and it is a litter bit lower than that of coded and uncoded AF&BE services in APS, which is known for high latency fairness of services in all the numerical analysis and simulations. Correspondingly in Fig. 15, the average end-to-end delays of coded and uncoded AF&BE services in HDBA are approximately equal to each other as illustrated in the zoomed insets, and so are all classes of coded and uncoded services in APS. In contrast, because of the guarantee to the fixed polling order of EF services, the EEFI of EF services belonging to the coded and uncoded ONUs in HDBA demonstrates lower performance as the

Table 4 Comparison between analytical and simulation results of average scheduling delay of AF&BE services.

Analytical results Simulation results Difference

IPACT (ms)

APS (ms)

HDBA (ms)

1.781 1.7835 0.0025

1.063 1.09 0.0027

0.85 0.8531 0.0031

number of coded ONUs varies. However, the EEFI of all classes of services in HDBA are still larger than those of IPACT. Finally, as shown in Tables 3 and 4, we compared the analytical and simulation results of average queuing and scheduling delay of AF&BE services among all three algorithms. Since there are no queuing or scheduling delay of EF services in HDBA, only results of AF&BE services in three algorithms were compared. Both Tables 3 and 4 show that the differences between analytical and simulation results of average queuing and scheduling delay of AF&BE services in three algorithms are all within 1%. These differences mainly come from the additional upstream transmission time for MPCP messages, but they are acceptable.

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5. Conclusion

Acknowledgments

In conclusion, we proposed a joint signaling and DBA scheme for efficiently supporting differentiated services of inter ONU communication in NC-PON. In the joint scheme, the signaling process can not only avoid the potential threat to downstream security in previous schemes but also be suitable for the proposed DBA scheme called HDBA. In HDBA, different coding, scheduling and bandwidth allocation strategies are applied to differentiated classes of services, and ‘‘slidable REPORT window’’ scheme is introduced so that the upstream idle time can be efficiently eliminated. We conducted both numerical analyses and simulations, and results of them show that compared with IPACT and APS algorithms deployed in NC-PON, the proposed HDBA demonstrates better queuing delay, scheduling delay and endto-end delay performance for differentiated classes of services in almost all cases analyzed and simulated. Specifically, the HDBA can eliminate queuing delay and scheduling delay of the highest class EF services, and also reduce the mean queuing delay and mean scheduling delay of AF&BE services by 20% as compared to those in APS, which is the first DBA algorithm proposed in NC-PON. In addition, as compared to the average end-to-end delay of coded and uncoded EF services in APS, those in HDBA can be reduced by 97.763% at most and 87.83% at least. Correspondingly, the average end-to-end delay of coded and uncoded AF&BE services in HDBA can be reduced by 96.428% at most and 56.87% at least. Notably, different coding strategies are efficiently combined into the proposed DBA scheme so that HDBA can have better QoS support to differentiated classes of services, and the ‘‘slidable REPORT window’’ scheme for upstream idle time elimination also contributes to the end-to-end delay performance in HDBA. Furthermore, the fairness for both scheduling delay and end-to-end delay between coded and uncoded lower class services in HDBA can achieve high performance because of the proper scheduling scheme, while the fixed polling order and end-to-end delay bound for high class services in HDBA are guaranteed by sacrificing the fairness of both scheduling delay and end-to-end delay, though which are better than those of IPACT in almost all cases. Since network coding in most of present studies is discussed under the architecture of time division multiplexing (TDM) PON, our future investigation may include the possible application of network coding in wavelength division multiplexing/time division multiplexing passive optical networks (WDM/TDM PON) and the corresponding dynamic wavelength and bandwidth allocation scheme.

This research was jointly supported by National 973 Program under Grant No. 2013CB329204, National High Technology Research and Development Program of China under Grant Nos. 2011AA01A104, 2011AA010303, National Natural Science Foundation of China under Grant No. 61100206, PR China, Research Fund for Doctoral Program of Higher Education of China under Grant No. 20120005130001, PR China, and the Fund of State Key Laboratory of IPOC(BUPT), PR China. References [1] X. Liu, K. Fouli, R. Kang, M. Maier, Network coding based energy management for next-generation passive optical networks, IEEE/OSA J. Lightw. Technol. 30 (6) (2012) 864–875. [2] K. Fouli, M. Maier, M. Médard, Network coding in next-generation passive optical networks, IEEE Commun. Mag. 49 (9) (2011) 38–46. [3] K. Miller, T. Biermann, H. Woesner, H. Karl, Network coding in passive optical networks, in: 2010 IEEE International Symposium on Network Coding (NetCod), 2010, pp. 1–6. [4] R. Kubo, M. Tadokoro, H. Nomura, H. Ujikawa, S. Nishihara, K. Suzuki, N. Yoshimoto, Bandwidth scheduling techniques in TDM-PON supporting interONU communication with network coding for smart grid applications’’, in: 2012 IEEE International Conference on Communications (ICC), 2012, pp. 3206–3211. [5] L. Yan, X. Chang, Secure virtual private network (VPN) over passive optical network (PON) based on network coding, J. Comput. Inform. Syst. 9 (9) (2013) 3651–3658. [6] R. Ahlswede, N. Cai, S. Li, R. Yeung, Network information flow, IEEE Trans. Inform. Theory 46 (4) (2000) 1204–1216. [7] M. Belzner, H. Haunstein, Network coding in passive optical networks, in: 2009 European Conference and Exhibition on Optical Communication (ECOC), 2009, pp. 6–20. [8] T. Ichikawa, M. Tadokoro, T. Kubo, T. Yamada, K.I. Suzuki, N. Yoshimoto, R. Kubo, Energy-efficient peer-to-peer communication with network coding over WDM/TDM-PON, in: 2013 IEEE 2nd Global Conference on Consumer Electronics (GCCE), 2013, pp. 481–482. [9] G. Kramer, B. Mukherjee, G. Pesavento, IPACT: a dynamic protocol for an ethernet PON (EPON), IEEE Commun. Mag. 40 (2) (2002) 74–80. [10] M. Beck Ethernet in the First Mile: The IEEE 802.3 ah EFM Standard, McGraw Hill Professional, 2005. [11] S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, W. Weiss, An architecture for differentiated services, IETF RFC 2475 (1998). [12] P. Wei, R.T. Gu, Y.F. Ji, Dynamic bandwidth allocation algorithm for nextgeneration time division multiplexing passive optical networks with network coding, Opt. Eng. 52 (8) (2013) 86–108. [13] A. Shami, X. Bai, C.M. Assi, N. Ghani, Jitter performance in ethernet passive optical networks, IEEE/OSA J. Lightw. Technol. 23 (4) (2005) 1745. [14] M.V. Dolama, A.G. Rahbar, Modified smallest available report first: new dynamic bandwidth allocation schemes in QoS-capable EPONs, Opt. Fiber Technol. 17 (1) (2011) 7–16. [15] W. Willinger, M.S. Taqqu, A. Erramilli, A bibliographical guide to self-similar traffic and performance modeling for modern high-speed networks, in: Stochastic Networks, Oxford Univ. Press, Oxford, U.K., 1996, pp. 339–366. [16] ITU-T Recommendation G.114, One-Way Transmission Time, in Series G: Transmission Systems and Media, Digital Systems and Networks, ITU-T Standards, 2000.