Analytical Model With Single Olt

Published Date: 02 Nov 2017

4.1 Introduction

The two major types are Ethernet PON (EPON) and Gigabit passive optical network (GPON) . PON with these different standards is called xPON. To have an efficient performance for the two standards of PON, EPON and GPON, some important issues will consider. In our work we will integrate a network with different queuing models such M/M/1 and M/M/m model. After analyzing IPACT as a DBA scheme for this integrated network, we modulate cycle time, traffic load, throughput, utilization and overall delay mathematically for single OLT and multi-OLT EPON system, and average delay and throughput for single OLT GPON system. A comparison of average delay and throughput between EPON and GPON is introduced with the same number of ONUs. Also link utilization and number of OLT ports (PON) had been studied and evaluated as a function of cycle time. Cost optimization was done through evaluation the total cost of PON system and who it affected with the number of ONUs (i.e splitting ratio), as well as cost ratio between EPON and GPON is

4.2 ANALYTICAL MODEL WITH SINGLE OLT

Traffic load ,cycle time, average delay, throughput and utilization of EPON, then average delay and throughput of both upstream and downstream GPON will be analyze with single OLT PON system.

A. EPON

To analyze traffic load we denote C as the upstream transmission speed (in bit/sec) of the EPON. The N ONU are d km distance from the OLT. The ONUs offer a fixed traffic load over time ρi , i =1, . . . , N. Furthermore, the ith ONU receives traffic from its users following a Poisson process with rate λi packets/sec. Also, each packet requires a fixed amount of service time [10]. Let X is the service time, [X] = computed as:

E[X] = . secs (2)

B refers to the packet size and C denotes the line rate. For B =1518 bytes and C = 1 Gbps, the service time required is E[X] =12.14μs per packet. Hence, the ith ONU offers ρi , i = 1, . . . , N traffic load as:

ρi = (3)

Total offered load ρT , that is, the sum of all individual traffic loads ρi must be smaller than unity [10]:

ρT = <1

L is the expected value of N and

(4) for M/M/1 model

Sub (1) in (2) we will get:

ρi = λi . (5)

Sub (4) in (3) to get:

L = (6)

Cycle length is measured as the time elapsed between two GATE messages sent to the same ONU. The longer the cycle, the longer stations have to wait for their turn and the longer packets have to be buffered. On average, if the order in which ONUs transmit their data is random, the waiting time is equal to half of the cycle length. The length of the polling cycle is adaptive and the minimum and maximum length of the cycle are not dependent on the bandwidth allocation algorithm deployed in the network. The functionality of this approach is briefly outlined by the following steps:

1. The total number of bytes Qtotal in all queues is calculated based on latest reports received.

2. The cycle time Ï„ is calculated from (7) where CL is the link rate.

Ï„(n) = (7)

3. It must be ensured that time τ(n) satisfy that τmin ≤ τ(n) ≤ τmax where τmin and τmax are the minimum and maximum length of the cycle. The minimum cycle time must be such that enough time is provided to process all REPORT messages that arrived during the last polling cycle and that GATE messages have enough time to arrive at all ONUs [12].

Let N be the number of ONUs that share the same channel with rate C bits per second and let all ONUs send packets of length B. The times between packets arrival to the same ONU are independent of each other and have exponential distribution with mean λ in packets per second. Hence, they create a Poisson process. To simplify the analysis let assume that the length of a single transmission window is equal to the length of the packet. The 1 Gbits/s bandwidth has to be shared amongst the N ONUs. This would mean that, if all ONUs have the same service level agreement, in a first approximation the bandwidth per ONU is equal to 1/N Gbits/s. However, one must take several sources of overhead into consideration, that cause the available bandwidth to be lower: the guard time Tguard, the time consumed by REPORT messages, and the Ethernet overhead [3]. Thus, in any cycle an ONU can send only one packet. Based on this assumption, the length of the cycle is calculated as follow:

Tcycle = N. + N . Tguad (8)

Where B is the packet size (in bits), and CL is the bit rate (1Gbps). From analysis of the TDMA scheme it can be noted that there are four main factors contributing to the total delay of a packet in the system:

The packet transmission time, which is equal to

The waiting delay, which is the time that ONU spends waiting for its turn to send data. On average the waiting delay is equal to .

The queuing delay equal to the time a packet spends in a buffer.

To calculate the queuing delay the model of the TDMA network was considered where every ONU was modeled as an independent and separate M/D/1 queue where λ is the mean arrival rate. The average queueing delay in the TDMA system is given by (8) [9]:

W = .X (9)

Where x is average service time, it can be calculated as :

X = (10)

Round-Trip Time (RTT) which is equal to , where d is the distance from the OLT (10km) and S is the speed at which signals travel on the transmission medium ( approx.= 2×105 km/s). RTT is equal to 100µs. The average delay in the system can be presented as a sum of the transmission, waiting and queuing delay and RTT and can be calculated as follow:

T =+( N.+ N. Tguard) + (11)

Throughput denotes the output rate in bit per seconds, and is computed simply by using:

(12)

Where W is the waiting window and T is the average delay.

Let T is timeslot size and R is a random variable representing unused remainder, then the maximum utilization achieved by an ONU is [12]

U= (13)

B- GPON

Let 𝛿 denote the frame duration of 125 𝜇s of the GPON. A packet generated at an ONU has to wait on average 𝛿/2 for the beginning of the next frame. This next frame has a duration (transmission delay) of 𝛿 and takes RTT to propagate to the OLT. Then, the packet is put into a general queue for the upstream channel. In terms of the mean packet delay, this channel can be modeled as an M/G/1 queue with corresponding delay ( finally, the packet experiences the transmission delay and propagation delay RTT.

Over all, the mean delay for the TDM upstream channel is[13]

𝐷 = 5 + ( . ) + + 3RTT (14)

The TDM downstream channel is analyzed analogously giving:

𝐷 = + ( + + RTT (15)

4.3 Analytical Model With Multi-OLT PON

In this section we introduce an access optical network architecture consisting of two OLTs as a m/m/m model, and N ONUs as a single PON network with a tree topology as shown in Figure 4.1.

Splitter

ONU1

OLT1

OLT2

ONU2

ر

ر

ر

ONU6000

Figure 4.1 Al-Gehad Multi-OLT PON

OLT1 is used to support FTTH and OLT2 is used to support FTTc. All transmissions in the proposed multi-OLT PON are performed between two OLTs in the root side and 6000 ONUs in the leaf side of the tree topology. In downstream transmission, the two OLTs will use the same polling table to start a transmission of the grant messages to all ONUs through the optical splitter and only the concern ONU will receive the packet according to its destination address. Upstream traffic uses TDMA, under control on the OLT located at the CO, which assigns variable time length slots to each ONU for synchronized transmission of its data bursts. In the multi-OLT PON, no guard time is required, because data of every two successive ONUs will be received by two different OLTs. So there is no possibility of data overlapping due to fluctuation of laser on/off timing and RTT. After receiving data from a particular ONU. every OLT gets enough time before receiving data from the next ONU. This way, packet delay of the network and computational complexity of OLTs can be decreased while bandwidth utilization will be increased [14].

The following formula represents the cycle time for the multi-OLT PON system

Tcycle = (16)

Where N is the number of ONU, B is the packet size, and CT is the link capacity. The average delay is

T = + + (17)

Transmission time and propagation delay of the data depend on the data transmission speed of the PON and physical distance between OLTs and ONUs. Usually this distance not equal but the data transmission speed is a constant for TDMA PON.

4.4 Link Utilization and Cost Analysis in GPON Access Networks

A gigabit passive optical network (GPONs) provide enormous capacity that can support next-generation applications and services such as IP high-definition television (HDTV), Video-on Demand (VoD), Voice-over-IP (VoIP) and High-Speed-Internet (HIS) services [1]. If more demanding services are requested, the fewer basic services can be supported on a GPON link and the lower the quality in provisioned streaming services subscribers are likely to experience since optical network units (ONUs) share PON link capacity (OLT port). A significant reduction in the bandwidth of a GPOL link causes an increase in latency and poor network applications performance at end-subscribers [2]. This requires planning for services that will be supported on each passive optical network (optical link terminal (OLT) port) to ensure that upstream and downstream traffic does not exceed PON link data rate. When the offered traffic load exceeds by a large factor the upstream or downstream capacity of the PON link, subscribers experience performance degradation in the offered services. From this, the need to resource dimensioning procedure is arises based on a performance metric like average traffic flow throughput, link utilization and OLT ports.

A dimensioning process aims to ensure that a GPON access network has sufficient resources to support current and novel services. Thus, the number of subscribers requesting each service that will be supported on the PON access link, average traffic data rates and concurrent usage of offered services must be known. This information will help to determine the average traffic data rate per ONU and PON (OLT port). Also an optical split ratio which can support generated traffic must be determined carefully. Based on the selected split ratio, the number of PONs and OLTs required to serve a whole region can be chosen as well as the number of splitter and OLT ports that should be left unused to cope with traffic growing rate.

Each port of the OLT should be guarantee current and future subscribers’ requirements in terms of QoS and offering service cost. Minimizing the cost of offering service implies finding the optimal allocation of GPON resources required

to accommodate traffic connections under current and future bandwidth requirements. A higher split ratio can increase GPON link utilization (OLT port) by sharing an OLT port (PON) among many drop points (ONUs/ONTs).

A tree topology of a GPON access network is shown in Figure 4.2, in which the root link connecting an OLT port with a splitter that shares the capacity of the root link, denoted by CFeeder, among a number of leaf links with Cdistribution capacity.

OLT

1:64 1:32 Residential 23 house

ONU Splitter unused ports (1)

ONU 1:2 1:32 (2)

ONU 1:2 1:32

ONU 1:32 Unused ports

Unused OLT ports

(PONs)

Figure 4. 2 Dimensioning GPON resources

Figure 4.2 illustrates different scenarios for OLT capacity. Scenario (1) shows that the selecting splitting ratio is 1:64 to allocate bandwidth for residential subscribers. Scenario (2) shows that tow splitters are used each with 1:32 splitting ratio to allocate bandwidth for 64 subscribers locating in different residential buildings. Any other splitting ratio can be selected but data signal transmission is affected at each splitting level [3]. The number of ports of both splitters and OLTs left unused can be deployed to support more subscribers or unpredicted traffic growth. Therefore, the challenging problem in dimensioning GPON resources is the allocation of resources which can meet the QoS of current and future traffic demands, while optimizing the cost of installing, configuring and upgrading GPON resources.

4.4.1 EPON and GPON Measures

The target is to compare the network cost of an EPON and GPON system based on the utilization of the optical link's transport capacity. The utilization affects directly the segmentation need in an optical network and this affect on the total network cost [4].

4.4.1.1 Utilization

Equation (1) calculates link utilization (Ï…Ed) of an EPON downstream channel.

Ï…Ed = (18)

Where is the EPON frame payload, the EPON frame overhead, it is taken to be 42 bytes, the bit rate of an EPON link, it is equal to 1.25Gbps, the ONUs number in the network segment which is taken 10000, the length of control message, it is equal to 88 bytes, and the cycle time.

Utilization (Ï…EU) of an EPON is given by equation (2)

Ï…Eu = (19)

Where is the physical layer overhead (i.e. guard band), it is taken 1.44µsec.

Utilization (Ï…Gd) of an GPON downstream is given by equation (20)

Ï…Gd = (20)

Where is the GEM framing overhead for Ethernet payload which is equal 30 bytes, is Ethernet payload, is GPON duration of downstream frame, its equal 125µsec, the GPON bit rate (1.25Gbps), (27 bytes) is the GPON downstream frame overhead, and (27 bytes)is the upstream allocation overhead.

Utilization (Ï…Gu) of an GPON upstream is given by equation (21)

Ï…Gu= (21)

Where is the length of physical layer overhead (include PLOAMu field) it taken 15 bytes, and is the average number of DBRu fields in an upstream GPON frame. Since an ONU can send several GEM frames during its time slot and only the first of them carries the PLOu field and all frames carry the DBRu field, is approximated by

= (22)

Where = +

Network Segmentation

At building a passive optical network , segmentation is the way to guarantee fair transport capacity per subscriber as shown in Figure 4.3.

Figure 4.3 Segmented PON layout [4]

A number of needed network segments is determined according to the total transport capacity and number of subscribers. For both EPON and GPON systems, assume that the total transport capacity of segment Segk is Ck, line coding efficiency is σ and utilization of the transport channel capacity is υ, so Bk the total bit rate available for user in segment Segk is:

Bk = σ υ Ck (23)

The total available bit rate for the segment Segk is the sum of the traffic of all ONUs connected to it as below:

Bk b k,I (24)

Where Mk represents the number of ONUs connected to the ith port of the OLT. Then the aggregate bit rate BT of all K OLT port (PONs) can be expressed as follows:

BT = (25)

The number of subscribers served by Segk is Nk, which is the sum of subscribers (nj) served by all ONUs in this segment, i.e.

Nk = (26)

Then the total number NT of subscribers connected to all the K segments is

NT = (27)

If we assume that each end-subscriber should have a minimum transport capacity of bo , then segment Segk can support up to

mk = (28)

Where m is the number of users, and is the average bandwidth required to support all requested services on one or all OLT ports. Then an OLT consisting of K ports (PONs) can support up to mT simultaneous subscribers, such as

mT = (29)

Assuming that all segments (PONs) offer the same transport capacity B. Denote the size of population by N and the broadband access (take rate) by Ω (0˂Ω˂1), and the percentage of active subscribers (β) that are operate during a busy hour is known, then the total bit rate available on all K ports (PONs) should be greater than or equal to the total requested bandwidth by all subscribers connected to these PONs, from (6) and from the above assumptions we can get:

BT = K σ υ C = Ω β N (30)

Thus, the number of required segments (OLT ports) will be:

K = (31)

The number of PONs determines the number of OLTs required serving a whole region. This enables network planners to know the cost required for installing, configuring and upgrading GPON resources. Each PON can serve up to ΩN/K subscribers, which can be expressed as follows:

Number of subscribers = = (32)

This formula indicates that the number of subscribers supported on a single OLT port (PON) depends mainly on ro and β.

4.4.1.2 Relative Network Cost

The number of network segments is the most important factor when calculating the cost of an EPON and GPON network. The number of segments indicates the difference between an EPON and GPON networks in the amount of installing fiber and the number of the needed transceivers in the network.

By using equation (31), the number of required segments can be calculated. This equation includes several parameters, and by varying one parameter at a time and keeping the others constant, we can notice how K will be a function of the selected parameter. By dividing the number of an EPON segments (KE) by the number of GPON segments (KG) we can get the relative cost (Ϙ) between the two networks, such as Ϙ = KE / KG.

Setting the parameters (β, Ω, N, and equal in both approaches,(i.e. EPON and GPON), the network cost can be obtain. Inserting the EPON and GPON parameters into (14) and solve for Ϙ we will get:

Ϙ = (33)

From equation above we can say that the relative network cost of an EPON and GPON depends on the total bit rate available for subscribers in the network segments [4].

4.4.1.3 GPON Capacity and Cost Optimization

Optimization approach aims to optimally allocate the capacity on GPON access network links, which can support current and future traffic demands, while guaranteeing a minimum throughput required for all class j traffic, ρjmin . This approach is expressed in an optimization problem as follows:

cost minimization of the capacity of the links in the GPON access network. Where cost per bit with each link l in the GPON access network, and Cl is the link capacity.

min Cl

Capacity constraints of these links, where the total traffic load generated by all flows sharing a link should be less than its capacity, Cl : l = Cl.

Subject to < Cl ,

Throughput performance constraint in a GPON access network, where the throughput of each class j traffic should be greater than the minimum required throughput of this class. Where denotes the set of flows that share link l.

, j = 1,2,…., Z

The throughput constraint can be expressed with respect to the average delay of generated traffic flows as follows: follows ρj = , where represent the volume of traffic flows.

Thus, the throughput performance can be written as follows:

E[Tj] ≤ , j=1, 2,…. , N (34)

Where ρj .

After some algebraic manipulations, the optimal capacities of both GPON feeder link and distribution links can be given by [5]:

Cfeeder = N ℱ + ρmin [ 1+ ] (35)

Cdistribution = ℱ + ρmin [ 1+ ] (36)

Where N is the number of ONUs, Cfeeder is the feeder link capacity and Cdistribution is the distribution links capacity. If we consider that the cost of transmitting traffic on feeder link is the same as that on a GPON distribution links, then , and for simplicity take . Then, as N ℱ , the optimal capacity of the GPON feeder link and distribution links respectively will be:

Cfeeder = N ℱ + ρmin (37)

Cdistribution = ℱ + ρmin (38)

So, the optimal total cost will be

Cfeeder + N Cdistribution = 2Nℱ + (N+1) ρmin (39)

4.5 Numerical Results

The results and discussions included the comparison of cycle time (Tcycle), average delay, throughput and utilization of EPON network in case of single OLT and multi-OLT system. Figure (4.4) shows that cycle time is increased as the number of ONUs increased in both cases single OLT system and multi-OLT system, but cycle time in multi-OLT system is shorter than cycle time in single OLT system with about 55. We can say the same observation on Figure (4.5). The average delay of multi-OLT system is shorter about 200 sec than the average delay of single OLT system. This is presents a better DBA utilization in the terms of cycle time and average delay, since the multi-OLT PON system can avoid the problem of delay due to the guard time.

Figure 4.4 EPON Cycle time

Figure 4.5 EPON Average delay

Figure 4.6 EPON Throughput

Figure 4.7 EPON Utilization

For the first part of the graph in Figure (4.6) the average delay increases very slowly; this is the domain determined by the ONU’s traffic and by the traffic of the ONUs that are polled right before that ONU. In this domain, the average delay is still very close to its minimum value. For higher traffic loads, the aggregate traffic load becomes the determining factor and the packet delay increases quickly. Again the average delay of multi-OLT system is less than the average delay of single OLT system. Utilization as a function of timeslot size is calculated (according to Equation 13) and its behaves as the plot in Figure (4.7). Obviously, increasing the timeslot size should result in increased utilization. Where the range for packet sizes is A ≤ size ≤B. In Ethernet A = 64 bytes, B = 1518 bytes. We assume that we always have packets waiting, i.e., load is heavy. Figure (4.8) compares the GPON mean delay (D) on the downstream and upstream TDM channels. The delay of upstream channel is higher than the delay of downstream channel because upstream transmissions are delayed by downstream transmissions . In downstream the link capacity is 2.25Gbps and 1.25Gbps in upstream, packet size is 1518 byte [13] and the ONU located at 20 km from the OLT. The difference in delay of both cases with the same number of ONUs is about 400sec.

Figure 4.8 GPON downstream and upstream delay

Figure 4.9 GPON throughput

Throughput in the GPON downstream channel with shorter delay than in the GPON upstream channel also with about 400sec, and they are behave in the same way as shown in the Figure (4.9). In EPON average delay increases linearly and sharply as the number of ONUs increase, while in GPON the increasing happened gradually and in small amount as clear in Figure (4.10). From this result we can deduce that GPON could serve a larger number of ONUs than those can be served by EPON without affecting very much on the average delay. Therefor Al-Gehad FTTH network was constructing as a GPON system not as an EPON system.

Figure 4.10 EPON-GPON delay

Figure (4.11) shows the throughput of EPON and GPON with the same number of ONUs. They are both in the minimum delay with the light traffic, but delay increases with the heavy traffic but still GPON throughput in its both cases downstream and upstream is higher than EPON throughput.

Figure 4.11 EPON AND GPON Throughput

4.6 Conclusions

We have introduce an analysis of the cycle time, queuing analysis of mean delay, throughput and utilization in an single OLT PON in an Ethernet passive optical network (EPON) and Gigabit passive optical network (GPON). Also a multi-OLT PON is proposed for FTTH and FTTc. From the results it found that the cycle time is reduced about 40-50µces as well as the average delay due to the avoidance of guard time. A multi-OLT PON can accommodate 10% more traffic load than the single OLT PON, this is because the load is distributed among more ONUs resulting shorter cycles and smaller grants and thus less queuing at the ONUs. Also, mean delay and throughput in GPON are investigated in downstream and upstream channels. A comparison between EPON and GPON in terms of mean delay and throughput had been illustrated. EPON achieves significantly lower delays than GPON at small to medium traffic load. This EPON advantage is due to its underlying variable-length polling cycle compared to the fixed length framing structure of the GPON. But GPON can serve very larger number of ONUs could be 128 ONUs, than EPON do, may be only 16 ONUs without very much delay increasing.

Now the target is to find the network cost of an EPON and GPON system based on the utilization of the optical link's transport capacity. In both PON concepts, the utilization of the transport channel capacity depends on the cycle time and payload size.

The locations of ONUs should be carefully chosen from the OLT (central office (CO)), as a shorter time slot could degrade the utilization of GPON transport channel capacity, even though a short time slot can offer a short access delay[5].

Figure (4.12) illustrate the utilization as a function of the cycle time in two cases when the payload size is 46 bytes and 1500 bytes in two cases single and multi-OLT EPON and single OLT GPON systems. This Figure shows that utilization is proportional with cycle time (i.e. short cycle time means less link utilization), with short access. Downstream direction achieves better utilization than the upstream does, but when cycle time increases the difference will be very little. Lower utilization obtained with multi-OLT EPON network, this is because the increasing number of ONUs since the total bandwidth must be divided among larger number of ONUs.

Figure 4.12 EPON and GPON link utilization Vs. cycle time

From equation (14) we evaluate number of PONs in the term of take rate with both payload values 46 and 1500 bytes and increases from 10 to 32Mbps , for single OLT and multi-OLT EPON and single OLT GPON systems only for upstream channel because the difference between upstream and downstream channel is negligible. The cycle time is 2ms, the transport capacity of the end user is 10Mbps and β was taken to be 20%. Figure (4.12) shows that the number of PONs grows linearly with take rate. For the same type of traffic, GPON needs fewer segments than EPON. Multi-OLT EPON network requires larger number of segments (PONs) than single OLT xPON to assure services required to the larger number of subscribers.

The analysis showed that a GPON system uses the link capacity more efficiently than an EPON system. This means that an EPON system require to implement a higher number of network segments than a GPON system in order to serve the same number of subscribers.

Figure 4.13 Number of PONs Vs. take rate

Figure 4.13 illustrate the relationship between cycle time and cost ratio (Ϙ) for 46 and 1500 bytes payload. For small payload size and short cycle time, cast ratio is higher, this refers to that GPON fits better for low volume and small delay traffic for example voice over IP (VoIP) and PSTN. For this type of traffic and in upstream direction, Ϙ is about 1.7.

Figure 4.14 EPON-to-GPON cost Ratio

When comparing the two systems, we find that the total number of subscribers does not affect the relative cost ratio between EPON and GPON as in Figure 4.14. Relative cost affected only by the utilization of the link capacity. The physical cost of constructing an EPON or GPON network segments is the same, so the relative cost reflects the cost of an EPON and GPON transceivers.

Figure 4.15 GPON Feeder Link Capacity Vs. Number of ONUs

Figure 4.15 shows the relationship between the capacity of the GPON link, CFeeder/ N, and the number of ONUs (N) for different amount of minimum throughput, ρmin . Subscribers are allocated less bandwidth as number of ONU increases. This is due that the capacity of GPON link is dimensioned such that Cfeeder equals the worst- case load (Mℱ). The optimum value of Cfeeder converges around the total capacity required for accommodating general traffic load in addition to ρmin .

Figure 4.16 GPON Distribution Link Capacity Vs. Number of ONUs

Figure 4.16 shows the optimal distribution link capacity required to guarantee different requirements of throughput, ρmin . Each ONU can support different applications therefor distribution links should have sufficient bandwidth such that the remaining capacity on distribution links, can guarantee the minimum throughput.

Figure 4.17 Total Cost of GPON Resources Vs. Number of ONUs

Figure 4.17 illustrate the optimal total cost of GPON access network for different throughput requirements. The total cost converge in a slower manner for a high minimum requirements, then when ρmin is taken to be smaller value.

Conclusion

A study of link utilization of channel capacity in both EPON and GPON has been done and uses that information to compare the cost of these two systems. From the numerical results we can say that the GPON system uses the link capacity more efficient than EPON system does. The cost to build an EPON or GPON system is almost the same, the relative cost affected widely by the cost of transceivers. For example, for VoIP service, the GPON transceiver about 70% most expensive than EPON transceivers [4].

GPON network planners should take into their considerations the number of demanding and basic services that will be supported on each PON (OLT port) to achieve traffic balancing among all PONs. Link utilization can be used to calculate the number of subscribers that can be supported on a single PON and then can determine the size of population and services that can be supported on OLT ports. An optimization problem has been formulated to find the optimal capacity and cost of GPON access network links guarantee that a minimum throughput can be ensured for supported traffic classes.

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