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Characterization and performance study of IP traffic in WDM networks
Computer Communications 24 (2001) 1702±1713
www.elsevier.com/locate/comcom
Characterization and performance study of IP traf®c in WDM networks Liren Zhang*, Junhua Tang School of EEE, Nanyang Technological University, Nanyang, Singapore 639798, Singapore Received 3 May 2001; accepted 3 May 2001
Abstract This paper investigates the characteristics of network performance, when IP traf®c is directly mapped into WDM networks using multiprotocol label switching (MPLS) techniques. The performance analysis focuses on the burstiness of IP traf®c that may have a remarkable effect on the network performance. On the other hand, the inter-channel interferences caused by ®ber nonlinear effect such as four wave mixing are also considered in the performance analysis. The statistics of network performance in terms of packet error probability, packet error free-run distribution and packet error-pattern distribution are presented. These illustrative results provide valuable information to the network designers. q 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The combination of the Internet protocol (IP) and the wavelength division multiplexing (WDM) technology has attracted much attention in the research and manufacturing community as a promising strategy for the next generation Internet. The development of WDM technology has yielded the bandwidth of more than 1 Tbps on a single ®ber that makes it feasible to support data, voice and other multimedia applications over the Internet [1±7]. The typical protocol currently used to support IP over WDM networks uses SDH/SONET as the physical layer which is based on time division multiple access (TDMA) and the ATM or frame relay on the top of SDH/SONET to provide integrated services. However, since this `full-stack' approach reduces the network ef®ciency and poses the increased management/operation costs, it is clear that a single ubiquitous mechanism for IP-WDM incorporation is desirable for the future long-term development. A good example in this trend is the appearance of multi-protocol lambda switching proposed by Internet Engineering Task Force (IETF) [8,9]. The multi-protocol lambda switching describes an approach to map the IP traf®c directly to WDM channels using multi-protocol label switching (MPLS) as the control plane for both IP routers and optical cross-connects (OXCs). Optical channels are dynamically provisioned by IP-routers and OXCs coordinately through MPLS. IP traf®c are labeled and transported on light paths irrespective of the protocol and coding used in each channel. * Corresponding author. Tel.: 165-7904508; fax: 165-7920415. E-mail address: [email protected] (L. Zhang).
Hence, this allows the use of uniform semantics for network management and operations control in hybrid networks consisting of OXCs and label switching routers (LSRs), and paves the way for the eventual incorporation of WDM multiplexing capabilities in IP routers [9±13]. As a result, the MPLS has been generally accepted as a straightforward approach to combine IP and WDM technology using existing standards and experiences. In addition to the de®nition of a simpli®ed protocol for IP-WDM integration, the further studies on the effect of bursty IP traf®c on the performance of such networks are necessary. In the future WDM networks, there more than one hundred optical channels may be packed into a single strand of ®ber. In this case, the ®ber nonlinear effect causes interference among signals carried in different channels which in turn leads to cross talk degradation of the signal channel. Of all the ®ber nonlinear effects, four-wave mixing (FWM) is one of the most signi®cant factors in the WDM network which generates various combinations of different channel frequencies and makes it dif®cult to detect the useful signal [14±17]. Although this effect is not obvious and is usually neglected in the WDM network with small number of optical channels, however, it may become significant in the WDM network with large number of optical channels, especially when the WDM network is directly loaded with bursty IP traf®c. 2. Network architecture for IP over WDM using MPLS In the traditional implementation of IP over WDM, IP traf®c is encapsulated in SDH/SONET frames by allocating
0140-3664/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0140-366 4(01)00355-3
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 1. IP paths in a label switching optical network.
the ®xed time slots to its payload in TDMA manner. Clock recovery in such a network is extremely important. Therefore, it is unlikely to directly transmit bursts of packets over the SDH/SONET link, and instead of sending dummy packets during silent period to keep a constant traf®c ¯ow. The switching of packets has to be done at electronic level. Therefore, the effect of IP traf®c on the performance of WDM network is signi®cantly reduced but the utilization of optical ®ber is also signi®cantly limited. By contrast, when IP is mapped directly into optical channels using MPLS, the switching is done at optical wavelength domain, in such a way, the bursty nature of IP traf®c is re¯ected on the optical channels, which in turn poses in¯uence on the non-linear inter-channel interference among channels. As a result, the characteristics of the light channel are correlated with the statistics of the IP traf®c. On the other hand, the characteristics of the optical channel determine the QoS of the IP traf®c when it is transported through the optical network. Therefore, in the era of IP and WDM integration, it has become increasingly important to understand the interaction of IP traf®c nature and WDM channel performance. However, there has been little work in this ®eld in the literature so far. As shown in Fig. 1, the edge nodes are label switching routers with WDM capabilities. The ingress edge node performs packet-by-packet routing, label assignment and framing electronically, and then forwards the traf®c ¯ow into the appropriate output port with the assigned output optical wavelength. The MPLS traf®c engineering control
plane is responsible for path selection and path management. Since light-paths are con®gured in the OXCs in the core optical networks as part of label switched paths (LSPs), signaling protocol such as RSVP or label distributing protocol (LDP) is used to exchange link states between access router and OXCs. Meanwhile, constraint-based routing is used to compute paths that satisfy certain speci®cations subject to certain constraints. The egress edge node extracts electronic signals from the optical interface and recovers IP packets from data link frames and forwards them to the appropriate destination network. Fig. 2 shows the reference model of an edge LSR. IP packets are routed and assigned with a label of Label Switched Path, which may consist of shortcut path bypassing intermediate layer-3 routing hops between LSRs and optical channels provided by optical transport networks. Traf®c of one or more LSPs is encapsulated and may be aggregated before put to selected optical channel wavelength. An OXC, however, does not check the content of the LSP, but switches channels on a prede®ned manner con®gured by control and management information. Each LSR or OXC consists of a connection table, called Label Information Base (LIB), which contains Forwarding Equivalence Class /label bindings and associated port, wavelength and media encapsulation information. Therefore, it can be mapped into a single label by an LSR [8]. In an OXC, a local adaptation layer may be designed to map this information to switch controller. Packet encapsulation for IP over WDM using MPLS is
Fig. 2. Reference model of a TC-LSR.
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Fig. 3. Encapsulation of IP packets over WDM.
shown in Fig. 3. The label switched paths can be mapped to optical channels provided by WDM elements. Currently the most common form of WDM element is programmable and re-con®gurable optical cross-connect that supports wavelength conversion/translation. This circuit switching nature of WDM element makes PPP (point to point protocol) suitable for encapsulation of IP over WDM [9,13]. Each label switched path is supported by a PPP link. The multiple protocol label switching control protocol is responsible for enabling and disabling the use of label switching on the PPP link When an IP packet arrives, a label of short ®xed-length contiguous value used to identify the IP stream is appended into its head. Then, HDLC header and trailer are added to the PPP frame to guarantee link layer data transmission. This proposed architecture has the following features. (1) Simpli®ed protocol stack, in which the ATM and SONET layer is replaced by PPP/HDLC encapsulation to guarantee layer 2 data transmission. (2) Reduction of conventional IP routing. This is done by the introduction of MPLS, which performs IP routing only at the edge nodes and uses shortcut paths (in layer 2) to deliver IP packets in the intermediate components. (3) IP ¯ow aggregation is easily achieved. Packets of one or more ¯ows (source-destination pair) that demand the same treat can be put together to form a stream and
Fig. 4. The optical frequency arrangement of four-wave mixing, fFWM fi 1 fj 2 fk.
be mapped to a single label. So even though the elementary capacity block in a WDM network is a single light path, it can be ¯exibly shared by packet ¯ows. This can be accomplished by the coordination of Label Switching Routers running Label Distribution Protocol (LDP). (4) A circuit switched wavelength route for each label switched path is provided by WDM based optical network, and the optical switch con®guration and wavelength arrangement are done in accordance with LDP. (5) Differentiated services can be readily supported in this architecture. Different label switched paths can be used to server users with different levels of QoS requirements. 3. Performance analysis of IP traf®c over WDM networks Although the architecture for IP packets over WDM has not been ®nalized yet, the trend of mapping IP traf®c directly into light path without other multiplexing scheme is clear in constructing IP backbones over WDM. This has led to the fact that the light paths will most probably be loaded with bursty IP traf®c in the network. Though sometimes the optical channels in the WDM system are considered to be totally independent of each other, it is not true especially when the ®ber input light power is high and the frequency spacing between wavelengths is narrow. In such case, some nonlinear characteristics may cause serious interference. One of these signi®cant effects is Four Wave Mixing (FWM) [14±17]. Fig. 4 schematically illustrates the optical frequency arrangement, where fi, fj, and fk are the signal light frequencies, and fFWM is the four-wave mixing light wave frequency satisfying fFWM i 1 fj 2 fk. We notice that only the effects of FWM and ASE with Gaussian approximation are taken into account in the following analysis.
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 5. Markov modulated ON-OFF process.
The output power PFWM of the four-wave mixing product is given by [14,15] PFWM fi ; fj ; fk
1024p6 2 2 Pi Pj Pk 2aL 1 2 e2aL 2 d x e h n4 l2 c2 A2eff a2 1
where Pi, Pj and Pk represent the input power of the frequencies fi, fj and fk respectively; PFWM is the power of the lightwave from four-wave mixing at the frequency fFWM; n is the ®ber refractive index; lis the wavelength; Aeff is the effective mode area of the ®ber; a is the ®ber loss coef®cients; L is ®ber length; d is the degeneracy factor(d 3 for i j, d 6 for i ± j), and xis the third-order nonlinear susceptibility. h (fi, fj, fk) is the mixing ef®ciency given by [14,15]: ( ) a2 4e2aL sin2 DbL=2 2 h 2 11 a 1 Db2 1 2 e2aL 2 where Db represents the phase mismatch and may be expressed in terms of signal frequency differences [14,15]: 2pl2 u fi 2 fk uu fj Db c ! ( ) dD l2 u fi 2 fk u 1 u fj 2 fk u ; 2 fk u´ D 1 d l 2c
3
where D is the ®ber chromatic dispersion. Eqs. (2) and (3) show that the four-wave mixing ef®ciency decreases with increasing signal frequency difference and chromatic dispersion due to increased phase mismatch between the signals. In WDM system, spacing between the wavelengths may be uniformly distributed ranging from a few gigahertz to 100 GHz [14]. In such systems, at any particular channel frequency, there will be a number of FWM waves generated from various combinations of interacting signals whose frequencies satisfy: fFWM fi 1 fj 2 fk . The total power generated at frequency fm may be expressed as a summation X XX Ptot fm PFWM fi ; fj ; fk 4 fk fi 1 fj 2 fm
fj
fi
FWM light is coherently detected at the receiver together with the signal light, and induces the interference noise. The FWM noise power NFWM is written as [17]: NFWM 2b2 Ps
PFWM ; 8
5
where Ps is the signal light power at the receiver and b is the quantum ef®ciency. In the case where the input light power to the ®ber is P0 and the ®ber length is L, and ®ber loss coef®cients is a, Ps P0 ´e2aL . The SNR can be expressed as [17]: bPs p Q p Nth 1 Nsh 1 NFWM 1 Nth
6
Since both the thermal noise Nth and shot noise Nsh are negligible, NFWM is usually the dominant factor of the denominator, so Eq. (6) can be written as: p p bPs 2bPs 2 Ps 2 P0 e2aL Q p p p p PFWM NFWM PFWM b2 Ps PFWM
7
If Gaussian approximation is used to describe the noise caused by FWM interference, the bit error probability pe for an intensity-modulated on±off keying signal is written as [17]: ! 1 Z1 t2 pe p dt 8 exp 2 2 2p Q Therefore, in WDM system, the nonlinear interaction among these channel lights may generate interference light to a signal channel, and cause degradation of signal to increase the bit error probability. Since the power of the interference light is proportional to the input light power and inverse proportional to the frequency spacing, we should note that when the input power is low enough and the frequency spacing is large enough, the effect of FWM is almost negligible. In present WDM systems where the input power is generally much less than 0 dBm, engineers often neglect this factor. But with the rapid development of optical component for all-optical networks, especially for a wide area WDM with the wide use of Erbium Doped Fiber
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Fig. 6. Bursts of IP traf®c.
ampli®er, the input light power to the ®ber can reach 10 dBm or even higher. In such case, the interference of FWM may impose a major limitation to the number of channels or the size of the WDM network. In this paper, IP packet stream generated by each user source is modeled as an ON±OFF process [18,19], in which the alternative state transition between the ON state and the OFF state is shown in Fig. 5, where the parameter a is the rate of transition from the OFF state to the ON state and the parameter b is the rate of transition from the ON state to the OFF state. The probability that the process is in the ON state is a /(a 1 b ). The packet is negative exponentially distributed in length. When K of such ON±OFF packet streams are multiplexed, the resultant stream can be represented by an (K 1 1)-state Markov modulated process as shown in Fig. 5, where state i represents that i (i 0, 1, 2, ¼, K) packet streams are in the ON state [12]. The transition rate from the state i to the state (i 2 1) is ib and the transition rate from the state i to the state (i 1 1) is (K 2 i)a . When the light intensity in the wavelength channel is directly modulated by such traf®c source, in the ON state, digital information is carried by the light, but in the OFF state, the light is off, or is so small that they can almost be neglected. Fig. 6 shows the digital signal carried by three wavelengths. We know that the FWM interference happens only when the three signal lights ( fi, fj, fk) contributing to it at fm ( fm fi 1 fj 2 fk) are all in ON state. When any one of the three lights is OFF, there is no FWM interference. As shown in Fig. 6, the FWM interference happens only during the time period that all the three light streams are in the ON state (t1 , t , t2). If the probability of the IP traf®c stream is in the ON state is pon, the probability that all the three be in 3 burst mode will be pon (assuming there are only three frequencies in the system). Hence, the actual FWM interference between the channels depends on the ON±OFF state of the IP traf®c streams transmitted in the light channels. Obviously, when the number of active channels that are in the ON state varies, the interference caused by FWM varies
correspondingly. The number of WDM channels increases, the combinations of channel frequencies that contribute to inter-channel interference increases dramatically, thus the light power generated by Four-wave mixing increases rapidly. Considering the different probability of different numbers of active channels at a time when IP traf®c is loaded, the effect of inter-channel interference in a WDM based system can be calculated as follows. For a WDM network consists of N optical channels (N is equal to or greater than 3), the average bit error probability caused by FWM interference is given by pe
N X i1
p ipei
9
where p(i) stands for the probability that i channels out of N are in the ON state at the same time, pei is the bit error probability caused by interference noise among these ichannels. Assuming that the traf®c load allocated to all the channels are uniformly distributed and the probability that IP traf®c stream is in the ON state is denoted as pon, then p(i) can be calculated as: ! N i p i pon 1 2 pon N2i 10 i In order to calculate the worst case interference when i channels out of N are in burst mode, we assume all the i channels are adjacent to each other, and we calculate the FWM interference in the central channel fm, where the frequency combinations are the most that satisfy fm fj 1 fk 2 fl, (j,k,l 1, ¼, i). From Eq. (8), the bit error probability on this condition is given by ! 1 Z1 t2 dt 11 exp 2 pei p 2 2p Qi where Qi is given by p 2 P0 e2aL Qi p ; PFWMi fm
12
and PFWMi is the summation of the four-wave mixing light power generated by all the possible frequency combinations when i channels are active. PFWMi fm
X
i X i X
fl fj 1 fk 2 fm j1 k1
PFWM fj ; fk ; fl
13
PFWM( fj, fk, fl) can be calculated from Eq. (1). For the illustrative purpose, the bit error probability caused by FWM interference in a WDM network loaded with IP
Table 1 Table1 Parameters used in the calculation N
L
l
n
D
dD/dl
Aeff
a
16
80 km
1.55 mm
1.46
0.3 ps/nm´km
0.07 ps/nm 2
5 £ 10 -7 cm 2
0.2 dB/km
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 7. Bit error probability vs. input light power.
traf®c is calculated using Eqs. (9)±(13), where the other noise factors such as SRS, SBS and ASE noise of the EDFAs are not considered. Since the input light power level used in the discussion is assumed to be below the SRS threshold. For a network span of 80 km, the in¯uence of EDFA noise can also be ignored. The parameters used in the calculation of the following numerical results are listed in Table 1.
Bit error probability vs. ®ber input light power for different traf®c load is shown in Fig. 7. It can be seen that the bit error probability is sensitive to both input light power and traf®c load. For example, when light power at the input of optical ®ber is less than 4 dBm, the corresponding FWM effect is negligible even for a very high traf®c load of 90% of link capacity. In this case, the corresponding bit error rate
Fig. 8. Bit error probability as the function of frequency spacing.
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Fig. 9. Packet error rate as the function of ON probability of the source.
is below than 10 215. By contrast, when input light power is higher than 4 dBm, the bit error probability increases sharply, even higher than 10 210 for heavy traf®c load ranging from 75 to 90% of the link capacity. However, when traf®c load is 30% of the link capacity, the allowable input light
power can be up to 8±9 dBm for very reliable transmission at bit error rate below than 10 220. Hence, the traf®c load has great in¯uence on the bit error performance. The reason is that when IP load is heavy, the probability that a WDM channel in burst mode is high, thus more WDM channels
Fig. 10. Bit error probability vs. traf®c load (with different frequency spacing).
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
Fig. 11. Optical layer model.
are likely to be in burst mode at the same time and more interference noise is generated. Frequency spacing between the optical channels is another important factor in the WDM system. Fig. 8 illustrates the effect of frequency spacing on the network performance in terms of bit error probability. It can be seen that when frequency spacing between the optical channels is less than 10 GHz, the FWM effect is remarkable to be taken into account, however, low traf®c load may be able to reduce the effect of FWM. We note that when frequency spacing between the optical channels increases, the ®ber nonlinear effect is reduced. However, when spacing is large enough, the ®ber can be considered as a linear media, and the light channels can be deemed as completely independent of each other. And this is often called sparse wavelength division systems. The WDM system used in point-to-point communication at present takes advantage of this. Fig. 9 illustrates the effects of traf®c load on the bit error performance of the wavelength channel at different input light power levels. The long packet represents that the packets generated by the ON±OFF model have the maximum length of 1500 bytes. It is clear that the corresponding data rate is the peak rate (Rp). By contrast, the short packet represents that the packets generated by the ON±OFF model is negative exponentially distributed with the average length of 150 bytes In practice, the packet length is determined by user's operation mode. For example, FTP user may have a large ®le of hundreds of Megabytes to transmit, but for an interactive web user, the message to be transmitted from the user to the server may be short for only a few hundred of bytes. Obviously, the long packet involves higher error probability comparing to the short packet. In order to keep the packer error rate low, one of the tasks for network management or the IP user is to segment these large ®les to small packets for the actual transmission in the wavelength channel. From Fig. 9, it can be seen that every 10% increase of the traf®c load can cause the increase of bit error rate by almost a magnitude of 4. On the other hand, the bit error rate is also sensitive to the input light power level, especially when traf®c load is heavy. Therefore,
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the input light power must be carefully budgeted in order to ensure that the wavelength channel has the appropriate performance to guarantee the QoS for the transmission of IP traf®c. Fig. 10 illustrates the bit error probability vs. the average traf®c load for different frequency spacing values between the wavelength channels. In order to take full advantage of the ®ber capacity, we need to place more wavelength channels into a single WDM ®ber, however, the relatively narrow frequency spacing between the wavelength channels may cause high bit error rate. Therefore, the trade-off between the number of wavelength channels in the WDM link and the IP traf®c load is one of most important issue to achieve the best performance in terms of error rate and link throughput. 4. Characterization of IP traf®c over WDM networks 4.1. Modeling of WDM light-paths Simulation is also conducted to study the statistics of high-order distribution for the performance with IP packet caused by the inter-channel interference in the WDM network which is modeled as a noise generator and evaluator to take full consideration of the four wave mixing effect as well as the bursty nature of IP traf®c. The input IP traf®c is modeled as the Markov modulated ON±OFF process as shown in Fig. 5. The characteristics of the output IP traf®c ¯ow is investigated in terms of packet error rate, error freerun distribution and error pattern distribution [18,19]. In ITU-T G.872, an optical transport network (OTN) is de®ned as a transport network bounded by optical channel access points, which is functionally divided into three layers: 1. optical channel (Och) layer network 2. optical multiplex section (OMS) layer network and 3. optical transmission section (OTS) layer network The WDM light-path discussed in this context is in the optical channel (Och) layer, which is a communication channel traversing one or more optical links between a source-destination pair. A light-path in a meshed optical network is provisioned by the optical cross-connect (OXC) which is a path switching element in an optical transport network that establishes routed paths by locally connecting an optical channel from the input port to the output port in the switch element. Unlike in the packet switched network, where the characteristics of the physical layer is usually negligible to the upper layers, it is essential for optical switching network to keep track of the physical layer parameters. This is because that the physical layer characteristics in optical switching network are much more pronounced than that in packet switched network. Therefore, a light-path in this context is modeled as a
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Fig. 12. (a) Error free run distribution for low link utilization (pon 0.50); (b) error free run distribution with high link utilization (pon 0.8).
function module that generates cross-talk interference and evaluates the optical layer performance in terms of bit error rate (BER). In Fig. 11, Ai denotes the input sequence in channel i,(i 1, 2, ¼, N), and Ai(k) denotes the traf®c arriving at time slot k,
( Ai k
1
if IP packet arrives in kth time slot
2 if no IP packet arrives in kth time slot
14
Ci denotes the output sequence in channel i. Ci(k) is the
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 13. Error free run distribution with different traf®c load.
output of channel i in time slot k, 8 1 correct IP packet received in kth time slot > > < Ci k 0 no IP packet received in kth time slot > > : 21 corrupted IP packet received in kth time slot 15 H(i, k) is the physical layer noise generator and performance evaluator. In the simulation time slot i, the interference noise generated by the FWM effects is calculated using the active ON±OFF status of the traf®c streams carried in the channels in that simulation time slot. The calculated FWM power Q, is compared with a threshold value NT to determine the status of the output packet Ci(k), that is ( 21 if Ni k . NT Ci k H i; kAi k 16 Ai k otherwise The performance measure focuses on the high-order distribution such as packet error free-run distribution and packet error pattern distribution which are de®ned as follows. 4.2. Packet error free-run distribution The packet loss-free run distribution P(0 r|1) is de®ned as the conditional probability that when a packet error occurs, it will be followed by ror more consecutive loss-free packets. To estimate P(0 r|1), we de®ne a loss-free interval of length h in {Ci(k)} to be a range between two error packets which contains exactly h consecutive loss-free intervals of
length h in {Ci(k)} and Ng the total number of loss-free intervals in {Ci(k)}. Ng and Ng(h) can be obtained from the output packet sequence {Ci(k)}. Recall the de®nition of P(0 r|1), then P(0 r|1) estimates the conditional probability that a loss-free interval of length h . 1 follows an errored packet. Then, P(0 1|1) Ng/NL. Likewise P(0 2|1) is de®ned as the conditional probability that a loss-free interval of length h . 2 follows an errorer packet. Obviously, P(0 1|1) will include P(0 2|1). Then we have P(0 2|1) P(0 1|1) 2 Ng(1)/NL. Similarly, we have P 0r u1 P 0r21 u1 2 Ng r 2 1=NL P 01 u1 2
Ng 1 1 Ng 2 1 ¼ 1 Ng r 2 1 17 NL
4.3. Packet error pattern distribution The packet error pattern distribution P(u, v) is the probability that a block of v packets received at the destination node of the light path contains exactly uerror packets due to optical impairment. We divide the output packet sequence {Ci(k)} into blocks of vcells. Let NB be the total number of the blocks and NB(u) the cumulated number of the blocks in which u packets contain errors (u 0, 1, 2, ¼, v). Then the packet error pattern distribution can be estimated by P u; v
NB u NB
18
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Fig. 14. Error pattern distribution, a comparison between short and long burst-length.
4.4. Characteristics of IP traf®c over WDM using MPLS In the simulation, we consider a WDM network with 16 optical wavelength channels. Each channel is fed by one IP traf®c stream which is modeled as an Markov modulated ON±OFF process as shown in Fig. 5. The optical layer parameters are typically selected as L 80 km, l 1.55 mm, n 1.46, D 0.3 ps/nm´km, dD/dl 0.07 ps/nm 2, Aeff 5 £ 10 27 cm 2, a 0.2 dB/ km. The all IP traf®c streams are considered as the homogeneous Markov modulated ON±OFF process, but they are generated independently as a sequence of 10 8 packets, respectively, corresponding to different traf®c parameters in terms of IP traf®c load pon, mean burst length, mean packet length and mean silence length which are selected for the illustrative purpose only. As the most serious inter-channel interference happens in the middle channel, the characteristics of the output IP traf®c in channel No. 8 are typically investigated in this study. Figs. 12 and 13 show the packet error free-run distribution. It can be seen that the packet error free-run is affected by the traf®c burst-length. For example, for the average traf®c load pon 0.5 in Fig. 12, P(0 1|1) 0.85 for traf®c burst-length of 5, P(0 1|1) 0.63 for traf®c burst-length of 10 and P(0 1|1) 0.5 for traf®c burst-length of 15. This is because that when burst is long, corrupted packets are likely to be clustered. The same trend can be observed in Fig. 13 for a heavy traf®c load situation of pon 0.8. Fig. 14 shows the effect of traf®c load on error free-run distribution. It can be seen that when traf®c load increases, the error free interval in the output IP traf®c stream
decreases. This is due to the fact that when traf®c load is high, bit error rate is high, so the number of consecutive error free packets is inevitably smaller. A comparison of error pattern distribution with short and long burst is illustrated in Fig. 14. It can see that impact of the traf®c burst-length on the packet error pattern distribution of the output IP traf®c stream is obvious. 5. Conclusion This paper presents a novel architecture for directly mapping the IP traf®c into WDM network using MPLS that effectively simpli®es the protocols for IP over WDM by removing the inter-layer protocols such as ATM/Frame Relay and SDH/SONET. However, under such network architecture, the bursty nature of IP traf®c may have may have remarkable effect on the performance of WDM networks. The performance with IP traf®c directly mapped into WDM networks using MPLS is investigated. On the other hand, the inter-channel interferences caused by ®ber nonlinear effect such as four wave mixing are also considered in the performance analysis. The statistics of network performance in terms of packet error probability, packet error free-run distribution and packet error-pattern distribution are presented. The numerical results have demonstrated that the impact of the optical channel parameters and the characteristics of IP traf®c can be summarized as follows. ² Optical parameters, such as light power in the ®ber, frequency spacing and number of wavelengths in the
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
system are still the dominant factors that determine the network performance. ² Burstiness of IP traf®c has a remarkable in¯uence on the network performance in terms of bit error rate. Therefore, the traf®c load need to be considered in the network design to guarantee performance. ² Burst-length of IP packet also has signi®cant effect on the performance of the packet error free-run distribution and the packet error pattern distribution. These illustrative results provide valuable information to the network designers.
References [1] Noda Golmie, Thomas D. Ndousse, David H. Su, A differentiated optical services model for WDM networks. IEEE Communications Magazine, February 2000, pp. 68±73. [2] Nasir Ghani, Sudhir Dixit, Ti-Shiang Wang, On IP-over-WDM integration. IEEE Communications Magazine, March 2000, pp.72±84. [3] Franco Callegati, Maurizio Casoni, Carla Raffaelli, Packet optical networks for high-speed TCP-IP backbones, IEEE Communications Magazine, January 1999, pp. 124±129 [4] Vincent W.S. Chan, Katherine L. Hall, Eytan Modiano, et al., Architectures and technologies for high-speed optical data networks, Journal of Lightwave Technology 6 (12) (1998) 2146±2216. [5] Eytan Modiano, WDM-based packet networks. IEEE Communication Magazine, March 1999, pp. 130±135 [6] Eytan Modiano, Richard Barry, Architecture considerations in the design of WDM-based optical access networks, Computer Networks 31 (1999) 327±341. [7] John M Senior, Michael R Handley, Mark S Leeson. Developments in wavelength division multiple access networking. IEEE Communication Magazine, December 1998, pp. 28±36.
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[8] Christapher Y. Metz, IP Switching, Protocols and Architectures, McGraw-Hill, 1999. [9] Daniel O. Awduche, Yakov Rekhter, John Drake, et al., Multi-Protocol Lambda Switching: Combining MPLS Traf®c Engineering Control with Optical Crossconnects, IETF draft-awduche-mpls-teoptical-00.txt, November 1999. [10] Debashis Basak, Daniel O Awduche, John Drake, Yakov Rekhter, Multi-protocol Lambda Switching: Issues in Combining MPLS Traf®c Engineering Control With Optical Cross-connects, draft-basakmpls-oxc-issues-01.txt, February 2000. [11] Kireeti Kompella, Yokov Rekher, Danial Hannan, et al., Extensions to IS-IS/OSPF and RSVP in support of MPL(ambda)S, draftkompella-mpls-optical-00.txt, February 2000. [12] Bharat T Doshi, Subrahmanya m Dravida, Enrique J HernandezValencia, A simple data link protocol for high-speed packet networks. Bell Labs Technical Journal, January±March 1999. [13] Sheng-Tzong Cheng, Backtrack routing and priority-based wavelength assignment in WDM networks, Computer Communications 22 (1999) 1±10. [14] Kiyoshi Nosu, Optical FDM Network Technologies, Artech House, 1997. [15] Mari W. Maeda, William B. Sessa, Winston Ingshih Way, et al., The effect of four-wave mixing in ®bers on optical frequency-division multiplexing systems, Journal of Lightwave Technology 8 (9) (1990) 1402±1408. [16] Ornan Gerstel, Rajiv Ramaswami, Galen H. Sasaki, Fault tolerant multiwavelength optical rings with limited wavelength conversion, IEEE Journal on Selected Areas in Communications 16 (7) (1998) 1166±1178. [17] Kyo Inoue, A simple expression for Optical FDM network scale considering ®ber four-wave mixing and optical ampli®er noise, Journal of Lightwave Technology 13 (5) (1995) 856±861. [18] L. Zhang, A. Vaidhiyanathan, K.R. Subramanian, Characterization of Singapore One ATM network, IEE Proc. Communications 6 (6) (1999) 372±378. [19] L. Zhang, Statistics of cell loss and its application for forward loss recovery in ATM networks, Proceedings of ICC '92, Chicago, IL, USA, 1992, pp. 694±698.
www.elsevier.com/locate/comcom
Characterization and performance study of IP traf®c in WDM networks Liren Zhang*, Junhua Tang School of EEE, Nanyang Technological University, Nanyang, Singapore 639798, Singapore Received 3 May 2001; accepted 3 May 2001
Abstract This paper investigates the characteristics of network performance, when IP traf®c is directly mapped into WDM networks using multiprotocol label switching (MPLS) techniques. The performance analysis focuses on the burstiness of IP traf®c that may have a remarkable effect on the network performance. On the other hand, the inter-channel interferences caused by ®ber nonlinear effect such as four wave mixing are also considered in the performance analysis. The statistics of network performance in terms of packet error probability, packet error free-run distribution and packet error-pattern distribution are presented. These illustrative results provide valuable information to the network designers. q 2001 Elsevier Science B.V. All rights reserved.
1. Introduction The combination of the Internet protocol (IP) and the wavelength division multiplexing (WDM) technology has attracted much attention in the research and manufacturing community as a promising strategy for the next generation Internet. The development of WDM technology has yielded the bandwidth of more than 1 Tbps on a single ®ber that makes it feasible to support data, voice and other multimedia applications over the Internet [1±7]. The typical protocol currently used to support IP over WDM networks uses SDH/SONET as the physical layer which is based on time division multiple access (TDMA) and the ATM or frame relay on the top of SDH/SONET to provide integrated services. However, since this `full-stack' approach reduces the network ef®ciency and poses the increased management/operation costs, it is clear that a single ubiquitous mechanism for IP-WDM incorporation is desirable for the future long-term development. A good example in this trend is the appearance of multi-protocol lambda switching proposed by Internet Engineering Task Force (IETF) [8,9]. The multi-protocol lambda switching describes an approach to map the IP traf®c directly to WDM channels using multi-protocol label switching (MPLS) as the control plane for both IP routers and optical cross-connects (OXCs). Optical channels are dynamically provisioned by IP-routers and OXCs coordinately through MPLS. IP traf®c are labeled and transported on light paths irrespective of the protocol and coding used in each channel. * Corresponding author. Tel.: 165-7904508; fax: 165-7920415. E-mail address: [email protected] (L. Zhang).
Hence, this allows the use of uniform semantics for network management and operations control in hybrid networks consisting of OXCs and label switching routers (LSRs), and paves the way for the eventual incorporation of WDM multiplexing capabilities in IP routers [9±13]. As a result, the MPLS has been generally accepted as a straightforward approach to combine IP and WDM technology using existing standards and experiences. In addition to the de®nition of a simpli®ed protocol for IP-WDM integration, the further studies on the effect of bursty IP traf®c on the performance of such networks are necessary. In the future WDM networks, there more than one hundred optical channels may be packed into a single strand of ®ber. In this case, the ®ber nonlinear effect causes interference among signals carried in different channels which in turn leads to cross talk degradation of the signal channel. Of all the ®ber nonlinear effects, four-wave mixing (FWM) is one of the most signi®cant factors in the WDM network which generates various combinations of different channel frequencies and makes it dif®cult to detect the useful signal [14±17]. Although this effect is not obvious and is usually neglected in the WDM network with small number of optical channels, however, it may become significant in the WDM network with large number of optical channels, especially when the WDM network is directly loaded with bursty IP traf®c. 2. Network architecture for IP over WDM using MPLS In the traditional implementation of IP over WDM, IP traf®c is encapsulated in SDH/SONET frames by allocating
0140-3664/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0140-366 4(01)00355-3
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 1. IP paths in a label switching optical network.
the ®xed time slots to its payload in TDMA manner. Clock recovery in such a network is extremely important. Therefore, it is unlikely to directly transmit bursts of packets over the SDH/SONET link, and instead of sending dummy packets during silent period to keep a constant traf®c ¯ow. The switching of packets has to be done at electronic level. Therefore, the effect of IP traf®c on the performance of WDM network is signi®cantly reduced but the utilization of optical ®ber is also signi®cantly limited. By contrast, when IP is mapped directly into optical channels using MPLS, the switching is done at optical wavelength domain, in such a way, the bursty nature of IP traf®c is re¯ected on the optical channels, which in turn poses in¯uence on the non-linear inter-channel interference among channels. As a result, the characteristics of the light channel are correlated with the statistics of the IP traf®c. On the other hand, the characteristics of the optical channel determine the QoS of the IP traf®c when it is transported through the optical network. Therefore, in the era of IP and WDM integration, it has become increasingly important to understand the interaction of IP traf®c nature and WDM channel performance. However, there has been little work in this ®eld in the literature so far. As shown in Fig. 1, the edge nodes are label switching routers with WDM capabilities. The ingress edge node performs packet-by-packet routing, label assignment and framing electronically, and then forwards the traf®c ¯ow into the appropriate output port with the assigned output optical wavelength. The MPLS traf®c engineering control
plane is responsible for path selection and path management. Since light-paths are con®gured in the OXCs in the core optical networks as part of label switched paths (LSPs), signaling protocol such as RSVP or label distributing protocol (LDP) is used to exchange link states between access router and OXCs. Meanwhile, constraint-based routing is used to compute paths that satisfy certain speci®cations subject to certain constraints. The egress edge node extracts electronic signals from the optical interface and recovers IP packets from data link frames and forwards them to the appropriate destination network. Fig. 2 shows the reference model of an edge LSR. IP packets are routed and assigned with a label of Label Switched Path, which may consist of shortcut path bypassing intermediate layer-3 routing hops between LSRs and optical channels provided by optical transport networks. Traf®c of one or more LSPs is encapsulated and may be aggregated before put to selected optical channel wavelength. An OXC, however, does not check the content of the LSP, but switches channels on a prede®ned manner con®gured by control and management information. Each LSR or OXC consists of a connection table, called Label Information Base (LIB), which contains Forwarding Equivalence Class /label bindings and associated port, wavelength and media encapsulation information. Therefore, it can be mapped into a single label by an LSR [8]. In an OXC, a local adaptation layer may be designed to map this information to switch controller. Packet encapsulation for IP over WDM using MPLS is
Fig. 2. Reference model of a TC-LSR.
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L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
Fig. 3. Encapsulation of IP packets over WDM.
shown in Fig. 3. The label switched paths can be mapped to optical channels provided by WDM elements. Currently the most common form of WDM element is programmable and re-con®gurable optical cross-connect that supports wavelength conversion/translation. This circuit switching nature of WDM element makes PPP (point to point protocol) suitable for encapsulation of IP over WDM [9,13]. Each label switched path is supported by a PPP link. The multiple protocol label switching control protocol is responsible for enabling and disabling the use of label switching on the PPP link When an IP packet arrives, a label of short ®xed-length contiguous value used to identify the IP stream is appended into its head. Then, HDLC header and trailer are added to the PPP frame to guarantee link layer data transmission. This proposed architecture has the following features. (1) Simpli®ed protocol stack, in which the ATM and SONET layer is replaced by PPP/HDLC encapsulation to guarantee layer 2 data transmission. (2) Reduction of conventional IP routing. This is done by the introduction of MPLS, which performs IP routing only at the edge nodes and uses shortcut paths (in layer 2) to deliver IP packets in the intermediate components. (3) IP ¯ow aggregation is easily achieved. Packets of one or more ¯ows (source-destination pair) that demand the same treat can be put together to form a stream and
Fig. 4. The optical frequency arrangement of four-wave mixing, fFWM fi 1 fj 2 fk.
be mapped to a single label. So even though the elementary capacity block in a WDM network is a single light path, it can be ¯exibly shared by packet ¯ows. This can be accomplished by the coordination of Label Switching Routers running Label Distribution Protocol (LDP). (4) A circuit switched wavelength route for each label switched path is provided by WDM based optical network, and the optical switch con®guration and wavelength arrangement are done in accordance with LDP. (5) Differentiated services can be readily supported in this architecture. Different label switched paths can be used to server users with different levels of QoS requirements. 3. Performance analysis of IP traf®c over WDM networks Although the architecture for IP packets over WDM has not been ®nalized yet, the trend of mapping IP traf®c directly into light path without other multiplexing scheme is clear in constructing IP backbones over WDM. This has led to the fact that the light paths will most probably be loaded with bursty IP traf®c in the network. Though sometimes the optical channels in the WDM system are considered to be totally independent of each other, it is not true especially when the ®ber input light power is high and the frequency spacing between wavelengths is narrow. In such case, some nonlinear characteristics may cause serious interference. One of these signi®cant effects is Four Wave Mixing (FWM) [14±17]. Fig. 4 schematically illustrates the optical frequency arrangement, where fi, fj, and fk are the signal light frequencies, and fFWM is the four-wave mixing light wave frequency satisfying fFWM i 1 fj 2 fk. We notice that only the effects of FWM and ASE with Gaussian approximation are taken into account in the following analysis.
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 5. Markov modulated ON-OFF process.
The output power PFWM of the four-wave mixing product is given by [14,15] PFWM fi ; fj ; fk
1024p6 2 2 Pi Pj Pk 2aL 1 2 e2aL 2 d x e h n4 l2 c2 A2eff a2 1
where Pi, Pj and Pk represent the input power of the frequencies fi, fj and fk respectively; PFWM is the power of the lightwave from four-wave mixing at the frequency fFWM; n is the ®ber refractive index; lis the wavelength; Aeff is the effective mode area of the ®ber; a is the ®ber loss coef®cients; L is ®ber length; d is the degeneracy factor(d 3 for i j, d 6 for i ± j), and xis the third-order nonlinear susceptibility. h (fi, fj, fk) is the mixing ef®ciency given by [14,15]: ( ) a2 4e2aL sin2 DbL=2 2 h 2 11 a 1 Db2 1 2 e2aL 2 where Db represents the phase mismatch and may be expressed in terms of signal frequency differences [14,15]: 2pl2 u fi 2 fk uu fj Db c ! ( ) dD l2 u fi 2 fk u 1 u fj 2 fk u ; 2 fk u´ D 1 d l 2c
3
where D is the ®ber chromatic dispersion. Eqs. (2) and (3) show that the four-wave mixing ef®ciency decreases with increasing signal frequency difference and chromatic dispersion due to increased phase mismatch between the signals. In WDM system, spacing between the wavelengths may be uniformly distributed ranging from a few gigahertz to 100 GHz [14]. In such systems, at any particular channel frequency, there will be a number of FWM waves generated from various combinations of interacting signals whose frequencies satisfy: fFWM fi 1 fj 2 fk . The total power generated at frequency fm may be expressed as a summation X XX Ptot fm PFWM fi ; fj ; fk 4 fk fi 1 fj 2 fm
fj
fi
FWM light is coherently detected at the receiver together with the signal light, and induces the interference noise. The FWM noise power NFWM is written as [17]: NFWM 2b2 Ps
PFWM ; 8
5
where Ps is the signal light power at the receiver and b is the quantum ef®ciency. In the case where the input light power to the ®ber is P0 and the ®ber length is L, and ®ber loss coef®cients is a, Ps P0 ´e2aL . The SNR can be expressed as [17]: bPs p Q p Nth 1 Nsh 1 NFWM 1 Nth
6
Since both the thermal noise Nth and shot noise Nsh are negligible, NFWM is usually the dominant factor of the denominator, so Eq. (6) can be written as: p p bPs 2bPs 2 Ps 2 P0 e2aL Q p p p p PFWM NFWM PFWM b2 Ps PFWM
7
If Gaussian approximation is used to describe the noise caused by FWM interference, the bit error probability pe for an intensity-modulated on±off keying signal is written as [17]: ! 1 Z1 t2 pe p dt 8 exp 2 2 2p Q Therefore, in WDM system, the nonlinear interaction among these channel lights may generate interference light to a signal channel, and cause degradation of signal to increase the bit error probability. Since the power of the interference light is proportional to the input light power and inverse proportional to the frequency spacing, we should note that when the input power is low enough and the frequency spacing is large enough, the effect of FWM is almost negligible. In present WDM systems where the input power is generally much less than 0 dBm, engineers often neglect this factor. But with the rapid development of optical component for all-optical networks, especially for a wide area WDM with the wide use of Erbium Doped Fiber
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Fig. 6. Bursts of IP traf®c.
ampli®er, the input light power to the ®ber can reach 10 dBm or even higher. In such case, the interference of FWM may impose a major limitation to the number of channels or the size of the WDM network. In this paper, IP packet stream generated by each user source is modeled as an ON±OFF process [18,19], in which the alternative state transition between the ON state and the OFF state is shown in Fig. 5, where the parameter a is the rate of transition from the OFF state to the ON state and the parameter b is the rate of transition from the ON state to the OFF state. The probability that the process is in the ON state is a /(a 1 b ). The packet is negative exponentially distributed in length. When K of such ON±OFF packet streams are multiplexed, the resultant stream can be represented by an (K 1 1)-state Markov modulated process as shown in Fig. 5, where state i represents that i (i 0, 1, 2, ¼, K) packet streams are in the ON state [12]. The transition rate from the state i to the state (i 2 1) is ib and the transition rate from the state i to the state (i 1 1) is (K 2 i)a . When the light intensity in the wavelength channel is directly modulated by such traf®c source, in the ON state, digital information is carried by the light, but in the OFF state, the light is off, or is so small that they can almost be neglected. Fig. 6 shows the digital signal carried by three wavelengths. We know that the FWM interference happens only when the three signal lights ( fi, fj, fk) contributing to it at fm ( fm fi 1 fj 2 fk) are all in ON state. When any one of the three lights is OFF, there is no FWM interference. As shown in Fig. 6, the FWM interference happens only during the time period that all the three light streams are in the ON state (t1 , t , t2). If the probability of the IP traf®c stream is in the ON state is pon, the probability that all the three be in 3 burst mode will be pon (assuming there are only three frequencies in the system). Hence, the actual FWM interference between the channels depends on the ON±OFF state of the IP traf®c streams transmitted in the light channels. Obviously, when the number of active channels that are in the ON state varies, the interference caused by FWM varies
correspondingly. The number of WDM channels increases, the combinations of channel frequencies that contribute to inter-channel interference increases dramatically, thus the light power generated by Four-wave mixing increases rapidly. Considering the different probability of different numbers of active channels at a time when IP traf®c is loaded, the effect of inter-channel interference in a WDM based system can be calculated as follows. For a WDM network consists of N optical channels (N is equal to or greater than 3), the average bit error probability caused by FWM interference is given by pe
N X i1
p ipei
9
where p(i) stands for the probability that i channels out of N are in the ON state at the same time, pei is the bit error probability caused by interference noise among these ichannels. Assuming that the traf®c load allocated to all the channels are uniformly distributed and the probability that IP traf®c stream is in the ON state is denoted as pon, then p(i) can be calculated as: ! N i p i pon 1 2 pon N2i 10 i In order to calculate the worst case interference when i channels out of N are in burst mode, we assume all the i channels are adjacent to each other, and we calculate the FWM interference in the central channel fm, where the frequency combinations are the most that satisfy fm fj 1 fk 2 fl, (j,k,l 1, ¼, i). From Eq. (8), the bit error probability on this condition is given by ! 1 Z1 t2 dt 11 exp 2 pei p 2 2p Qi where Qi is given by p 2 P0 e2aL Qi p ; PFWMi fm
12
and PFWMi is the summation of the four-wave mixing light power generated by all the possible frequency combinations when i channels are active. PFWMi fm
X
i X i X
fl fj 1 fk 2 fm j1 k1
PFWM fj ; fk ; fl
13
PFWM( fj, fk, fl) can be calculated from Eq. (1). For the illustrative purpose, the bit error probability caused by FWM interference in a WDM network loaded with IP
Table 1 Table1 Parameters used in the calculation N
L
l
n
D
dD/dl
Aeff
a
16
80 km
1.55 mm
1.46
0.3 ps/nm´km
0.07 ps/nm 2
5 £ 10 -7 cm 2
0.2 dB/km
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 7. Bit error probability vs. input light power.
traf®c is calculated using Eqs. (9)±(13), where the other noise factors such as SRS, SBS and ASE noise of the EDFAs are not considered. Since the input light power level used in the discussion is assumed to be below the SRS threshold. For a network span of 80 km, the in¯uence of EDFA noise can also be ignored. The parameters used in the calculation of the following numerical results are listed in Table 1.
Bit error probability vs. ®ber input light power for different traf®c load is shown in Fig. 7. It can be seen that the bit error probability is sensitive to both input light power and traf®c load. For example, when light power at the input of optical ®ber is less than 4 dBm, the corresponding FWM effect is negligible even for a very high traf®c load of 90% of link capacity. In this case, the corresponding bit error rate
Fig. 8. Bit error probability as the function of frequency spacing.
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Fig. 9. Packet error rate as the function of ON probability of the source.
is below than 10 215. By contrast, when input light power is higher than 4 dBm, the bit error probability increases sharply, even higher than 10 210 for heavy traf®c load ranging from 75 to 90% of the link capacity. However, when traf®c load is 30% of the link capacity, the allowable input light
power can be up to 8±9 dBm for very reliable transmission at bit error rate below than 10 220. Hence, the traf®c load has great in¯uence on the bit error performance. The reason is that when IP load is heavy, the probability that a WDM channel in burst mode is high, thus more WDM channels
Fig. 10. Bit error probability vs. traf®c load (with different frequency spacing).
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
Fig. 11. Optical layer model.
are likely to be in burst mode at the same time and more interference noise is generated. Frequency spacing between the optical channels is another important factor in the WDM system. Fig. 8 illustrates the effect of frequency spacing on the network performance in terms of bit error probability. It can be seen that when frequency spacing between the optical channels is less than 10 GHz, the FWM effect is remarkable to be taken into account, however, low traf®c load may be able to reduce the effect of FWM. We note that when frequency spacing between the optical channels increases, the ®ber nonlinear effect is reduced. However, when spacing is large enough, the ®ber can be considered as a linear media, and the light channels can be deemed as completely independent of each other. And this is often called sparse wavelength division systems. The WDM system used in point-to-point communication at present takes advantage of this. Fig. 9 illustrates the effects of traf®c load on the bit error performance of the wavelength channel at different input light power levels. The long packet represents that the packets generated by the ON±OFF model have the maximum length of 1500 bytes. It is clear that the corresponding data rate is the peak rate (Rp). By contrast, the short packet represents that the packets generated by the ON±OFF model is negative exponentially distributed with the average length of 150 bytes In practice, the packet length is determined by user's operation mode. For example, FTP user may have a large ®le of hundreds of Megabytes to transmit, but for an interactive web user, the message to be transmitted from the user to the server may be short for only a few hundred of bytes. Obviously, the long packet involves higher error probability comparing to the short packet. In order to keep the packer error rate low, one of the tasks for network management or the IP user is to segment these large ®les to small packets for the actual transmission in the wavelength channel. From Fig. 9, it can be seen that every 10% increase of the traf®c load can cause the increase of bit error rate by almost a magnitude of 4. On the other hand, the bit error rate is also sensitive to the input light power level, especially when traf®c load is heavy. Therefore,
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the input light power must be carefully budgeted in order to ensure that the wavelength channel has the appropriate performance to guarantee the QoS for the transmission of IP traf®c. Fig. 10 illustrates the bit error probability vs. the average traf®c load for different frequency spacing values between the wavelength channels. In order to take full advantage of the ®ber capacity, we need to place more wavelength channels into a single WDM ®ber, however, the relatively narrow frequency spacing between the wavelength channels may cause high bit error rate. Therefore, the trade-off between the number of wavelength channels in the WDM link and the IP traf®c load is one of most important issue to achieve the best performance in terms of error rate and link throughput. 4. Characterization of IP traf®c over WDM networks 4.1. Modeling of WDM light-paths Simulation is also conducted to study the statistics of high-order distribution for the performance with IP packet caused by the inter-channel interference in the WDM network which is modeled as a noise generator and evaluator to take full consideration of the four wave mixing effect as well as the bursty nature of IP traf®c. The input IP traf®c is modeled as the Markov modulated ON±OFF process as shown in Fig. 5. The characteristics of the output IP traf®c ¯ow is investigated in terms of packet error rate, error freerun distribution and error pattern distribution [18,19]. In ITU-T G.872, an optical transport network (OTN) is de®ned as a transport network bounded by optical channel access points, which is functionally divided into three layers: 1. optical channel (Och) layer network 2. optical multiplex section (OMS) layer network and 3. optical transmission section (OTS) layer network The WDM light-path discussed in this context is in the optical channel (Och) layer, which is a communication channel traversing one or more optical links between a source-destination pair. A light-path in a meshed optical network is provisioned by the optical cross-connect (OXC) which is a path switching element in an optical transport network that establishes routed paths by locally connecting an optical channel from the input port to the output port in the switch element. Unlike in the packet switched network, where the characteristics of the physical layer is usually negligible to the upper layers, it is essential for optical switching network to keep track of the physical layer parameters. This is because that the physical layer characteristics in optical switching network are much more pronounced than that in packet switched network. Therefore, a light-path in this context is modeled as a
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Fig. 12. (a) Error free run distribution for low link utilization (pon 0.50); (b) error free run distribution with high link utilization (pon 0.8).
function module that generates cross-talk interference and evaluates the optical layer performance in terms of bit error rate (BER). In Fig. 11, Ai denotes the input sequence in channel i,(i 1, 2, ¼, N), and Ai(k) denotes the traf®c arriving at time slot k,
( Ai k
1
if IP packet arrives in kth time slot
2 if no IP packet arrives in kth time slot
14
Ci denotes the output sequence in channel i. Ci(k) is the
L. Zhang, J. Tang / Computer Communications 24 (2001) 1702±1713
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Fig. 13. Error free run distribution with different traf®c load.
output of channel i in time slot k, 8 1 correct IP packet received in kth time slot > > < Ci k 0 no IP packet received in kth time slot > > : 21 corrupted IP packet received in kth time slot 15 H(i, k) is the physical layer noise generator and performance evaluator. In the simulation time slot i, the interference noise generated by the FWM effects is calculated using the active ON±OFF status of the traf®c streams carried in the channels in that simulation time slot. The calculated FWM power Q, is compared with a threshold value NT to determine the status of the output packet Ci(k), that is ( 21 if Ni k . NT Ci k H i; kAi k 16 Ai k otherwise The performance measure focuses on the high-order distribution such as packet error free-run distribution and packet error pattern distribution which are de®ned as follows. 4.2. Packet error free-run distribution The packet loss-free run distribution P(0 r|1) is de®ned as the conditional probability that when a packet error occurs, it will be followed by ror more consecutive loss-free packets. To estimate P(0 r|1), we de®ne a loss-free interval of length h in {Ci(k)} to be a range between two error packets which contains exactly h consecutive loss-free intervals of
length h in {Ci(k)} and Ng the total number of loss-free intervals in {Ci(k)}. Ng and Ng(h) can be obtained from the output packet sequence {Ci(k)}. Recall the de®nition of P(0 r|1), then P(0 r|1) estimates the conditional probability that a loss-free interval of length h . 1 follows an errored packet. Then, P(0 1|1) Ng/NL. Likewise P(0 2|1) is de®ned as the conditional probability that a loss-free interval of length h . 2 follows an errorer packet. Obviously, P(0 1|1) will include P(0 2|1). Then we have P(0 2|1) P(0 1|1) 2 Ng(1)/NL. Similarly, we have P 0r u1 P 0r21 u1 2 Ng r 2 1=NL P 01 u1 2
Ng 1 1 Ng 2 1 ¼ 1 Ng r 2 1 17 NL
4.3. Packet error pattern distribution The packet error pattern distribution P(u, v) is the probability that a block of v packets received at the destination node of the light path contains exactly uerror packets due to optical impairment. We divide the output packet sequence {Ci(k)} into blocks of vcells. Let NB be the total number of the blocks and NB(u) the cumulated number of the blocks in which u packets contain errors (u 0, 1, 2, ¼, v). Then the packet error pattern distribution can be estimated by P u; v
NB u NB
18
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Fig. 14. Error pattern distribution, a comparison between short and long burst-length.
4.4. Characteristics of IP traf®c over WDM using MPLS In the simulation, we consider a WDM network with 16 optical wavelength channels. Each channel is fed by one IP traf®c stream which is modeled as an Markov modulated ON±OFF process as shown in Fig. 5. The optical layer parameters are typically selected as L 80 km, l 1.55 mm, n 1.46, D 0.3 ps/nm´km, dD/dl 0.07 ps/nm 2, Aeff 5 £ 10 27 cm 2, a 0.2 dB/ km. The all IP traf®c streams are considered as the homogeneous Markov modulated ON±OFF process, but they are generated independently as a sequence of 10 8 packets, respectively, corresponding to different traf®c parameters in terms of IP traf®c load pon, mean burst length, mean packet length and mean silence length which are selected for the illustrative purpose only. As the most serious inter-channel interference happens in the middle channel, the characteristics of the output IP traf®c in channel No. 8 are typically investigated in this study. Figs. 12 and 13 show the packet error free-run distribution. It can be seen that the packet error free-run is affected by the traf®c burst-length. For example, for the average traf®c load pon 0.5 in Fig. 12, P(0 1|1) 0.85 for traf®c burst-length of 5, P(0 1|1) 0.63 for traf®c burst-length of 10 and P(0 1|1) 0.5 for traf®c burst-length of 15. This is because that when burst is long, corrupted packets are likely to be clustered. The same trend can be observed in Fig. 13 for a heavy traf®c load situation of pon 0.8. Fig. 14 shows the effect of traf®c load on error free-run distribution. It can be seen that when traf®c load increases, the error free interval in the output IP traf®c stream
decreases. This is due to the fact that when traf®c load is high, bit error rate is high, so the number of consecutive error free packets is inevitably smaller. A comparison of error pattern distribution with short and long burst is illustrated in Fig. 14. It can see that impact of the traf®c burst-length on the packet error pattern distribution of the output IP traf®c stream is obvious. 5. Conclusion This paper presents a novel architecture for directly mapping the IP traf®c into WDM network using MPLS that effectively simpli®es the protocols for IP over WDM by removing the inter-layer protocols such as ATM/Frame Relay and SDH/SONET. However, under such network architecture, the bursty nature of IP traf®c may have may have remarkable effect on the performance of WDM networks. The performance with IP traf®c directly mapped into WDM networks using MPLS is investigated. On the other hand, the inter-channel interferences caused by ®ber nonlinear effect such as four wave mixing are also considered in the performance analysis. The statistics of network performance in terms of packet error probability, packet error free-run distribution and packet error-pattern distribution are presented. The numerical results have demonstrated that the impact of the optical channel parameters and the characteristics of IP traf®c can be summarized as follows. ² Optical parameters, such as light power in the ®ber, frequency spacing and number of wavelengths in the
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system are still the dominant factors that determine the network performance. ² Burstiness of IP traf®c has a remarkable in¯uence on the network performance in terms of bit error rate. Therefore, the traf®c load need to be considered in the network design to guarantee performance. ² Burst-length of IP packet also has signi®cant effect on the performance of the packet error free-run distribution and the packet error pattern distribution. These illustrative results provide valuable information to the network designers.
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