Delay Performance of WDM-EPON forMulti-dimensional Traffic Under the IPACT

Fixed Service and the MultiPoint Control ProtocolM. D. Logothetis (1), I. D. Moscholios (2), A. C. Boucouvalas (2) and J. S. Vardakas (3)

Abstract—Passive Optical Networks (PONs) gain ever moreground in the Telecom market, because of their low cost andsignificant advantages over legacy broadband access systems. Weconcentrate on the performance evaluation of Ethernet PONs(EPONs) and particularly on Wavelength Division Multiplexing(WDM)-EPONs which support Internet traffic. We considertraffic of multiple service-classes and focus on the calculationof the mean total delay from the so-called Optical NetworkUnit (ONU) to the Optical Line Terminator (OLT). The PONoperates under the fixed service of the IPACT (Interleaved PollingWith Adaptive Cycle) algorithm, which uses the MultiPointControl Protocol (MPCP). The delay analysis is based on aunified approach for EPONs and WDM-EPONs, through theformation of two classical queuing models: an M/D[x]/C forthe packets waiting in the local queues of the ONUs and anM/D/C for the frame transmission to the OLT. The number ofservers C corresponds to the number of wavelengths used in theuplink. Through simulation, we verify our analysis and show theaccuracy and the consistency of the results.

I. INTRODUCTION

In recent years there have been several studies and manyresults have been presented on Passive Optical Networks(PONs), the most promising and cost-effective fiber basedaccess systems. The latter made ITU-T to issue several relatedstandardizations. The most widely used PON configuration isthe Time Division Multiplexing (TDM)-PON, while the Wave-length Division Multiplexing (WDM)-PON is a successor ofthe TDM-PON capable to convey much more offered trafficload and more Internet users [1]- [3].

A PON consists of a number N of Optical Network Units(ONUs), or Optical Network Terminals (ONTs), which arelocated in the customers’ premises and are connected througha Passive Optical Combiner/Splitter (PO-CS, remote node) tothe Optical Line Terminator (OLT). The OLT is located nextto an ISP Internet Router and through the router it providesaccess to the Internet (Fig. 1). Communication between ONUsis realized through the OLT, only. Figure 1 portrays a WDM-EPON with individual wavelengths per ONU (per traffic-flowdirection). However, the number of wavelengths can be muchless than the number of ONUs, when the WDM-EPON usesa Dynamic Wavelength Assignment (DWA) algorithm, and itis equipped with a proper device for PO-CS [4], [5]; thesenetworking capabilities are considered in this paper.

(1) WCL, Dept. of Electrical & Computer Engineering, University of Patras,265 04 Patras, Greece. E-mail: mlogo@upatras.gr

(2) Dept. of Informatics & Telecommunications, University of Peloponnese,Tripolis 221 00, Greece. E-mail: {idm, acb}@uop.gr

(3) Iquadrat, Barcelona, Spain. E-mail: jvardakas@iquadrat.com

Fig. 1. A WDM-EPON servicing Internet traffic.

In TDM-PONs, only two wavelengths are utilised; one inthe uplink and the other in the downlink (usually 1310 nmand 1490 nm, respectively) [6]. The transmission channel(that uses a single wavelength) between the ONUs and theOLT is divided into equal time-slots, according to the TDMprinciple; a time-slot is assigned to each ONU for the uplinkconnection. The different time-slots from the different ONUsare multiplexed in the PO-CS and transmitted toward the OLTthrough a single fibre, thanks to the directional properties ofthe PO-CS (that is, they do not reach the other ONUs).

The Ethernet protocol fits well to the TDM-PON; it has beenstandardized as a link layer protocol in the TDM-PON since2004, and the PON is named EPON (IEEE 802.3ah standard)[7]. Although in the uplink the EPON has a point-to-point ar-chitecture, collisions are possible at the PO-CS, among packetstransmitted simultaneously from different ONUs (see Fig 3).To tackle the problem of collisions, the MultiPoint ControlProtocol (MPCP) has been standardised as a MAC sublayerprotocol. On the other hand, to enable the transmission of datafrom all users, and hence from all ONUs, there must be analgorithm which will make a fair partitioning of the providedbandwidth. We make use of the so called Interleaved Pollingwith Adaptive Cycle Time (IPACT) algorithm, which usesthe MPCP to allocate bandwidth to each ONU in a dynamicmanner [8].

According to the IPACT algorithm, the available bandwidthof the wavelength is divided into time-slots. A time-slot islarge enough to transmit batches of packets and is an integermultiple of a time-unit c, during which a single packet can

be transmitted. The time-slots are allocated to each ONU.There are several methods (called services) of determining thelength (duration) of the time-slot, which is assigned to eachONU by the OLT: the fixed, limited, gated, constant credit,linear credit and the elastic service. In this study, we referto the fixed service, according to which, the time-slot of themaximum length is assigned to each ONU, irrespectively ofwhat length each ONU has asked for. The fixed service hasthe advantage of simplicity; also, it has been investigated thatit performs satisfactorily under a heavy offered traffic-load, asfar as the packet-delay performance is concerned [9]. Severalother studies on the IPACT services exist in the literature [10]-[13], however, in all these studies, the EPON accommodates asingle service-class, only, which is a rather extraordinary casein the traffic environment of contemporary communicationsnetworks. In this paper, we first present the delay perfor-mance of a TDM-PON (EPON) which accommodates multipleservice-classes, and then we proceed to the delay performanceof a WDM-EPON. The delay analysis of the TDM-PON withmultiple service-classes is not new [14], but it is included inthis paper in order to facilitate the presentation of the delayanalysis of the WDM-EPON. Moreover, we show that, in thecase of the fixed IPACT service, our analysis can cover ina parametric way both EPONs and WDM-EPONs; from theteletraffic point of view, the number of wavelengths used inthe uplink (parameter) denotes the EPON or the WDM-EPON.

In TDM-PONs, as it has been already mentioned, thebandwidth of each wavelength is shared among the ONUs,according to the TDM principle. In WDM-EPONs multiplewavelengths are accommodated per traffic flow direction, andtherefore the transmission bandwidth in the PON is drasticallyincreased (Fig. 1). Specifically, for each connection betweenthe OLT and ONU a different wavelength is allocated staticallyor dynamically (by a DWA algorithm) to the ONU, dependingon the specific device which implements the PO-CS. Thanks toa tunable λ− router (capable to route different wavelengths),the wavelengths can be technically manageable and used bythe users in a cost-effective way. Each wavelength is sharedamong calls of different service-classes accommodated in eachONU, according to the TDM principle, as in the case ofEPONs. Both in EPON and WDM-EPON, when an ONU hasto transmit a total number of packets, a frame is formed whosesize depends on the fixed-service of the IPACT algorithm. TheONU transmits the frame within the duration of one time-slot.Given that K is the number of different service-classes, theframe is composed by K batches of packets. The greater thesize of a batch, the higher the priority of the service-class. Inthis way, not only multiple service-classes but also prioritiesamong service-classes are supported in a PON.

The packet delay analysis in EPONs is based on twoqueuing models: (a) one model for the packets in the localqueues of an ONU, and (b) another model for the completeframe of packets to be transmitted to the OLT. For the firstqueuing model, we assume the ONU architecture of Fig. 2,where the K service-classes are separated by assigning anindividual buffer to each service-class. Batches of packets fromeach service-class form the frame, while it holds: m1>m2>. . . > mk > . . . > mK , that is, the number of packets from

service-class 1 is the highest, which means service-class 1has the highest priority (contrary to service-class K whichhas the least priority). The number mk is the same for allONUs. If we suppose that the portion of the time-slot (frame),which is devoted to service-class k (k=1,. . . ,K) is betweena minimum wk and a maximum mk number of packets, thenthe delay analysis is based on an M/D[wk,mk]/1 queueingmodel. By this model we calculate the queueing delay ofeach service-class in the corresponding queue, or, in otherwords, the delay in forming the frame. Consequently, sinceone frame is transmitted within one time-slot, we use anothersimple queueing model M/D/1 (to calculate the queueingdelay by considering the entire frame as a unit). Based on thestatistics (queueing delay, queue length) obtained for the entireframe, the corresponding statistics for the individual packetsare determined. After having determined the queuing delay,we determine the total delay by adding to it the transmissiondelay and the propagation delay.

Fig. 2. An ONU as a queueing model for the uplink.

The basic difference between EPONs and WDM-EPONs isthat in WDM-EPONs a multiple of C frames are transmittedtoward the OLT during a time-slot that correspond to thenumber of the allocated wavelengths in the uplink (C < N ).Therefore, in the case of WDM-EPONs the queueing modelscomprise C servers. Each ONU has C transmitters, where eachone transmits in a different frequency. In the beginning of eachtransmission cycle, the transmitter sends a frame to the OLTand C frames in total by the end of the transmission cycle.

The analytical results, for the uplink, have been comparedwith simulation results to verify the validity of the analysisand the accuracy of the calculations. As far as the downlinkdirection is concerned, the transmission procedure is muchsimpler from a scientific point of view. Signals from OLT toONUs are split at the PO-CS and are received by the ONUsbased on the Ethernet addresses. Even in the case of WDM-EPONs, only one wavelength can be used in the downlink.

The structure of this paper is as follows. In Section II,we describe the PONs under study, concentrating on theinvolved protocols. In Section III, we concentrate on the fixedservice, and we review the delay performance analysis ofEPONs supporting multiple service-classes. In Section IV, wepresent the delay performance analysis for multiple service-classes in WDM-EPONs. In Section V, we present applicationresults which verify the analysis; comparative results betweenthe EPON and WDM-EPON are presented and show theconsistency of our analysis. We conclude in Section VI.

II. MPCP AND IPACT

The basic PON architecture, either of an EPON or a WDM-EPON, is shown in Fig. 1, as far as the PON topologyis concerned, where one OLT supports N ONUs through aPO-CS. All data-packets are encapsulated in Ethernet frames(IEEE 802.3ah). As it is shown in Fig. 3, in the downlinkwhere the OLT broadcasts all packets to ONUs (Fig 3a), thereis no bottleneck problem, whereas, in the uplink, collisionsmay appear when packets arrive simultaneously at the PO-CSfrom the ONUs. For collision avoidance the MPCP is used.Moreover, the MPCP contributes to the Dynamic BandwidthAllocation (DBA) among the ONUs, which is defined by theIPACT algorithm.

Fig. 3. (a) Broadcasting in the downlink. (b) In the uplink, since ONUsmay transmit packets simultaneously (e.g 2 and 3), the MPCP arbitrates thetransmission.

A. Multi-Point Control Protocol

The MPCP is a protocol of Data Link Layer, and specificallyof the MAC sublayer, that controls the TDM transmission ofthe uplink [7]. This is the normal mode of operation wherebytransmission opportunities are assigned to ONUs, while thereis an additional mode of operation whereby a newly connectedONU in the PON is detected; the OLT is informed about thephysical address and the transmision capabilities of the ONU,as well as the round-trip time between the OLT and the ONU.In the normal mode, MPCP uses the MAC Control messagesGATE (from OLT to ONU) and REPORT (from ONU toOLT). To accomplish the ONU detection, MPCP uses threemore messages: REGISTER REQ (from ONU to OLT),REGISTER (from OLT to ONU) and REGISTER ACK(from ONU to OLT). The discovery mode of the MPCPoperation is applied by the OLT periodically. A general rule ofthe MPCP is that an ONU is allowed to transmit (either dataor a control message) only during the time interval indicatedin the GATE message.

Figure 4 shows a communication scenario between the OLTand an ONU according to the MPCP, where all five messagesare included; both the discovery and the normal mode ofoperation are shown. Initially the OLT allocates a time-slot,in which unregistered ONUs are allowed to transmit. Thestart time of the initialization time-slot and its duration areincluded in the GATE message which is advertised (a multicastaddress is used) by the OLT (message GATE Discovery(0)in Fig. 4). An unregistered ONU may respond to this GATEmessage by sending the REGISTER REQ(1) message,when the local timer of the ONU reaches the start time ofthe initialization slot; the latter is included in the receivedGATE message and must not be violated. The OLT answerswith the REGISTER(2) message. Then, the OLT terminatesthe discovery phase by sending the GATE grant(3), inwhich the ONU must answer with REGISTER ACK(4).After a while, but within the time-interval indicated inGATE grant(3), the ONU asks the OLT for transmis-sion by sending REPORT (5) and waiting for receiving theGATE(6). In the REPORT (5) message, the ONU describeshow many packets are stored in its queues; based on thisinformation the OLT assigns the proper bandwidth to theONU, that is, decides on the duration of a transmissionwindow, which is sent to the ONU in GATE(6). In this way,the ONU has a first transmission cycle. Since a second cycleis needed, the ONU sends the REPORT (7), in order for theOLT to issue the GATE(8) and so on.

Fig. 4. A communication scenario between OLT and ONU.

B. The Interleave Polling with Adaptive Cycle Time (IPACT)Algorithm

The IPACT algorithm is used for dynamic bandwidth al-location by performing inter-ONU scheduling. Based on theREPORT message of the MPCP, the OLT knowns thedynamic traffic load in each ONU and can distribute the uplinkbandwidth of the PON according to the requirements of theONUs in a fair way. This is done by the IPACT algorithm; the

OLT polls the ONUs and assigns to each ONU transmissiontimeslots, in round-robin [9].

More precisely, IPACT is a centralized algorithm which runsin a DBA agent of the OLT (at the service layer sitting abovethe MAC protocol layer). IPACT uses the control messagesGATE and REPORT of the MCMP, in order to estimateand allocate bandwidth to each ONU, as well as the ServiceLevel Agreements in order to guaranteeing a minimum degreeof service. Needless to say that buffers of a different size existin ONUs. In case that an ONU of a large buffer was attemptingto transmit all the content of the buffer at once (i.e. in onetransmission cycle), this would monopolize the transmissionand no one else could transmit for a long time. To face thisproblem in a fair way, the IPACT algorithm applies severalmethods for bandwidth assignment, which are called services.

As it was mentioned in the Introduction, the availablebandwidth of the wavelength is divided into time-slots. A time-slot is large enough to transmit a frame of packets and is aninteger multiple of a time-unit c, during which a single packetcan be transmitted. The length (duration) of the time-slot isdetermined according to the applied service; the most popularservices are the following:

• Fixed service – The maximum possible length of thetimeslot is assigned to the ONU, regardless of the re-quested size. The resultant transmission cycle is fixed andequals to the maximum possible length.

• Limited service – The assigned length of the timeslotequals the required one by the ONU, as long as this lengthdoes not exceed the maximum possible (determined bythe fixed service).

• Gated service – No certain limit is denoted; each ONUcan transmit in one transmission cycle as many packets asthey have been stored in its queue. This service is mainlyapplicable, when the queue buffers of the ONUs have arelatively small length (not exceeding a threshold).

• Constant credit – The assigned length of the timeslotequals the required one by the ONU plus a fixed value.It is supposed that some more packets have been storedin the queue of the ONU, while it waits for the GATEmessage in order to start transmission.

• Linear credit – The assigned length of the timeslot equalsthe required one by the ONU plus a value, not fixed butproportional to the required one.

• Elastic service – The assigned length of the timeslot isnot limited. The assigned bandwidth capacity per ONUis determined so that the sum of the last N bandwidthrequirements does not exceed the sum of the correspond-ing lengths of the assigned timeslots. Therefore, if onlyone ONU needs to transmit, the entire bandwidth of allN ONUs can be assigned to a single ONU.

In this paper, we consider the fixed service of the IPACTalgorithm and examine the delay performance of the PON(both the EPON and WDM-EPON) when the ONUs supportmultiple service-classes. The basic principles of the IPACTalgorithm for the implementation of the fixed service are thesame both for the EPON and the WDM-EPON [15].

III. DELAY ANALYSIS OF EPONS FOR THE IPACT FIXEDSERVICE

In the uplink, the PON acts as a multipoint-to-point network,where ONUs are able to transmit packets in batches (frames),during different time intervals. The set of packets which havebeen stored in the local queues of each ONU (Fig. 2) willformulate a frame to be transmitted. The duration of this framecorresponds to the timeslot whose size is assigned by the OLT.Since we consider the fixed service of the IPACT algorithm,the duration of each timeslot (frame) is constant; in otherwords, the service time of the packets in the frame is constant.

As far as the packet arrival process to the local queuesis concerned, it is assumed Poisson. Although the Poissoncharacteristics of independent and identically distributed ran-dom arrivals do not perfectly reflect the packet-level traf-fic characteristics of PONs, the Poisson process is broadlyconsidered as the starting point of a teletraffic analysis. Thereason is twofold: (a) The Poisson process is analyticallysimple, and (b) the teletraffic model in which the Poissonprocess is incorporated, is usually a well studied model withsafe results. Besides, another reason is the fact that, usually,analysis under the Poisson assumption is used as a referencepoint for comparison against other considerations of the inputtraffic, because randomness as it is expressed by the Poissonmodel can easily be understood and compared. Anyway, batcharrivals, event correlations and traffic burstiness are importantfactors of the packet-level characteristics of PONs [16], whichnecessitate the use of heavy tailed distributions and of self-similarity of Ethernet traffic [17]; therefore, assumptions likea Batch Poisson Arrival Process, or a Markov ModulatedPoisson Process are much more realistic than Poisson atpacket-level.

The consideration of multiple service-classes is a sine quanon in the traffic environment of PONs. The service-classesdistinction is done according to the required bandwidth percall, only. In addition, we assign a transmission priority to eachservice-class, which is the same for all ONUs. This is doneas follows: Since the timeslot of each ONU is shared amongthe K service-classes, we introduce a different transmissionpriority to each service-class, by assigning a different portionof the timeslot to each service-class. In this way, we can con-sider as many priorities as the number of service-classes, i.e. Kpriorities: mn,1>mn,2>. . .>mn,k>. . .>mn,K , where forthe ONU n, (n = 1, . . . , N), mn,k is the transmission priorityof service-class k, and corresponds to the portion of the time-slot (frame), which is devoted to packets of service-class k.More precisely, given that a single packet is transmitted duringa time-unit c, the portion of mk means a time-interval of mk ·c.We can also assume that the portion of the frame, which isdevoted to service-class k is between a minimum wn,k and amaximum mn,k number of packets.

We shall analyse the total packet delay, when a service-class k packet is transmitted from an ONU to the OLT, byconsidering the queueing delay, the transmission delay andthe propagation delay, during the transmission time as it isindicated in Fig. 4. That is, we ignore other type of delaywhich is introduced by the MPCP/IPACT.

As it is shown in Fig. 2, the determination of packet delaydepends both on the K local queues which correspond to theK service-classes of each ONU, and one more queue for theframe transmission. In what follows, we show that the queuingdelay can be determined based on two queuing models: i) theM/D[wk,mk]/1 for the K local queues and ii) one more model,the M/D/1, for the frame.

Let Tn denote the entire duration of the frame assigned toONU n. Then, for each ONU n, it holds:

K∑k=1

mn,k = Tn (1)

The successful recovery of the arriving frames at the OLT isassisted by the insertion of a safety time interval, with durationf , between two consecutive frames. The elapse time betweentwo consecutive frame transmissions Tf,n, of the same ONUn determines the service time of the K local queues of ONUn. That is, Tf,n equals to the sum of the duration of the framesfrom the remaining N−1 ONUs, plus the safety time intervalbetween two consecutive frames:

Tf,n =

N∑i=1

Ti − Tn +N · f (2)

From eq. (2) it is clear that Tf,n is constant. This is thereason that justifies our assumption that each local queue ofservice-class k follows the M/D[wk,mk]/1 queuing model. Inthis model, given that one frame is transmitted from eachONU, one server is considered as the system’s capacity.

The calculation of the mean queue length and the meanwaiting time of the M/D[wk,mk]/1 queuing model for service-class k is based on the formulation of a second queuing model,which is the M/D/1, because each frame is treated as asingle independent unit. Again, a unique server is considered,because within the time-inteval Tf,n only one frame of ONUn is serviced. Since we consider Poisson arrivals, if we denoteλn,k to be the arrival rate of individual packets of service-classk for ONU n, then the arrival rate λ

′

n,k of a batch with sizemn,k is:

λ′

n,k =λn,kmn,k

(3)

while the corresponding equivalent offered traffic load of thebatches is:

A′

n,k = λ′

n,k · Tf,n · c (4)

Taking into account the offered traffic load of batches, themean waiting time of a batch is determined through the M/D/1queuing system [18]:

W′

n,k =Tf,n · c ·A′

n,k

2 · (1−A′n,k)

(5)

Through Little’s law, we can calculate the mean queuelength of the M/D/1 queuing system:

L′

n,k = λ′

n,k ·W′

n,k =λ

′

n,k · Tf,n · c ·A′

n,k

2 · (1−A′n,k)

(6)

The mean queue length of service-class k packets in thelocal queue of ONU n is given by the following approximation[19]:

Ln,k≈mn,k ·L′

n,k+Pwn,k ·

mn,k− 1

2+(1−Pw

n,k)·wn,k−1

2(7)

where Pwn,k is the probability of delay (waiting) in the corre-

sponding M/D/1 queuing system [18]:

Pwn,k = P (j ≥ 1) =

∞∑j=1

πn,kj = 1− πn,k

0 = A′

n,k (8)

According to eq. (8), to calculate the probability Pwn,k,

the knowledge of the steady-state distribution πn,ki of the

M/D/mn,k queueing system is required; it is given by [18]:

πn,ki =(1−A

′

n,k)

i∑j=1

[(−1)i−jejA′n,k(

(jA′

n,k)i−j

(i−j)!+(jA

′

n,k)i−j−1

(i−j−1)!)]

(9)From eq. (7) and Little’s law, we can calculate the mean

waiting time of service-class k packets in the local queue ofONU n, as follows:

Wn,k =Ln,k

λn,k(10)

To calculate the average total packet delay, we sum up themean waiting time in the queue, the transmission delay and thepropagation delay. We consider that all ONUs transmit packetswith fixed length of l bits, while the bit-rate in the uplink isC bits/sec. Then, if the transmission delay of a packet is:

Ttrans =l

C(11)

and the propagation delay of a packet transmitted from ONUn to OLT, in a distance of dn far from ONU n, is:

Tprop,n =dnc̃

(12)

where c̃ is the speed of light in the optical fibre,then, the average total packet delay Tn,k of service-class ktransmitted from ONU n to OLT is given by:

E[Tn,k] =Wn,k + Ttrans + Tprop,n (13)

IV. DELAY ANALYSIS OF WDM-EPONS FOR THE IPACTFIXED SERVICE

The application of the WDM technology in an EPONincreases the available bandwidth of each ONU, and con-sequently of the users, through the utilization of multiplenon-overlapping wavelengths. A unique wavelength pair isassigned to each ONU for communication with the OLT: onewavelength for the downlink and another for the uplink. In thisway, a separate point-to-point connection is provided between

each ONU and the OLT, through the shared point-to-multipointphysical PON architecture [6]. The ONU is characterisedcolorless, because the wavelength is not fixed but it is assignedto the ONU dynamically, when it is required in the uplink.A key difference between an EPON and a WDM-EPON isthe PO-CS, which, in the case of WDM-EPON, is a tunablerouter to any of the wavelengths assigned to the ONU (bya DWA algorithm) in the uplink. By considering again thefixed service of the IPACT algorithm, a time-slot of a certainduration is assigned to each ONU. Within this time-slot, eachONU transmits a batch of packets at a specific wavelength.The set of packets which have been stored in the local queuesof each ONU, and are going to be transmitted during a time-slot, formulate a frame. The WDM-EPON supports multipleservice-classes with different transmission priorities. That is,each service-class occupies a different portion of the frameaccording to its transmission priority. The packet arrival pro-cess is assumed Poisson, while the service time is deterministicbecause of the fixed service of the IPACT algorithm. The basicdifference with the EPON is the fact that multiple frames aresimultaneously transmitted in each time-slot; the number ofthe transmitted frames equals the number of wavelengths. Thetotal number of simultaneously transmitted frames within atime-slot cannot exceed the total number C of wavelengthswhich are available to ONUs in the uplink. We assume thatall ONUs support an equal number of wavelengths. On theother hand, the total number of wavelengths C (in the uplink)may be less than N ; in that case, which is under considerationin this paper, a DWA scheme is assumed in the WDM-EPON,together with the IPACT algorithm for DBA (alternatively,this combination of DBA and DWA can be considered as anextension of the IPACT algorithm to WDM-EPONs) [15].

We analyse the total packet delay, when a service-class kpacket is transmitted from an ONU to the OLT, while ignor-ing any other delay which is introduced by the DBA/DWAprocedures. As in the case of EPON, we shall base ourstudy of queueing delay on two queueing models: i) theM/D[wk,mk]/C for the K local queues of the ONU, and ii)the M/D/C for the transmission of the frames. The numberof servers in both queueing systems becomes C, since itcorresponds to the total number of the supported wavelengthsin the uplink and therefore to the number of frames which canbe transmitted within a time-slot.

Each ONU possesses C transmitters which operate in dif-ferent wavelengths. At the beginning of each transmissioncycle, each transmitter is going to send to the OLT one frame.Therefore, in each transmission cycle the maximum numberof frames that can be transmitted from each ONU is C.

Since the fixed service of the IPACT algorithm remains thesame as in the EPON, the fixed frame duration is given againby eq. (1). Also, the time interval between two consecutiveframes is given by eq. (2). Likewise, since the input processremains Poisson, the frame is formed from batches of packetswith a mean arrival rate of λ

′

n,k, given by eq. (3), where mn,k

is the batch size. Besides, the corresponding offered trafficload from batches is given by eq. (4). Based on the latter, themean waiting time of a batch is determined from the M/D/Cqueueing system [19]:

W′

n,k=C

C+1· E2,C(An,k

′) · Tf,nC−A′

n,k

·1−(

A′n,k

C )C+1

1−(A′n,k

C )C(14)

where E2,C(A′

n,k) is the famous Erlang-C formula [18]:

E2,C(An,k′) =

(A′n,k

C )C · CC−An,k

′

C−1∑r=0

(An,k′)r

r! + (A′n,k

C )C · CC−An,k

′

(15)

Based on Little’s law, we calculate the mean queue lengthLn,k

′ of the M/D/C queueing system as follows:

Ln,k′ = λn,k

′W′

n,k =

= λn,k′ · C

C+1 · E2,C(An,k′) · Tf,n

C−A′n,k

· 1−(A′n,kC )C+1

1−(A′n,kC )C

(16)

Another way to determine the mean queueing delay of theM/D/C queueing system is through the following approx-imation, which results from the generalized model M/G/C(and can be compared to eq. (5)) [19]:

W′

n,k = Pwn,k ·

Tf,n · c ·A′

n,k

2 · (1−A′n,k)

· 1

C(17)

where Pwn,k is the probability of delay (waiting) in the

M/D/C queueing system [19]:

Pwn,k=

(C ·A′

n,k)C

(1−A′n,k)·C!

C−1∑j=0

(C ·A′

n,k)j

j!+

(C ·A′

n,k)C

(1−A′n,k)·C!

(18)

This alternative method is preferred, because it providesa unified calculation of the mean queueing delay, for bothEPONs and WDM-EPONs. Specifically, when C = 1, eq.(17) provides the same results with eq. (5).

The mean queue length Ln,k of the service-class k packetsin the local queue of ONU n is estimated by eq. (7), as in thecase of EPON. Likewise, the mean waiting time of service-class k packets in the local queue of ONU n is determined byeq. (10).

Subsequently, we can use eqs. (11), (12) and (13) todetermine the packet transmission delay, the propagation delayand the average total delay (respectively) of service-class kpackets transmitted from ONU n to OLT, in a WDM-EPON.

V. NUMERICAL RESULTS – EVALUATION

As an application example, we consider a WDM-EPONconsisting of N = 30 ONUs which all are 20 Km far fromthe OLT. Each ONU supports K = 3 service-classes; the 1st

service-class has the highest transmission priority, while the3rd has the lowest transmission priority. In the uplink of thisWDM-EPON, C = 4 wavelengths are used; when only onewavelength is assumed (instead of four), the system reducesto an EPON. In the case of WDM-EPON, the ONUs arecolorless, that is, each ONU employs one tunable transmitter

capable of tuning to any of the four uplink wavelengths(channels); tuning times are negligible.

We evaluate our analysis for the total packet delay (sumof queueing delay, the transmission delay and the propagationdelay) by comparing analytical results with simulation results.Simulation is performed by using the SIMSCRIPT III simu-lation language [20]. The simulation results are obtained asmean values of five runs (replications with a different seednumber). For the mean values, confidence intervals of 95%were determined; however, they are not shown in the figures,since they are small enough.

As it has been aforementioned, a service-class k packet istransmitted within a frame from an ONU to the OLT; thesize of this frame is fixed, 50 time-units (correspond to 50packets); each time-unit c equals 10 µsec. The safety timeinterval between consecutive frames is f = 20µsec, i.e. 2 time-units. The distribution of the frame to service-classes is thesame in each ONU, and corresponds to the priorities amongthe service-classes, as follows: (m1,m2,m3) = (25, 15, 10).The length of each data-packet is 1000 bits. All transmissionchannels (each channel corresponds to a different wavelength)operate at a rate of 1 Gbps. The optical fibres have a reflectionindex of 1.45, therefore the speed of light in a fibre isdetermined c̃ = 2.06 · 108 m/s. As far as the local queuesof the ONUs are concerned, they are of sufficient length, sothat no packet overflow occurs.

A. Delay results in EPON

In Fig. 5, we show the total delay versus the packet arrivalrate. For presentation purposes, the three service-classes havethe same mean packet arrival rate, which is shown in the x-axisof Fig. 5. The 1st service-class has the lowest delay, becauseof its highest transmission priority. In consistency with theirtransmission priorities, the 3rd service-class suffers the highestdelay. This is clear when the packet arrival rate increases inthe x-axis of Fig. 5. The simulation results are very close tothe analytical results.

In Fig. 6, we present the total delay when different distri-butions of the frame size to the service-classes is considered.More precisely, the frame size remains constant to 50 time-

Fig. 5. Analytical and simulation results of the total packet delay vs. packetarrival rate in EPON.

units, as well as the transmission priorities among the service-classes do not alter (the 1st service-class keeps the highesttransmission priority, while the 3rd service-class has the lowestpriority). However, the 50 time-units are distributed to theservice-classes, as it is shown in Table I, where the time-unitsdevoted to the 1st service-classes increase against the time-units devoted to the other two service-classes. In Fig. 6, weobserve that, for the scenario of Table I, as the batch size ofthe 1st service-class increases, the total delay of this service-class slightly reduces, while the total delay of the other twoservice-classes (whose the batch size is reduced) increases.The effect of the frame distribution on the total delay of the3rd service-class is more important, because the batch sizeof the 3rd service-class, as a percentage, has been drasticallyreduced (from 12 to 7, i.e. it became almost the half).

Fig. 6. Analytical results of the total packet delay vs. different distributionpoints of the frame size to the service-classes.

In Fig. 7, we present the total delay versus the number ofONUs. That is, a different EPON configuration is assumed,as far as the supported ONUs are concerned. The meanpacket arrival rate for each service-class is kept constantto 25 packets/sec. Therefore, an increase in the numberof ONUs will increase the offered traffic load and the to-tal delay for each service-class, with transmission priorities(mn,1,mn,2,mn,3) = (25, 15, 10). This anticipation is veri-fied in Fig. 7.

B. Delay results in WDM-EPON

Similar to the EPON case, in Fig. 8, we show the totaldelay versus the packet arrival rate in the WDM-EPON,where the three service-classes have the same mean packetarrival rate, as it shown in the x-axis of Fig. 8. Again, the

TABLE IFRAME DISTRIBUTION POINTS SHOWN IN THE X-AXIS OF FIG. 6.

Point (mn,1,mn,2,mn,3)1 (22, 16, 12)2 (24, 15, 11)3 (26, 14, 10)4 (28, 13, 9)5 (32, 11, 7)

Fig. 7. Total delay versus the number of ONUs.

total delay of all service-classes is in consistency with thetransmission priorities of the service-classes, with the 1st

and the 3rd service-class to have the lowest and the highestdelay, respectively. Clearly, the total delay of the service-classes increases together with the mean packet arrival rate.To compare with the EPON case, it is worth-noticing that, inthis example, the maximum total delay in WDM-EPON (Fig.8) is less than the lower total delay in EPON (Fig. 5). As faras the accuracy of the proposed analysis is concerned, it isevaluated absolutely satisfactory, since the simulation resultsare very close to the analytical results, in Fig. 8.

Fig. 8. Analytical and simulation results of the total packet delay vs. packetarrival rate in WDM-EPON.

In Fig. 9, we examine how the total delay (analytical results)varies according to the number of wavelengths used in theuplink of a WDM-EPON. The mean packet arrival rate is keptconstant to 25 packets/sec. As it was anticipated, because ofthe increase of the transmission bandwidth when the number ofwavelengths increases, the total delay drastically decreases. Tofacilitate the reader, it is worth-mentioning that the total delayresults per service-class of Fig. 9 for one wavelength, coincidewith the corresponding results of Fig. 5 when the arrival rateis 25 packets/sec. Also, when the number of wavelengths is4, the total delay per service-class in Fig. 9 coincide with thecorresponding results of Fig. 8 for arrival rate 25 packets/sec.

Finally, in Fig. 10, we present the total delay per service-

Fig. 9. Analytical results of the total packet delay vs. the number ofwavelengths in WDM-EPON.

class versus the length of the data-packets. As it is shownin this figure, for the packet arrival rate of 20 packets/secthat achieves the relatively lowest total delay in Fig. 8, thelength of the data-packets must be significantly increased (e.g.from 1000 bits to 10,000 bits) in order to cause a remarkableincrease in the total delay per service-class.

Fig. 10. Analytical results of the total packet delay vs. the length of thedata-packets in WDM-EPON.

VI. CONCLUSION

We present an uplink delay performance analysis forboth EPONs and WDM-EPONs, which operate under theMPCP/IPACT fixed service (and under the cooperation ofa DWA in the case of WDM-EPONs). The PON supportsmultiple service-classes with priorities; the latter can readilybe introduced by defining the number of packets per service-class (batches) which can be transmitted within a frame (ineach transmission period). We determine the mean queueingdelay of packet (per service-class), in a unified way for EPONsand WDM-EPONs, in a parametric way, through the formationof two queuing models; an M/D[x]/C model for the packetswaiting in the local queues of the ONUs, and another M/D/Cmodel for the frame transmission to the OLT. The parameterC corresponds to the number of wavelengths in the uplink.From teletraffic point of view, when C = 1, an EPON is

assumed, otherwise a WDM-EPON is considered. Havingdefined the total delay per service-class from an ONU to theOLT, as the sum of the queueing delay, the transmission delayand the propagation delay, we present in figures how it isaffected from several factors; this shows the usefulness ofthe analytical tools. The considered factors which affect thetotal delay are: the packet arrival rate, the distribution of thebatches (number of packets per service-class) in a frame, thenumber of ONUs, the number of wavelengths in the uplinkand the length of the data-packets. The fact that the simulationresults of the total delay per service-class are pretty close tothe corresponding analytical results verifies our analysis underthe assumption of Poisson arrivals; the calculation accuracy isabsolutely satisfactory. As far as the anticipated superiorityof WDM-EPONs against EPONs is concerned, in respectof the delay performance, it is evident when comparing theresults. Moreover, the proposed analysis is proved consistentto parameter C, since the delay analysis of WDM-EPONs forC = 1 leads to the same results with the delay analysis ofEPONs, as it was expected. As a future work, packet arrivalprocesses other than Poisson can be considered in the queueingsystem of the ONUs. For example, as a first subsequent step,one may consider a Batch Poisson Arrival Process, the packetarrival process from the local queues to the frame, whilethe packet arrival process to the local queues may remain aPoisson process (Fig. 3).

ACKNOWLEDGMENTThe authors are grateful to the student Ms Antonia Kokiou

(ECE, University of Patras, Greece) who has carried out herDiploma Thesis on this subject, and has supported this work.

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