1. Introduction

Beside the ever-increasing capacity upgrades (100 Gb/s), it has been shown lately that there is also a tremendous need for decreasing the latency (1ms) and the jitter in edge optical networks [1,2]. The emphasis on both the capacity and the latency improvements has been extensively studied with the introduction of 5G ultra-high-speed low-latency/jitter applications, most notably the so-called Tactile Internet [1]. For this reason, optical code-division multiple-access (OCDMA) is recapturing attention as a prospective technology to be integrated in next generation passive optical networks (stage 3) (NG-PON3) so as to respond to the outgrowth of today’s bandwidth-addicted traffic as well as ultra-low latency requirements [3,4]. Owing to the key aspects of OCDMA such as the asynchronous-transmission (“tell-and-go”) nature of OCDMA, the on-demand resource allocation accessibility by large numbers of users without contention, the low latency access due to the all-optically encoding/decoding process and the ability to coexist with the wavelength division multiplexing (WDM) [5,6], OCDMA NG-PON can meet the requirement of the scalability and the fiber-reach capability [7]. In addition, advance modulation formats for the high capacity requirement of 5G mobile networks can now be optically realized by using advanced Mach-Zhender-based modulators [8–12].

Owing to the maturity of all-optical devices at the physical (PHY) layer, feasible and cost effective OCDMA NG-PON architectures are designed and successfully experimented [13–14]. Advanced coding techniques and modulation schemes are also proposed for OCDMA NG-PON to scale up the network [5,15]. In addition, novel transmission-power control algorithms have been developed to extend the network reach and the split ratio [1]. On the other hand, scheduling and dynamic resource allocation algorithms are designed to improve the performance, scalability and coverage of OCDMA NG-PONs either through the medium access control (MAC) layer or through the cross-layer coordination between PHY and MAC layers [3,16].

The next generation Ethernet passive optical network (NG-EPON) architecture mainly consists of an optical line terminal (OLT), located at the central office, optical network units (ONUs), located at the users premises, and a shared passive optical fiber that connects the OLT to the ONUs in a tree topology via a passive optical splitter/combiner. The data generated by the end users are encapsulated in Ethernet frames. A multipoint control protocol (MPCP) has been developed to coordinate the data transmission among the OLT and the ONUs for collision avoidance. The MPCP is based on the exchange of control messages – the Report message and the Gate message – for bandwidth allocation and scheduling. The NG-EPON has been standardized by the IEEE P802.ca [7] taskforce based on time/wavelength-division-multiplexing (TDM/WDM) platforms. The aim is to handle more capacity and to improve the transmission efficiency of the data along the access network through the multiple-wavelength transmission capability and the channel bonding.

In the literature, many DBA algorithms have been designed for NG-EPON mostly based on TDM, WDM or a combination of both. The ONU is allocated one or multiple wavelengths (up to four wavelengths) as transmission channels over which the bandwidth allocation and scheduling are arbitrated by the proposed dynamic wavelength and bandwidth allocation (DWBA) [17–20]. For instance, the authors in [17] suggested multiple wavelength assignments for NG-EPON to upgrade the transmission capacity and proposed a wavelength assignment mechanism with an online water-filling scheduling algorithm (WF-DWBA). In this case, the ONU’s request is allocated over one or multiple wavelengths, depending on the request size, starting from the first available wavelength. The authors in [18] suggested a first-fit algorithm (FF-DWBA) for NG-EPON whereby four wavelength channels are available. In FF-DWBA, the ONU’s request is allocated one wavelength to be completely transmitted. The OLT selects the first available wavelength as soon as possible to be allocated to the requesting ONU. On the other hand, [19] suggested a single channel with a grant readjustment (GR) as an offline scheduling algorithm to mitigate the frame reordering and to improve the latency. In [20], a Flexible wavelength and dynamic bandwidth allocation (FW-DWBA) has been proposed. In FW-DWBA, a threshold is set on the request size. Starting from the first available wavelength, if the residual request time is greater than the threshold, the OLT allocates an additional wavelength. In [21], a DWBA was proposed for 5G networks to minimize the use of active wavelengths while increasing the number of transmitting ONUs. In this algorithm, the ONUs are sorted in ascending order of their propagation delays. The OLT starts allocating sequentially one fixed transmission timeslot per ONU per wavelength while respecting the fronthaul delay constraint. On the other hand, the authors of [22] have proposed to calculate the allocated bandwidth based on the mobile scheduling information of the baseband unit (BBU) at the fronthaul through a mobile DBA (M-DBA) algorithm.

Likewise, a CDMA-based multi-channels EPON system has been proposed in [23]. A Code-division multiple-access enabled dynamic bandwidth allocation (CDBA) scheme has been investigated at the MAC layer to meet the requirements of the first generation EPON [16,23]. The CDBA has been designed to meet the EPON standards [24] in which some ONUs can be heavily loaded while others are lightly loaded. On the other hand, the rationale of NG-EPON expects from the ONUs to handle a very-high bandwidth which may reach 100 Gb/s. Recently, the convergence of the wireless network and the CDMA NG-EPON has been discussed as a way to fulfill the ever-increasing bandwidth demand of mobile end-users [6]. For this reason, the CDBA in [23] is no more capable of dealing with the new network performance requirements of the NG-EPON. Therefore, new DBA algorithms are required for the CDMA-based NG-EPON.

In this paper, we propose two DBA algorithms to improve the delay jitter and throughput performance for the CDMA-based NG-EPON: the First-In-First-Out DBA (FIFO-DBA) and the Reservation Pattern DBA (RP-DBA) scheduling algorithms. In both algorithms, each ONU is assigned a CDMA code signature as its transmission channel and multiple ONUs can transmit simultaneously while meeting the PHY layer quality of service (QoS) requirements.

In FIFO-DBA algorithm, the scheduled ONU will be allocated a bandwidth to transmit the entire reported queue-content per request. Once the transmission is accomplished, the ONU will be on hold for the next transmission, waiting for all other ONUs to have their turns in a first-in first-out manner to transmit their reported queue contents, as well. In RP-DBA algorithm, a reserved pattern of scheduled timeslots is established for every active ONU. Each of the scheduled ONUs starts transmitting its queue content in its reserved timeslot, continuously without the need for Request-Grant messages. In case of inactive ONUs, a rescheduling will be performed and a new reservation pattern will be established. In both proposed scheduling algorithms the full asynchronous nature of OCDMA is exploited in an attempt to improve the latency/jitter and throughput performance in order to meet the NG-EPON standards. The scheduling in FIFO-DBA and the rescheduling process in RP-DBA are achieved online.

The rest of the paper is organized as follows. In Section 2 we present a short summary of the CDBA. Section 3 describes the proposed scheduling schemes. The Pseudo-code algorithms for the proposed schemes are presented in section 4. The performance evaluation method is discussed in Section 5. Results, comparison and discussion are provided in section 6. Finally, section 7 concludes this paper.

2. Native CDBA scheme

The CDBA has been fully described and analyzed in [23]. In this section we present only a summary of the CDBA as follows. The OLT collects the transmission requests from N ONUs and sorts them by their queue size in a decreasing order as shown in Fig. 1 by ${Q_{u,i}}$ at the time instant ${t_i}$ for $i = 0,1$. Each ONU can transmit a fixed number of packets at a time, encoded with a unique CDMA code. The time window of sending those coded packets defines the transmission subcycle time. Due to the multiple-access interference (MAI), not all the ONUs can transmit simultaneously [25]; however, multiple ONUs are able to transmit at the same time per each subcycle. Those ONUs determine the transmission bandwidth K during a subcycle, where $K < N$. The optimal value of K is derived in a way to meet the physical layer QoS requirements as fully explained in [23]. The OLT calculates the cycle time in a way that the first sequence of K transmitting ONUs repeats itself in a round robin (RR) polling of K ONUs per subcycle. The heavily loaded ONUs will not finish transmitting their entire requests during the cycle time. The remaining packets will be delayed for the next cycle and transmitted with the new arrivals. On the other hand, the lightly loaded ONUs will terminate transmission before the cycle time elapses. Thus, the empty ONU has to wait for a new cycle to transmit although new arrivals are available in its queue as explained in the example shown in Fig. 1. Figure 1 shows the case where the maximum cycle time is seven subcycles. Only the packets reported from the previous cycle are scheduled for transmission in the current cycle. During a subcycle time, a maximum number of packets denoted by ${W_{\max }}$ is transmitted.

 

Fig. 1. CDBA timing diagram.

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For Example, at the time instant ${t_0}$ the polled ONUs {1,2,3,4} have initial requests of (8,6,4,3) subcycles, respectively as shown in Fig. 1. They transmit simultaneously in one subcycle and it remains (7,5,3,2) subcycles for the next scheduled transmission turns. At the beginning of subcycle 2 (at ${t_1}$) ONUs {5,6,7,1} of initial requests of (2,2,1) subcycles for ONUs {5,6,7} and a remaining request of 7 subcycles for $ON{U_1}$ are next polled to transmit respectively and so on. The remaining request is decremented by one subcycle every time a transmission occurs. At the time instant ${t_2}$, the lightly loaded $ON{U_7}$ finishes its request transmission, sends its report message and it is removed from the scheduling process for the upcoming cycle time. The new packet arrivals during the current cycle time are reported to the next cycle. Since $ON{U_7}$ does not belong to the next polling sequence of ONUs, the OLT continues with the scheduling regularly at ${t_2}$. At the time instant ${t_3}$, the OLT updates the number of the remaining ONUs, sorts them in a decreasing order of their remaining request size and initiates a new scheduling sequence. Every time an ONU gets empty, the sorting process and the rescheduling occur as indicated by the single arrow at time instants ${t_3}$ to ${t_7}$ in the current cycle time, and ${t_{10}}$, ${t_{12}}$, ${t_{13}}$ in the next cycle time.

Due to this scheduling process and the variable request size, there exist variable waiting times between consecutive scheduled transmissions as pointed out by the solid-bidirectional arrows shown in Fig. 1. During the waiting time, no transmission takes place. In addition, the packets which do not have a turn to be transmitted in the current cycle are backlogged and become vulnerable to a variable queueing delay. For example, the heavy loaded $ON{U_1}$ at the end of the cycle time (at ${t_7}$) has two remaining transmission subcycles whose queued packets will be rescheduled with the new arriving packets for the next cycle. Both the waiting time and the variable queueing delay have a significant influence on the jitter performance of CDBA. For this reason, we will discuss new scheduling algorithms that minimize the delay variation and thus improving the jitter performance while boosting the capacity of the CDMA-based NG-EPON.

3. Newly proposed scheduling schemes

The objective of FIFO-DBA and RP-DBA is to minimize the mean waiting time of the arriving packets (mean packet delay), and the delay variation (jitter) while improving the network capacity for the CDMA-based NG-EPON.

3.1 FIFO-DBA scheme

In FIFO scheduling scheme, the OLT polls a sequence of $K$ ONUs to transmit simultaneously all their requests. Once one or more ONUs in the sequence finish transmitting their requests, their turns in the sequence will be given to the next ONUs requesting transmission. In this scheme, the requests are not sorted in order of their queue sizes as in the case of the CDBA; instead they are ordered in terms of their request arrival time as revealed in Fig. 2. In addition, each ONU follows its proper transmission cycle time, consisting of the request transmission time, request processing time, guard time, round-trip time and waiting time between two consecutive requests. The new packet arrivals during the ONU cycle time will wait in the queue for the next ONU cycle time. A new report message about the queue content will be sent at the end of the current transmission. In the example depicted in Fig. 2, initially four ONUs {1,2,3,4} are polled at the time instant ${t_0}$ to transmit their requests of sizes (8,6,4,3) subcycles, respectively. When $ON{U_4}$ first finishes its request, $ON{U_5}$ will be polled the next one to transmit its request of size two subcycles at the time instant ${t_3}$ and so on. $ON{U_4}$ will wait for its turn for the next transmission after all other ONUs have got their turns. The order of the ONUs changes following the request arrival time, and the transmission cycle for each ONU changes according to its request size.

 

Fig. 2. FIFO-DBA timing diagram.

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For example, all the packets arriving at $ON{U_5}$ between the time instances ${t_0}$ and ${t_5}$ will be reported for the transmission in the next scheduled turn which will start at ${t_6}$. The time interval between ${t_0}$ and ${t_5}$ forms the current cycle time of $ON{U_5}$ as pointed to by a dashed bidirectional arrow, and illustrated in Fig. 2.

The cycle time of $ON{U_5}$ includes the waiting time between two consecutive requests (pointed to by a solid-bidirectional arrow), the request transmission time (pointed to by a dotted bidirectional arrow and occupied by the packet request in a gray color), and the report transmission time with other processing times (in a white color). The cycle time length changes according to the request arrival time and the request size. The request arrival time is considered to be the time at which the OLT receives the report message. On the other hand, the request size determines the request transmission time window. For instance, the OLT at the time instant ${t_5}$ receives the report message from $ON{U_5}$ with a request of size seven subcycles starts at ${t_6}$. Thus, the new request arrival time is ${t_5}$, and the next transmission cycle time of $ON{U_5}$ will be eight subcycles plus ${T_\rho }$ (the report transmission time, guard time, request processing time and RTT time). Note that with the same amount of requests and execution time (14 subcycles) as in the case of the CDBA presented in Fig. 1, the FIFO-DBA timing diagram in Fig. 2 shows a considerable reduction in the overall number of waiting time between consecutive requests. As shown in Fig. 1 and Fig. 2, the waiting time for the CDBA is 49 subcycles while it is 32 subcycles in the case of the FIFO-DBA. This in turn yields a considerable improvement in the delay/jitter performance. In addition, the FIFO-DBA can schedule more than 54 transmission subcycles that fit all ONUs’ requests. However, the CDBA can schedule 49 transmission subcycles which are less than the requests. This means that FIFO-DBA can also decrease the queueing delay and increase the throughput.

3.2 RP-DBA scheme

The proposed RP-DBA is presented in Fig. 3. In this case, the pre-allocated transmission bandwidth per subcycle determines the round-robin polling pattern through which all the ONUs transmit their requests.

 

Fig. 3. RP-DBA timing diagram for active ONUs.

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In RP-DBA, an ONU can be in one of two possible states “active” or “inactive”. An ONU is considered active only when it has packets to transmit. When no packets are available, the ONU becomes inactive and out of the scheduling process. This is done through sending an OFF activation signal to the OLT at the end of the subcycle. If inactive ONUs are willing to transmit again, they send ON activation signals to the OLT during the current subcycle. The OLT appends them to the end of the list of active ONUs according to their arrival times. Respecting the signal-to-interference ratio (SIR) requirement at the physical layer, the OLT determines the number of simultaneous transmissions per subcycle. Consequently, the pre-defined scheduling pattern will be established such that up to K transmissions per subcycle are reserved for K out of N active ONUs at a time in a round robin fashion. All ONUs that are not active will not be considered for scheduling.

Each active ONU transmits in its reserved pattern, accordingly (whereas in CDBA the ONU will report its current queue content at the end of the current cycle and based on this the OLT will schedule its transmission in the next upcoming cycle). In this case, the first K arrivals are scheduled followed by the next $K$ arrivals and so on until all the active ONUs have their transmission turns in the round. Then, the rounds repeat as long as the ONUs are active. In each subcycle turn, an active ONU transmits a fraction of its queue content that counts for a window of size ${W_{\max }}$ packets. The remaining packets and the new arrivals will be delayed for the next transmission turns following their reserved pattern. When the ONU is voided of packets, it becomes inactive and out of the scheduling process. The timeslot of the inactive ONU will be given to another active ONU in such a way that there are always up to K $({K < N} )$ simultaneous transmissions per subcycle. The OLT in this case broadcasts an updated ordered-list of the active ONUs in the network, excluding the inactive ones. The OLT broadcasts over a separate wavelength (downlink channel) the ordered list of active ONUs once every time an ONU changes its state from an active state to inactive state or vice versa.

In addition, when determining the number of simultaneous transmissions per subcycle, the OLT takes into account the impact of the coded activation signal on the MAI in a way to meet the SIR requirement.

Thus, in RP-DBA we consider that the active ONUs do not report back to the OLT. Once registered, the ONU starts transmitting its queue content in its predefined subcycles following a fixed pattern known a priori. This avoids bandwidth wastage induced by the request transmission time, guard time, request processing time and channel round-trip time. In addition, the waiting time throughout the cycle time process exhibited for both the CDBA and the FIFO-DBA is completely eliminated. The round robin turn of subsequent transmissions for a given ONU forms an apparent cycle time which consists of the waiting time between the two subsequent transmissions plus one subcycle.

For instance, Fig. 3 illustrates the RP-DBA scheme for seven active ONUs. The first four ONUs transmit simultaneously in continuous round robin turns. That is the sequence of ONUs {1, 2, 3, 4} transmits first starting at ${t_0}$, then ONUs {5, 6, 1, 2} follow at ${t_1}$ and so on, irrespective to the size of their queue contents. Notice that the overall number of the waiting time between the consecutive scheduled transmissions is 36 subcycles. The jitter in this case is mainly due to the queueing delay variation of backlogged packets. In addition, the new packet arrivals during the waiting time will be transmitted in the subsequent scheduled transmission subcycle. The packet arrivals during the transmission subcycle are immediately transmitted as long as they fit the allocated bandwidth; otherwise, they will be backlogged. As illustrated in Fig. 3, the RP-DBA can schedule 56 transmission subcycles which can handle more packets than the CDBA (Fig. 1) and the FIFO-DBA (Fig. 2). The scheduled transmission subcycles in the latter schemes are load-dependent. Thus, the absence of the usual Request/Grant message-transmission and the bandwidth allocation process in RP-DBA contribute in minimizing the queueing delay and reducing the jitter.

4. Algorithms

4.1 FIFO-DBA

We define the following parameters.

${t_{{i_k}}}$: The current clock time instant of index ${i_k}$; $i,k \in {\mathbb N}$, where k represents the sequence of the irregular increment of $i$.

${T_P}$: The packet transmission time.

${T_\rho }$: The period of time comprising the report transmission time, guard time, request processing time and RTT time.

${\mathcal U}$: The set of all the registered ONUs in the network.

${\boldsymbol{\mathcal U}_{transmitting}}$: The set of ONUs that is polled to transmit its requests at the current time instant.

${\boldsymbol{\mathcal U}_{finish}}$: The set of ONUs that finishes transmitting its requests first.

${\boldsymbol{\mathcal U}_{remaining}}$: The set of ONUs whose transmission requests has not been accomplished yet.

${\boldsymbol{\mathcal U}_{waiting}}$: The set of ONUs which is still waiting for its turns.

The pseudo-code of FIFO-DBA algorithm is shown in Algorithm 1

In FIFO-DBA, the ONU’s request represents the number of transmission windows of size ${W_{\max }}$ packets. The OLT collects the requests of K ONUs at a time. In line 1, the OLT identifies the set of all ONUs registered in the network. In line 2, the algorithm runs continuously as long as the ONUs have packets to transmit. The OLT polls the set of transmitting ONUs $({{\boldsymbol{\mathcal U}_{transmitting}}})$ in line 3. It involves some remaining ONUs which have been already granted at previous time instants to transmit and continue transmitting at the current time instant ${t_{{i_k}}}$, and some other waiting ONUs that are granted to start their new request transmission at the current time instant ${t_{{i_k}}}$. The transmission start time of the first sequence of polled ONUs is ${T_u} = {t_0} ({{t_0} = 0})$. In line 4, the OLT finds out the minimum request ${Q_{\min }}$. Based on ${Q_{\min }}$, the OLT in lines 5 to 7 determines the ONUs that finish first their requests $({{\boldsymbol{\mathcal U}_{finish}}} )$, the ONUs that still have packets to transmit $({{\boldsymbol{\mathcal U}_{remaining}}} )$ and the ONUs that are waiting for their turns to be polled $({{\boldsymbol{\mathcal U}_{waiting}}} )$. In line 8, the OLT updates the requests of the transmitting ONUs after ${Q_{\min }}$ transmission subcycles. Lines 9 and 10 calculate the time index and the time instant at which ONUs of ${\boldsymbol{\mathcal U}_{finish}}$ terminate their transmission and ONUs from ${\boldsymbol{\mathcal U}_{waiting}}$ will start transmitting. The OLT in Line 11 polls the first available ONUs that are requesting transmission in the next subcycle from ${\boldsymbol{\mathcal U}_{waiting}}$ and assigns them their new starting transmission time. Note that there are K ONUs transmitting simultaneously at a time. In line 12, the OLT moves to the next polling sequence. Finally, in line 13, the OLT swaps the order of all ONUs at every poll. The one which finishes first waits for its turn in the last in a cyclic shift manner.

Consider the case study shown in Fig. 2 where four ONUs from seven are transmitting simultaneously at every subcycle time. Table 1 shows the scheduling of ONUs at every subcycle in which a poll occurs. For example, during the third subcycle, $ON{U_4}$ finishes transmitting its request. It will be shifted to the end of the sequence of waiting ONUs. $ON{U_5}$ is the next polled ONU to transmit with the remaining ONUs {1, 2, 3} in the fourth subcycle.

Table 1. FIFO-DBA scheduling table at every polling subcycle

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$ON{U_6}$, $ON{U_7}$ and $ON{U_4}$ are now waiting for their turns to be polled and transmit new requests. At the fourth subcycle, $ON{U_3}$ finishes its request and it is placed at the end of the sequence of waiting ONUs. $ON{U_6}$ is polled the next to transmit with ONUs {1, 2, 5} in the fifth subcycle. $ON{U_7}$, $ON{U_4}$ and $ON{U_3}$ are waiting for their turns and so on. For the calculation of the transmission start time, we consider as an example subcycle 6. At the beginning of this subcycle, $ON{U_5}$ finishes its current request at the time instant ${t_5} = 5{W_{\max }}{T_P} + {T_\rho }$. Then, at this time instant, the OLT grants transmission to $ON{U_7}$ which is the next available ONU requesting transmission. At the time instant ${t_6} = {t_5} + {W_{\max }}{T_P} + {T_\rho }$, ONUs {2, 6, 7} finish transmitting and ONUs {3, 4, 5} are polled to transmit at the beginning of the 7^th subcycle.

4.2 RP-DBA

We define the following parameters.

${\boldsymbol{\mathcal U}_{transmitting}}$: The set of ONUs that is polled to transmit its requests.

${\boldsymbol{\mathcal U}_{waiting}}$: The set of ONUs which is still waiting for its turns.

The other parameters are the same as defined in part 4-A for the FIFO-DBA. The RP-DBA algorithm is as follows.

The pseudo code is shown in Algorithm 2. In line 1 the OLT identifies the set of all the ONUs registered in the network defined as $\boldsymbol{\mathcal U}$. Based on the bandwidth allocation per subcycle, K, the OLT determines the scheduling pattern and schedules the transmission subcycles for the first K registered ONUs as indicated by the set ${\boldsymbol{\mathcal U}_{transmitting}}$ in line 3. ${\boldsymbol{\mathcal U}_{transmitting}}$ represents the set of ONUs that is currently polled to transmit ${W_{\max }}$ packets during their scheduled subcycle time. The transmission start time of the first sequence of the polled ONUs is ${T_u} = {t_0}$ (in this case t₀ = 0). In line 5, the time index is incremented by one after one transmission subcycle. The OLT sets the time instant the next polled ONUs start transmitting in line 6. In line 7, the OLT identifies the set of other registered ONUs (from $K + 1$ to $N$) that are still waiting for their turns to transmit. This set is defined as ${\boldsymbol{\mathcal U}_{waiting}}$. Finally, in line 8 the OLT swaps the order of ONUs in a cyclic manner. The turn of the ONUs that finish transmitting is moved to the end of the set $\boldsymbol{\mathcal U}$. The waiting ONUs get their transmission turns in the fixed scheduling pattern.

Consider the case described in Fig. 3. Table 2 shows the scheduling of ONUs at every subcycle in which a poll occurs.

Table 2. RP-DBA scheduling table at every polling subcycle

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In the first subcycle, the sequence of ONUs {1, 2, 3, 4} is polled first to start transmitting at ${t_0}$ up to ${W_{\max }}$ packets, while ONUs {5, 6, 7} are waiting for their turns. Then, in the second subcycle, the sequence of ONUs {5, 6, 7, 1} is polled to start transmitting at ${t_1} = {t_0} + {W_{\max }}{T_p}$ and so on. Since four ONUs from seven, have to transmit at every poll, $ON{U_1}$ is polled twice for two consecutive subcycles. A similar situation can occur with other ONUs at different time instants. This leads the waiting time between the consecutive scheduled transmissions to alternate between zero and one subcycle.

In general, since the scheduling pattern is known a priori, the transmission start time of the ${n^{th}}$ transmission of ONU u, denoted as ${T_u}[n]$, can be calculated as follows.

Lemma1: the waiting time between any two consecutive scheduled transmissions $({n,n + 1} )$ for a target ONU u in RP-DBA scheme is ${w_u}({n,n + 1} )$ subcycles for $\lceil{{N \mathord{\left/ {\vphantom {N K}} \right.} K}} \rceil \ge 2$ and zero otherwise, where

Proof: Consider N ONUs connected to the network where K ONUs can transmit simultaneously per subcycle ($K$ is the transmission bandwidth per subcycle) such that $0 \;\lt \;K\;\le\;N$. Let ${T_u}[n ]$ be the transmission start time of the ${n^{th}}$ transmission and ${T_u}[{n + 1} ]$ the transmission start time of the next ${({n + 1} )^{th}}$ transmission of ONU u. Since $ON{U_u}$ is scheduled to transmit in one subcycle at a time, the waiting time between the ${n^{th}}$ and the ${({n + 1} )^{th}}$ transmissions is given by

However, the term $({{N \mathord{\left/ {\vphantom {N K}} \right.} K} + ({\alpha - \beta } )} )$ in (6) represents an integer number of subcycles, and the sign of $({\alpha - \beta } )$ depends on the index u of the transmitting ONU. This means that:

If $({\alpha - \beta } )> 0$, then ${N \mathord{\left/ {\vphantom {N K}} \right.} K} + ({\alpha - \beta } )= \lceil{{N \mathord{\left/ {\vphantom {N K}} \right.} K}} \rceil$. On the other hand, if $({\alpha - \beta } )\le 0$, then ${N \mathord{\left/ {\vphantom {N K}} \right.} K} + ({\alpha - \beta } )= \lceil{{N \mathord{\left/ {\vphantom {N K}} \right.} K}} \rceil - 1$. Therefore, (3) is satisfied.

For ${{1 \le N} \mathord{\left/ {\vphantom {{1 \le N} K}} \right.} K} \le 2$, $\lceil{{N \mathord{\left/ {\vphantom {N K}} \right.} K}} \rceil$ can be either 1 or 2. If $\lceil{{N \mathord{\left/ {\vphantom {N K}} \right.} K}} \rceil = 1$ then all the N ONUs transmit simultaneously and continuously without any delay and ${w_u}({n,n + 1} )= 0$; otherwise, (3) is satisfied which proves Lemma 1.

5. Performance evaluation

In our simulation, the queue dynamics of the ONUs is modeled as follows. The packets arriving at the ONU with a given arrival rate are queued before being transmitted through the network. When the ONU is granted transmission, the grant is completely transmitted at a full channel capacity i.e. at a rate of 25 Gbps and removed from the queue. In FIFO-DBA, no backlogged packets from current grants are left for the rescheduling in the subsequent transmission cycle time. In RP-DBA, because no report transmission is needed, we assume that the time duration between two consecutive transmissions forms an apparent cycle time. This apparent cycle time consists of the subcycle transmission times and the waiting time between two consecutive transmissions. From Lemma 1, the cycle time is constant and asynchronous among the ONUs. During this cycle time only one window size of ${W_{\max }}$ packets is transmitted from the queue and the new arrivals are backlogged for the next scheduled transmission.

In case of NG-EPON CDMA-based scheduling algorithms, four coded ONUs simultaneously transmit their grants on a single wavelength at 25 Gbps. The size of the grant is the main parameter that determines the ONU cycle time and hence the number of new packet arrivals which will be granted transmission in the next cycle. The larger is the cycle time, the higher is the queue size, and vice versa.

On the other hand, in case of NG-EPON WDM-based scheduling algorithms, each ONU transmits its queue content over one or multiple wavelengths of 25Gbps each depending on the grant size. In one cycle time, all ONUs transmit their requested queued-packets over several wavelengths using TDM. The timeslot size of each ONU, using a given wavelength, is proportional to the allocated bandwidth on that wavelength. At the end of the cycle, all ONUs report their queue contents of new arrivals which will be scheduled and transmitted in the subsequent cycle time.

In both cases, for a large cycle time and a high arrival rate, the packet arrivals exceed the maximum queue size. We assume that the excess packets will be dropped. In addition, the packets are assumed to follow a Poisson arrival process with an arrival bit rate of ${\lambda _u}$ bits/s for each ONU u during non-overlapping irregular cycle times. Consider that B is the size of a packet in bits. At discrete time instants s, the cycle time of ONU u is $T_{cycle}^{(u)}(s )$. The queue size, measured in packets, of ONU $u$ is denoted as ${Q_u}(s )$. The queue dynamics relative to the transmission of the grant $Gran{t_u}(s )$ and the arrival of new packets $T_{cycle}^{(u)}(s ){{{\lambda _u}} \mathord{\left/ {\vphantom {{{\lambda_u}} B}} \right.} B}$ can be modeled as a discrete homogeneous Markov chain such that the queue transition from a cycle $({s - 1} )$ to a cycle s is described as

In addition, the transition probability that describes the queue behavior of each ONU is calculated as

Let A be the random number representing the packet arrivals during the cycle time. If the new arrivals find an empty queue, the queue size becomes $\ell = {{T_{cycle}^{(u)}(s ){\lambda _u}} \mathord{\left/ {\vphantom {{T_{cycle}^{(u)}(s ){\lambda_u}} B}} \right.} B}$, then

Equations (9) and (10) indicate that at the end of the cycle time a queue always contains packets. Thus the ONUs have always packets to be transmitted.

It follows that the steady-state queue occupancy vector of ONU u is ${\pi ^{(u )}}$ and is obtained by solving the linear system

The average packet delay is the average waiting time of packets in the buffer. By virtue of Little’s theorem, the mean packet delay is expressed as

Also, by using Littles theorem, we define the packet delay of ONU u at a discrete time instant s as

The throughput rate of each ONU u, measured in bits per second, is the grant transmitted per cycle time and is written as

The cycle time represents the period of time during which packets accumulate and stay in the queue before being transmitted. At the same time, it describes the time required for the ONU to serve its grant.

6. Numerical results

In this section, we will evaluate the mean packet delay, jitter, packet drop ratio, bandwidth allocation, utilization and network aggregate throughput of our newly proposed algorithms in comparison with the CDBA, WF-DWBA, FW-DWBA and FF-DWBA. For the WF-DWBA, FW-DWBA and FF-DWBA, we consider that the number of ONUs that can transmit simultaneously during a time instant is 4 (because there are 4 wavelengths) but each of the 3 algorithms will distribute them differently following [17], [18] and [20] respectively.

The simulation parameters are summarized in Table 3. For DWBA algorithms four wavelengths are used.

Table 3. simulation parameters

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We assume that the RTT is the same for all the ONUs. We consider the average packet arrival rate as the offered traffic at the ONU. In order to highlight the impact of the burst-mode traffic on the proposed scheduling algorithms we assume that the offered traffic varies from 10% to 100% of ${{{R_u}} \mathord{\left/ {\vphantom {{{R_u}} 5}} \right.} 5}$, (i.e. from 0.5 to 5 Gbps).

In addition, each ONU can transmit up to ${W_{\max }}$ packets of a fixed size in any allocated subcycle time at the full link capacity. Also, for a fair comparison, we consider that $K = 4$ simultaneous coded transmissions per subcycle for an arbitrary physical layer QoS requirement, as described in [23], in accordance with the four wavelengths used for the DWBA. It is important to mention that in our simulation, we are comparing among the DBAs using two different multiple access techniques: the hybrid time and wavelength division multiplexing (TWDM) for the WF-DWBA, FW-DWBA and FF-DWBA and the CDMA for the CDBA, FIFO-DBA and RP-DBA. In the case of TWDM, the ONU’s request is distributed over multiple wavelengths (in this case 4), with a total capacity of 4 × 25Gbps = 100Gbps. On the other hand, each ONU request in the CDMA case is allocated its own dedicated code and all the ONUs transmit over one uplink wavelength at a capacity of 25Gbps. In addition, the 4 coded ONUs can transmit simultaneously to reach a total capacity of 4 × 25Gbps = 100Gbps. Thus, the 4 wavelengths in the case of TWDM correspond to the 4 codes in the case of CDMA per transmission time. Also, we consider that all the ONUs are always active.

In the three DWBAs a guard time is set at the end of the transmission over each allocated wavelength to separate between two different ONUs. The amount of guard times has a perceptible impact on the channel utilization that differs among the three DWBAs.

Figure 4 shows the average packet delay per ONU versus the offered traffic. It is clear that the average packet delay of the proposed FIFO-DBA and RP-DBA schemes are better than that of the CDBA for all the offered traffic. The reason is that in CDBA case, the scheduled transmissions mismatch the requests during the cycle time. The backlogged packets and the new arrivals wait in queue until scheduled in subsequent cycles. This makes packets in CDBA suffer a higher delay that might exceed 1ms at a low offered traffic of 1Gbps. In the case of the FIFO-DBA, the scheduled transmission subcycles answer the ONU’s request during the ONU’s cycle time in such a way that no backlogged packets remain for the next cycle. This leads to a dramatic decrease in the packet delay at all offered traffic. However, as the offered traffic exceeds 2.75Gbps, the request transmission time increases. Then, new requesting ONUs will maintain their packets in queue for a longer period of time, waiting for the channel to become free. At this point the delay starts increasing. This situation has been resolved by RP-DBA. The absence of reporting back to the OLT makes the ONU benefit from the whole transmission bandwidth and send more packets and therefore reduces the delay. Also, the ONU starts transmitting its queue content as soon as it reaches its scheduled turn. Even during the scheduled transmission subcycle, the ONU arrivals can be immediately transmitted as long as their numbers suit the scheduled subcycle. Accordingly, the RP-DBA can achieve the lowest delay which can reach 0.5ms at 3Gbps of the offered traffic. In addition, note that our proposed CDMA-based scheduling algorithms provided an improved delay performance compared to that of DWBA algorithms. The reason is that in DWBA schemes, an ONU can transmit over multiple wavelengths (up to four) that are occupied for the whole request transmission time. During this period, new requesting ONUs cannot transmit immediately and their requests will remain in the queue. This will increase the overall queueing time. However, in FIFO-DBA and RP-DBA four ONUs can occupy the wavelength channel at the same period of time.

 

Fig. 4. Average delay of CDBA, FIFO-DBA and RP-DBA schemes versus offered traffic compared to that of DWBAs.

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Figure 5 shows the jitter versus the offered traffic. It is shown that the jitter of the FIFO-DBA and RP-DBA has been significantly reduced for the low and medium offered traffic as compared to that of the CDBA, which exhibits a high jitter as expected. The RP-DBA is able to stabilize the packet delay and thereby reducing the jitter. On the other hand the jitter degradation of FIFO-DBA is due to the request mismatch and the variable waiting time between two consecutive scheduled transmissions. At a high offered traffic (above 3Gbps), the jitter of all the schemes converges towards 0.5ms and the three schemes follow the same jitter behavior. However, FIFO-DBA and RP-DBA exhibit a better jitter performance than the DWBA algorithms for the offered traffic below 3Gbps. Nevertheless, when the offered traffic becomes greater than 3Gbps, the DWBA algorithms give a lower jitter. The peak in the jitter occurs due to the fact that as the offered traffic increases, the queue size variation increases and hence the ONU’s request bandwidth. The jitter starts growing until it reaches a maximum at which the queue saturates. At this point, all ONUs will have almost equal request bandwidth. Thus, the jitter will start decreasing.

 

Fig. 5. Jitter of CDBA, FIFO-DBA and RP-DBA schemes versus offered traffic compared to that of DWBAs

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The packet drop ratio calculated using 1Mbyte buffer size is illustrated in Fig. 6. Low packet-drop ratios are delivered by the proposed schemes as compared to that of the CDBA and DWBAs. This ensures that a low buffer size requirement for ONUs is sufficient to handle the offered traffic. Notice that the packet-drop ratio starts increasing when the traffic reaches 60% (3Gbps) in FIFO-DBA and 65% (3.25Gbps) in RP-DBA. On the other hand, in DWBAs the packet-drop ratio starts increasing when the offered traffic reaches 50% (2.5Gbps) for WF-DWBA and 55% (2.75Gbps) for FW- DWBA and FF-DWBA.

 

Fig. 6. Packet drop ratio of CDBA, FIFO -CDBA and RP-DBA schemes versus offered traffic compared to that of DWBAs

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Figure 7 depicts the average grant bandwidth which is defined as the number of allocated bits per second per ONU. Although DWBA algorithms allocate efficiently the bandwidth over multiple wavelengths, the RP-DBA reveals that CDMA-based DBAs enable the ONUs to allocate a full channel capacity over a single wavelength. Notice that for the RP-DBA there is no bandwidth wastage and the allocated bandwidth is the highest for all the offered traffic. In the case of the CDBA the allocated bandwidth is the lowest. This is due to the wasted bandwidth from the large waiting time, the report transmission/processing time, the guard time and the RTT. On the other hand, for the FIFO-DBA the grant bandwidth is bounded between that of the CDBA and the RP-DBA since the waiting time between the consecutive scheduled transmissions is much smaller than that of CDBA. The increase of the grant bandwidth is due to the bandwidth request size, which converges at higher offered traffic to that of the RP-DBA.

 

Fig. 7. Average grant bandwidth per ONU of CDBA, FIFO-DBA and RP-DBA schemes versus offered traffic compared to that of DWBAs.

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The aggregate throughput of the network, defined as the actual number of transmitted bits of all ONUs, is presented in Fig. 8 for all the schemes. It is obvious that the higher the granted bandwidth, the higher the throughput as more packets can be transmitted when the offered traffic increases. The highest grant bandwidth offered by RP-DBA can serve more traffic at a higher rate. The throughput of RP-DBA is comparable to that of DWBAs up to 3Gbps of the offered traffic. Again the FIFO-DBA performs better than the CDBA and provides a pretty good throughput as compared to that of DWBAs.

 

Fig. 8. The aggregate throughput of the network for CDBA, FIFO-DBA and RP-DBA schemes versus offered traffic compared to that of DWBAs

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In CDMA-based DBA, at a low offered traffic the packet arrivals may be less than the ${W_{\max }}$ packets at any subcycle. This issue is assessed in Fig. 9 where we show the average grant utilization per ONU as a function of the offered load. Note that the low grant utilization of the RP-DBA results from the fixed bandwidth allocation which overestimates the request bandwidth at a light load < 2.5Gbps. This result is expected because once an ONU is active, it follows its own pre-defined transmission pattern independently of its load. On the other hand, at a high load (>3Gbps), the RP-DBA shows the best grant utilization performance. The bandwidth allocation of FIFO-DBA and CDBA shows a much better grant utilization at a lower offered load. In DWBA algorithms, the grant utilization is superior and it is highly dependent on the consecutive allocation of the TDM-based timeslots over multiple wavelengths and the number of guard time insertions.

 

Fig. 9. Average grant utilization per ONU versus offered traffic for all schemes

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Figure 10 illustrates the transmission efficiency of all the schemes using the throughput-delay characteristic. Once again the RP-DBA scheme outperforms FIFO-DBA scheme with a higher throughput and a lower delay. Nevertheless, both newly proposed schemes show a remarkable improvement over the CDBA scheduling scheme. In addition, the DWBA algorithms provide a performance bounded by that of RP-DBA and FIFO-DBA. Note that both the FF-DWBA and RP-DBA algorithms provide the best performance among other scheduling algorithms

 

Fig. 10. The throughput-delay characteristic of CDBA, FIFO-DBA and RP-DBA schemes compared to that of DWBAs.

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The jitter variation per ONU with respect to time is illustrated in Fig. 11 for a uniformly distributed arrival rate between 1% and 100% of ${{{R_u}} \mathord{\left/ {\vphantom {{{R_u}} 5}} \right.} 5}$ for all the schemes. For the CDBA, the jitter variations vary within ${\pm} 5$ms. For the proposed schemes, the jitter variations have been reduced to within ${\pm} 3$ms for FIFO-DBA and ${\pm} 0.2$ms for RP-DBA. In comparison with FF-DWBA, the jitter is very low and smooth when the traffic is not bursty. When the traffic becomes bursty, the jitter starts to increase to within ${\pm} 2$ms.

 

Fig. 11. Jitter variations with respect to time for CDBA, FIFO-DBA and RP-DBA schemes compared to that of FF-DWBA.

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The probability density function of the jitter is investigated in Fig. 12. As expected, the CDBA has the highest standard deviation of $\sigma = 2.0731$ ms. On the other hand, the FIFO-DBA and RP-DBA have standard deviations of $\sigma = 0.8288$ms and $\sigma = 0.0944$ ms, respectively. This indicates that the proposed scheduling algorithms have indeed improved the jitter performance. On the other hand, $\sigma = 0.7896$ms and $0.6814$ms for WF-DWBA and FF-DWBA, respectively. Thus, our proposed CDMA-based algorithms can offer a jitter improvement as good as the WDM-based DWBA algorithms.

 

Fig. 12. The probability density function (PDF) of the Jitter for CDBA, FIFO-DBA and RP-DBA schemes compared to that of DWBAs.

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7. Conclusion

In this paper, two new scheduling algorithms, namely the RP-DBA and the FIFO-DBA have been proposed for performance improvement in CDMA-based NG-EPON. The performance of both schemes has been investigated in terms of the latency, jitter, bandwidth allocation, network aggregate throughput, packet drop ratio and bandwidth utilization. In addition, the performances of the newly proposed protocols are compared to that of the CDBA, WF-DWBA, FW-DWBA, and FF-DWBA. Both newly proposed schemes show a radical improvement over the previously proposed CDBA scheme. Simulation results show that the FIFO-DBA significantly improved the latency and the jitter performance with respect to the CDBA and also confirms that the RP-DBA has the best performance at a high load. On the other hand, the results show that CDMA-based DBA can offer a comparable performance with respect to that of the WDM-based DWBAs. Therefore, the CDMA-based DBA can be a good candidate to meet the requirements of the NG-EPON, especially if we take into consideration that using a set of passive encoders/decoders would be cheaper than using a set of laser sources.