Investigation of The Time-Offset-Based QoS Support with Optical Burst Switching in WDM Networks

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1 Investigation of The Tie-Offset-Based QoS Support with Optical Burst Switching in WDM Networks Pingyi Fan, Chongxi Feng,Yichao Wang, Ning Ge State Key Laboratory on Microwave and Digital Counications, Departent of Electronic Engineering, Tsinghua University, Beijing, China, Abstract IP over WDM networks have been receiving uch attention as a proising approach to building the next generation Internet since it can reduce coplexities and overheads associated with the ATM and SONET layers. Provision of quality of service (QoS) is one iportant topic in next generation Internet. Recently, An optical burst switching schee to support basic QoS at the WDM layer, the offset-tie-based QoS schee, was proposed by Yoo, Qiao and Dixit (YQD schee). In this paper, we propose a union bound ethod to estiate the loss probability for different priority service, which is an extension of the bounds given by Yoo, Qiao and Dixit. It is proved that the proposed union bound is tighter than that given by Yoo, Qiao and Dixit. Meanwhile, based on the conservation law, we also present a ethod to estiate the required axiu delay length of fiber delay lines (FDLs) if FDL buffers are eployed in YQD schee in IP over wavelength division ultiplexing (WDM) networks. Soe nuerical results on the effect of fiber delay lines on the syste perforance and the required axiu delay length of FDLs for different service classes are presented. I. Introduction There has been explosive growth in Internet Protocol (IP) traffic in the last few years. It has triggered a lot of research activities in devising new high speed transission and switching technology. Wavelength division ultiplexing (WDM) has eerged as a core transission technology due to its capability of supporting a nuber of high speed (gigabit) channels in one single fiber. In order to efficiently use the bandwidth at WDM layer, it requires to develop the corresponding fraeworks and protocols at higher layers. Aong the, IP over WDM networks have received uch attention since it can reduce coplexities and overheads associated with the ATM and SONET layers. Meanwhile, provision of quality of service (QoS) supports is another iportant issue in next generation Internet. This is because current IP provides only best effort service, but soe critical and real tie applications require a high QoS. ( e.g. low delay, jitter and loss probability). Thus supporting QoS in IP over WDM networks is becoing an iportant research field. There are soe works focusing on the switching technologies [1]-[6]. Most of the think that optical burst switching is a proising paradig since it cobines the desirable feature of wavelength routing and optical packet switching. It features out of band control signal processing that eliinates buffering of data burst at interediate nodes, while iniizing the setup tie, and axiizing the cross-connect bandwidth efficiency. In [1] [4], they proposed an offset-tie-based optical burst switching schee which can use the extra offset tie to isolate classes of traffic instead of the buffer. Meanwhile, if soe fiber delay lines (FDLs) are eployed, the syste perforance canbeiprovedgreatly. ThiskindofQoSsupportare ipleented at WDM layer, which can be considered as a copleent to QoS enhanced version of IP ( IPv6 ). In [4], they only presented the upper and lower bounds on the burst loss probability in theory. However, the estiation of the axiu delay length of FDLs for different classes of traffic are based on siulation. If the product of the wavelength nuber per fiber and the FDL nubers is relatively larger, the siulation will take too uch tie to converge, especially for cases with low loss probability (e.g. less than 10 7 ). In this paper, we investigate the QoS perforance of YQD schee and propose an union bound ethod to estiate the loss probability of traffic fordifferent service classes. Coparing to the bounds of loss probability given in [4], the ain difference in the proposed union bound is that it considers the factor of axiu delay length of FDLs. Furtherore, we also present a ethod to evaluate the required axiu delay length of FDLs based on the conservation law. II. Optical Burst Switching and Offset-tie Based QoS Schee In this section, we shall review the offset-tie-based QoS schee given in [1][4]. In IP over WDM networks, IP routers connect to optical switching nodes (OSN). Inside the WDM backbone network, each OSN is interconnected with neighboring OSN through fiber links. Fig. 1 illustrates possible structure of an OSN. There are L incoing (and outgoing) fiber links, each of which has k wavelengths for carrying data burst

2 and one additional wavelength for carrying control packet. Every control packet is processed by the electronic control odule inside OSN, which generates appropriate control signals to set up the wavelength converters, FDL buffers and switching fabric. The optical switching fabric, which functionsasanlk : Lk no blocking switch, switches each burst on an incoing wavelength as it arrives. The ebedded FDL buffer is assued as variable delay FDL buffers, each FDL buffer can provide a different axiu delay ranging fro b to (N 1)b, whereb is the delay that a single fiber delay eleent can provide. the blocking tie is larger than the axiu delay tie B, no FDLs will be reserved and the burst will be siply dropped without wasting any buffer capacity. In [1][4], it has shown that if an appropriate extra offset tie for each higher priority class to reserve the wavelengths and FDLs is given, higher priority class can be alost copletely isolated fro the lower priority classes in the sense of blocking probability. That is to say, it is alost true that the burst of higher priority will not be blocked by the bursts with lower priority. III. Union Bounds on Loss Probability Fig. 1. structure of optical switching node. Note that one physical FDL can be shared by all k wavelengths and creates k virtual FDLs. The offset tie based QoS schee is as follows. At a source edge router, a base offset tie is predefined/calculated based on the total processing tie to be encountered by a control packet on its way to the destination edge router. The basic idea is that the control packet will be sent first, but the corresponding data burst (e.g. several IP packets) will be buffered at the source edge router for this base offset tie while the control packet is processed at each and every interediate OSN. To establish an all optical path, the burst will cut through the preconfigured OSNs along the established path. For a higher priority of bursts, an extra offset tie is given. The control packet carries the value of the total offsettie(suoftheextraoffsettieandthebaseoffset tie) along with other inforation such as destination address (or label), and the burst duration. As a result of processing the control packet at each interediate OSN, a wavelength on the desired output link will be reserved using delayed reservation (DR), where reservation is ade fro the burst arrival tie to the burst departure tie. If no wavelength is available, the burst will be blocked and one FDL will be reserved using DR as well. Note that in OBS, since every wavelength reservation is ade with known duration, the blocking tie of the burst can easily deterined. Based on the blocking tie, the FDL with an appropriate length (delay tie) will be reserved. If In this section, we shall analyze the blocking probability of two OBS protocols, naely, classless OBS and prioritized OBS. In classless OBS, no extra offset tie is assigned to any burst except the base offset tie ( i.e., no priority, as in current IPs best effort service), whereas in prioritized OBS, a longer extra offsettiewillbeas- signed to a higher priority class. In order to distinguishes n classes where class i has higher priority ( longer offset tie) over class j if i>j. Assue that class i arriving process of bursts belongs to the Possion distribution with average rate λ i and an exponentially distributed service rate with an average µ i = 1/L i, where L i is the average length of the bursts of class i. Thus, the traffic intensity of class i is given by ρ i = λ i /(µ i k)=γ i /k, whereγ i = λ i /µ i, and the total traffic intensity is ρ = P n i=1 ρ i. The following odel is siilar to that used in [1]. We consider an OSN shown in Fig. 1, and focus on a given output link having k wavelengths and asinglefiber FDL buffer containing N FDLs. Let us first consider the bounds on loss probability in classless OBS. Assuing that the switch has an FDL buffer which can be roughly odeled as M/M/k/D (whered is to be deterined). Since the nuber of physical FDLs is N, the nuber of virtual FDLs is d = Nk. In order to siplify the analysis, we also assue that all the n classes have the sae average burst length, that is, L i = L. Let β denote the axiu length of FDLs in the FDL buffer. The probability of bursts having length larger than β is 1 exp( β/l). Thus the average nuber of virtual FDLs which can be really occupied is d(1 exp( β/l)). The average nuber of bursts in the switch ( including those being transitted and those being delayed) is D = k +Nk(1 exp( β/l)). Because D ay not be an integer, we replace it by D 1 and D 2,whereD 1 is the largest integer less than D, andd 2 is the least integer greater than D. AccordingtotheM/M/k/D odel [7], the union bounds on the loss probability are, respectively, pb = PB(k, ρ,d )= γd k D k k! p 0,=1, 2, (1)

3 where γ = ρk and k 1 X p 0 =( n=0 γ n DX n! + n=k γ n k n k k! ) 1,=1, 2. (2) It is easy to see that when there is no FDL buffer, i.e., β =0, (1) is the sae as the upper bound of loss probability given in [4]. When the axiu length of FDL buffer is very large, i.e., β, then, D 1 = D 2 = k+nk. In this case, the result in (1) is the sae as the lower bound on the loss probability given in [4]. Thus, the union bounds can be considered as a general for of the bounds of loss probability given in [4]. We now consider the union bounds on the loss probability of class i in prioritized OBS. The ethod can follow that presented in [4]. It has been proved in [4] that when the traffic intensity is relatively high, i.e., ρ 0.8, the conservation law holds, that is the overall perforance (i.e. loss probability and throughput averaged over all classes) of the network stays the sae regardless of the nuber of classes and the degree of isolations. In the following discussion, we assue that class i is copletely isolated fro class i 1. Let ρ n 1,j be thesuofthetraffic intensity fro class (n 1) through class j, i.e., ρ n 1,j = P n 1 i=j ρ i. By using the class isolation, we know that the traffic fro lower priority classes ( class (j 1) through class 0) does not affect the loss probability of higher priority classes (class (n 1) through class j). Thus, the union bounds on the loss probability of different classes can be calculated by the following iterative algorith, pb n 2 pb n 1 = PB(k, ρ n 1,D ), (3) = PB(k, ρ n 1,n 2,D ) c n 1 pb n 1, (4) c n 2 pb j = PB(k, ρ n 1,j,D ) P n 1 i=j+1 c ipb i c j, (5) for j = n 2,n 3,..., 1, 0, where pb j represents the union bound on the loss probability of class j with the average nuber of FDLs D,c j = ρ j /ρ represents the ratio of the traffic intensity in class j over the total traffic intensity. IV. Maxiu Delay Length of FDLs For the M/M/k/H odel, the average queue occupancy can be calculated by Q c (k, ρ,h)= ( P 0 ργ k k!(1 ρ) R(ρ) if ρ 6= 1 2 H 2 k H H+1 otherwise, (6) where γ = kρ,r(ρ) =1 ρ H k (H k)ρ H k (1 ρ), and k 1 X P 0 =( n=0 γ n H n! + X n=k γ n k n k k! ) 1. (7) In [4], soe exaples on the axiu delay length of the traffic with different priority were given by siulation. They did not present a theoretical ethod to estiate it. In this part, we also use the conservation law in order to investigate the axiu delay length of different priority service. The basic idea is that the overall average queue occupancy in the OSN stays the sae regardless of the nuber of classes and the degree of isolation. Let q j represent the average queue occupancy of class j with average delay nuber of FDLs D. By using the class isolation, we know that the traffic fro lower priority classes ( class (j 1) through class 0) does not affect the queue occupancy of higher priority classes (class (n 1) through class j). Thus, the average queue occupancy of different classes can be calculated by the following iterative algorith, q n 2 q n 1 = Q c (k, ρ n 1,D ), (8) = Q c(k, ρ n 1,n 2,D ) c n 1 q n 1, (9) c n 2 q j = Q c(k, ρ n 1,j,D ) P n 1 i=j+1 c iq i. (10) c j In fact, while using the M/M/k/H odel to calculate the average queue occupancy, it iplicitly iplies that every unit in the buffer with axiu buffer size H has the ability to storage one basic inforation unit. But in our discussed OBS schee, the basic inforation unit is the inforation burst. It is reasonable to think that the averageburstlengthisthesizeofthebasicinforation unit. On the other hand, since the FDL buffer is not a real buffer as rando access eory (RAM), it can only keep the optical burst a liited tie, that is to say, it can only keep the optical burst as long as the period of tie in which the optical signal travels through the axiu delay lines. In order to keep a reasonable probability on burst dropping, the required axiu length of FDLs should not be shorter than the axiu aong all the average queue sizes on the prioritized service. Therefore, the required axiu delay length of FDLs should satisfies B ax q j,=1, 2 ª. (11) j In general, the lowest priority traffic will wait for uch ore tie than others. Thus, q 0 is likely to be a lower bound of the required axiu delay length of FDLs. It is worthy to note that in soe cases, it ay be iportant to estiate the values of q j (j =0, 1, 2,..., n 1).

4 Observing (10), we can easily obtain a siple way to estiate q j, that is, q j <Q c (k, ρ n 1,j,D )/c j (12) V. Nuerical Results In [4], they discussed the effect of different paraeters on the systeatic QoS perforance such as the loss probability, the average queuing delay etc. It assued that all classes generate an equal aount of traffic. In this paper, we consider a general case where the classes ay have different aount of traffic. In the following siulation, we also assue that all the classes have equal ean burst length, all offset tie differences are equal to 3L+B, where B is the axiu delay length of FDLs. for the prioritized classes service also include the inforation on the axiu delay length of FDLs. Fig.2 shows the results of the different bounds via the axiu delay tie B. The paraeters used are n =4,k =2,N =3, ρ =0.8, ρ 1 = ρ 2 = ρ 3 = ρ 4 =0.2. (the sae as that in Fig. 7 in [4]). The dashed lines denote the first kind of union bounds for all the four classes. The solid lines without any ark denote the second kind of union bounds for all the four classes. The solid lines with ark x denote the lower bounds obtained in [4]. It is easy to see that when no FDLs is eployed, the two kinds of union bounds are equal. When the axiu delay length of FDLs increases, the two kinds of union bounds decrease. Especially, as the axiu delay length of FDLs is large enough, the union boundswillnotdecreaseanyore,andkeepthesaevalues. Meanwhile, for each priority class, its second union bound converges to its lower bound obtained in [1]. The difference between the two kinds of union bounds is depended on the difference between D 1 and D 2. In Fig. 3, the paraeters are selected as n =4,k =16,N =4, ρ =0.8, ρ 1 = ρ 2 = ρ 3 = ρ 4 =0.2. It has been shown that as the product of the nuber of wavelengths in a single fiber and the nuber of FDL in the switch becoes relatively large ( Nk = 64), the difference between the two kinds of union bounds will becoe relatively sall. Fig. 2. in [4] coparison of the union bounds and the lower bounds given Fig. 4. Perforance coparison on the siulation results the theoretical results Fig. 3. Coparison of the two kinds of union bounds on the loss probability In Fig. 4, the sae set of paraeters as those used in Fig. 2 is adopted, where the dashed lines denote the siulation results, the solid lines denote the second kind of union bound, and the solid lines with ark x denote the lower bound given in [4], respectively. It indicates that the second union bound provides a tighter bound than the lower bound presented in [4]. A. Coparison of Bounds on Loss Probability Coparing the union bounds (1) with that presented in [4] for the classless service, we know that the union bounds include the inforation on the axiu delay length of FDLs. Siilar to the classless service, the union bounds B. Evaluation of Maxiu Delay Length of FDLs In [4], it has shown that when FDL buffers are introduced into OBS switches, the loss probability can be iproved considerably. When the FDL length is relatively short, it will result in higher dropping probability of bursts, especially for the lower priority services. When

5 the FDL length is too long, it will increase the end to end latency (tie delay). In this part, we shall investigate the required axiu delay length. Recall that q 0 is the upper bound of the axiu delay length of FDL in general. Fro(12), we know that q 0 is upper bounded by Q c (k, ρ,d )/c 0. Thus, it will be iportant to have a good knowledge on the property of function Q c (k, ρ,d ). Fig. 5 shows the nuerical results of Q c (k, ρ,d )fordifferent N and k, wheren =4, ρ =0.8, ρ 1 = ρ 2 = ρ 3 = ρ 4 =0.2. It has been shown that for fixed traffic intensityρ, when k is relatively larger (larger than 4), the values of Q c (k, ρ,d)(whered = k + kn) are ainly deterined by k and nearly independent of paraeter N. This result indicates that when WDM technique is adopted in OBS switch, and the wavelength nuber in each single fiber is relatively large, the axiu delay length of FDLs required is not depended on the nuber of FDLs in each OBS switch. This exaple in Fig. 5 also shows that k 4, the required axiu delay length of FDLs needs not to be selected ore than 10 ties the average burst length regardless of the paraeter N. Fig. 5. Q c function on different paraeters k and N. C. VariationofAountofTrafficinDifferent classes As an application, we discuss the effect of the variation of the aount of traffic indifferent classes on the syste QoS perforance. As an alternative, we shall use the second kind of union bound to discuss it. In fact, siilar results can be obtained by using the first kind of union bound. In Fig.6, the set of paraeters coonly used is n =4, ρ =0.8,N =4,k =4. Three different traffic intensity distributions are selected as following. In the first group (solid lines), c 0 = c 1 = c 2 = c 3 =0.25. In the second group (dashed lines), c 0 = c 1 =0.3,c 2 = c 3 =0.2. In the third group (solid lines with ark + ), c 0 = c 1 = 0.2,c 2 = c 3 =0.3. TheresultsinFig. 6haveshownthat the loss probability of the higher priority traffic isrela- tively sensitive to the variation of the aount of highest priority traffic, but the loss probability on the lowest priority traffic nearly keeps the sae value. When the traffic intensity with higher priority increases, the corresponding loss probability of the higher priority service will increase. Fig. 6. Loss probabilities via variation of the aount of traffic in different classes. VI. Conclusions In this paper, we discussed the perforance estiation of the offset-tie-based QoS schee given in [4], when applied to an optical burst switched WDM network with liited fiber lines (FDLs). We first proposed an union bound ethod to estiate the loss probability for different priority classes. Siulation results have shown that our union bound is tighter than the lower bound obtained in [4]. We also present a ethod to estiate the required axiudelaylengthoffdlsbasedonthereservation law. By using the proposed theory,we further discuss the affect of the variation of the aount of traffic indifferent classes on the QoS perforance of different prioritized classes by using our union bound ethod. References [1] M. Yoo, C. Qiao and S. Dixit, Optical burst switching for service differentiation in the next-generation optical internet, IEEE Co. Mag. pp , Feb [2] S.Vera,H.Chaskar andr.ravikanth, Opticalburstswitching : a viable solution for terabit IP backbone, IEEE Network, pp , Nov./Dec [3] J. Y. Wei and R. I. Mcfarland Jr, Just-in-tie signaling for WDM optical burst switching networks, Journal of lightwave Technology, Vol. 18, No. 12, pp , Dec [4] M. Yoo, C. Qiao, and S. Dixit, Qos perforance of optical burst switching in IP over WDM Networks, IEEE Journal on Selected Areas in Coun., Vol. 18, No. 10, pp , Oct [5] Y. J. Xiong, M. Vandenhoute and H. C. Cankaya, Control architecture in optical burst-switched WDM networks, IEEE Journal on Selected Areas in Coun. Vol. 18, No.10, pp , Oct [6] C. Qiao, Labeled optical burst switching for IP-over-WDM integration, IEEE Co. Mag. Vol. 38, No.9, pp , Sept., [7] D. Gross and C. Harris, Fundaentals of Queueing Theory, New York: Wiley-Interscience, [8] S.D,Qianet.al,Introduction to Operations Research, Beijing: Publishing Office of Tsinghua University, 1990.