Lightpath Blocking Performance Analytical Model for a Single ROADM Node with Intra-Node Add/Drop Contention [Invited]

Transcription

1 Lightpath Blocking Performance Analytical Model for a Single ROADM Node with Intra-Node Add/Drop Contention [Invited] Li Gao, Yongcheng Li and Gangxiang Shen* School of Electronic and Information Engineering, Soochow University Suzhou, Jiangsu Province, P. R. China * shengx@suda.edu.cn Abstract In colorless and directionless ROADMs based on broadcast-and-select architectures, due to the intra-node contention, the number of lightpaths that can be added/dropped with the same wavelength is limited by the add/drop contention factor. In this paper, we develop an analytical model to evaluate the lightpath blocking performance for a single ROADM node with intra-node add/drop contention. The study indicates that the model is accurate to effectively predict the simulation results. Also, the add/drop contention factor shows an important impact on the lightpath blocking performance and properly raising contention factor can significantly improve the lightpath blocking performance. Keywords: Reconfigurable optical add/drop multiplexers (ROADMs), intra-node contention, analytical model, lightpath blocking I. INTRODUCTION Reconfigurable Optical Add/Drop Multiplexers (ROADMs) are popular in today s optical transport networks owing to their advantages of high flexibility and easy reconfigurability. Currently ROADMs are evolving to support three important features, i.e., colorless, directionless, and contentionless. Colorless means that a ROADM can add/drop any wavelength on any of its add/drop ports. Directionless means that a ROADM allows any wavelength ingress from any nodal degree to be dropped at any drop port, and vice versa. Finally, contention (also called intra-node contention ) means that there are common conflict points in the node, which does not allow more than one identical wavelength to simultaneously traverse. As the opposite situation, contentionless means that such common conflict points do not exist and any wavelength can go through the node freely [1]. Today most of ROADMs have been able to support the colorless and directionless features, while the contentionless feature is still not popular due to its high cost though many promising solutions [2]-[3] have been proposed to address this. Some studies exist evaluating the impact of intra-node contention on the lightpath blocking performance for a single node [4]-[5]. However, these studies are mostly based on simulations. Analytical models are also important for evaluating such an impact so as to better understand the fundamental principles of lightpath service provisioning. Early representative approaches using analytical models for lightpath blocking performance prediction are reported in [6]-[8]. The work in [6] presented two approximate analytical models under the assumptions of independent link loads and fixed lightpath routes. In [7], the performance of wavelength-routed optical networks with both limited numbers of wavelengths and add/drop ports for both virtual wavelength path (VP) and wavelength path (P) networks were evaluated. The studies in [8] evaluated the impact of the color and direction features of contentionless ROADMs on the performance of optical transport networks. Other studies of using analytical models to predict the lightpath blocking performance can also be found in [9]-[12]. Recently, in [13] we developed an analytical model that can effectively predict the lightpath blocking performance for an optical network with colorless, directionless, and contentional ROADM nodes. In this study, we extend the analytical model to specifically focus on a single ROADM node that is colorless, directionless, and with intra-node add/drop contention. e evaluate how the intra-node add/drop contention will affect the lightpath blocking performance specifically from the node perspective. The rest of the paper is organized as follows. Section II introduces ROADM architecture with the colorless, directionless, and contentional features. In Section III, we develop an analytical model for evaluating the lightpath blocking performance under the intra-node contention constraint. The results obtained both from the analytical model and simulations are presented in Section IV. e conclude the paper in Section V. II. COLORLESS, DIRECTIONLESS, AND CONTENTIONAL ROADM ARCHITECTURE Fig. 1 shows a colorless, directionless ROADM with intranode add/drop contention. On the add side, a coupler combines the signals from the add ports to a common connecting fiber. These combined signals are then distributed to all the outbound nodal degrees through a subsequent splitter. In each outbound nodal degree, a SS combines the signals from all the other degrees and the add ports. On the drop direction, the signals from all the nodal degrees are aggregated on a common SS; these signals then pass a common connecting fiber to another SS which further splits the signals onto different drop ports. The client-side fiber cross-connect (C-FXC) module in Fig. 1(b) enables sharing of colorless add/drop ports among all the 97

2 add/drop banks. ith the colorless add/drop ports and the above connection pattern between the nodal degrees and add/drop ports, the ROADM architecture in Fig. 1 is colorless and directionless. However, the contention arises on the connecting fiber between the pair of splitter and coupler on the add part and between two wavelength selective switches (SSs) on the drop part. No more than one lightpath using the same wavelength can pass any of the common fibers. Fig. 1(a) shows a ROADM with a single contentional add/drop bank, and Fig. 1(b) shows a ROADM with two contentional add/drop banks. The total number of add/drop banks is defined as the add/drop contention factor C [14]. This factor limits the maximum number of add/drop lightpaths that are allowed to use the same wavelength. Given the same number of add/drop ports, a node with a larger add/drop contention factor C is expected to suffer less from intra-node contention, thereby achieving better lightpath blocking performance. Degree2 SS III. ANALYTICAL MODEL EVALUATING LIGHTPATH BLOCKING PERFORMANCE Intra-node contention imposes a strong impact on the lightpath blocking performance of a ROADM. In this section, we develop an analytical model to evaluate such an impact on intra-node lightpath blocking performance for the colorless and directionless ROADM with contentional add/drop banks as described in Section II. e simplify the ROADM node with the structure as shown in Fig. 2. Specifically, we introduce an auxiliary node to represent the C-FXC module. Each connecting fiber in each add/drop bank (i.e., the fiber between a pair of coupler and splitter in the add module and the fiber between a pair of SSs in the drop module) is modeled as an auxiliary link. C add/drop banks in Fig. 1(b) correspond to C auxiliary links in Fig. 2. To successfully add/drop a lightpath associated with a certain nodal degree at the node, the following conditions should be satisfied: (i) at least one free add/drop port is available at the node; (ii) at least one common free wavelength is available on both the nodal degree link and one of the auxiliary links (i.e., the connecting fibers in the add/drop banks). Degree1 SS Degree3 Degree-1 Degree-2 λ Degree-n SS Node λ SS Coupler SS Add/Drop Ports (a) Colorless, directionless (C=1) Degree2 SS SS Degree1 (b) Colorless, directionless (C=2) Fig. 1. A three-degree ROADM architecture with intra-node contention SS SS SS Bank1 Bank2 Coupler SS Coupler SS Client-side Fiber Cross Connect (C-FXC) Add/Drop Ports Degree3 Degree Link Add/Drop Auxiliary Link Ports Fig. 2. Simplified ROADM node model for performance analyses The analytical model is extended from the ones that we developed in [8]. e have the following assumptions: Lightpath requests are assumed to follow a Poisson arrival process and the holding time of each lightpath is assumed to follow a negative exponential distribution. For simplicity, we normalize the time such that the average holding time of each established lightpath is unity (i.e., ); the above assumption is common in many analytical models for circuitswitched networks, including DM optical networks [8]-[1]; The random wavelength assignment strategy [8]-[1] is applied for lightpath establishment; The lightpath traffic load on each link (nodal degree link or auxiliary link) is independent from each other. For modeling, we also have the following notations: : the maximal number of wavelengths on each nodal degree (fiber) link and auxiliary link. : the total number of add/drop ports per bank. : the add/drop contention factor, namely the maximum number of lightpaths that can be added/dropped at the node using the same wavelength (i.e., the number of auxiliary links or add/drop port banks). 98

3 : the offered lightpath traffic load on nodal degree link k. : the total offered lightpath traffic load at the node. : the node lightpath blocking probability due to the limited number of add/drop ports. wavelengths available for connection establishment between the add/drop ports and a certain nodal degree link. wavelengths on a nodal degree link. : the probability that there are free wavelengths on a nodal degree link. : the call setup rate on a nodal degree link when there are free wavelengths on the link. : the probability that a particular wavelength is free on a nodal degree link. wavelengths on an auxiliary link. : the probability that there are free wavelengths on an auxiliary link. : the call setup rate on an auxiliary link when there are free wavelengths on the link. : the probability that a particular wavelength is free on an auxiliary link. the average lightpath blocking probability of the node. The detailed analysis for lightpath blocking performance of a single node is made as follows. First, the approximate offered load at the node is calculated as (1) where term sums the offered loads of all the nodal degrees, and term finds the load carried by the node, which is approximately smaller than the total offered load of the node by factor. Next we calculate the lightpath blocking probability due to the limited number of add/drop ports by Erlang-B formula as E(, ) T C λ n (T C)! j T C λ n j= j! where is the number of add/drop ports per bank at the node. ith C add/drop banks, there are a total of add/drop ports at the node. e assume a birth-and-death process for wavelength status on each fiber link. Thus, the probability that there are free wavelengths on a nodal degree link is calculated as [8]-[9] where ( + ) (2),, (3) [ + ( + ) ] =1 The call setup rate on the degree link when there are wavelengths on the link,, can be further derived as { 1 i { > } i,, (4) free The probability that a particular wavelength is free on the nodal degree link,, can be derived from as + (2) For an auxiliary link, we have similar equations to those of the nodal degree link. Specifically, the probability that there are free wavelengths on the auxiliary link is calculated as where ( + ) =1 [ + ( + ) ] =1 (5) (6),, (7) Based on the previous equations for calculating of the nodal degree link (i.e., equations (3) and (4)), we can get similar equations for the auxiliary link by replacing with, where is calculated as {, i 1 ( ) { > } i,, Here ( ) calculates the average offered traffic load on each add/drop bank with the assumption that the traffic loads on all the nodal degrees are shared by C add/drop banks. Similarly, based on in equation (6), we get the probability that a particular wavelength is free on the auxiliary link by replacing with as + (2) =1 (8) (9) (1) To successfully add/drop a lightpath at the node, we need to ensure both a nodal degree link (through which the lightpath ingresses/egresses) and an auxiliary link to have at least one common free wavelength, and also that there is at least one free add/drop port available at the node. Thus, the probability that a lightpath can be successfully added/dropped when there are free wavelengths on the nodal degree link is { > } ( C ) ( C ) (11) Here term C finds the probability that a specific wavelength is busy on all the auxiliary links of the node, term 99

4 finds the probability that there is at least one common free wavelength on all the auxiliary links when there are free wavelengths on the nodal degree link, and term computes the probability that the node has free add/drop ports. Similarly, the probability that a lightpath can be successfully added or dropped when there are free wavelengths on the auxiliary link is { > } ( ) ( ) (12) Here term finds the probability that there is at least one common free wavelength on the nodal degree link when there are free wavelengths on the auxiliary links. Finally, the node lightpath blocking probability calculated as can be ( ( ( C ) )) (13) Here term is the probability that there are free add/drop ports and term ( ( ( C ) )) finds the probability that there is at least one common free wavelength on both a nodal degree link and an auxiliary link. To calculate the node lightpath blocking probability, we employ an iterative relaxation approach [8]. In the iterative process, let,,,,,,,, and be the values obtained for,,,,,,,, and in the iteration. Here is a predefined small error threshold. The detailed steps of the iterative solution are given below: (1) Let and be ; let and be arbitrary values between and 1.; (2) Set t=1; (3) Calculate using (1) and using (2); (4) Calculate using (5) (11) and using (9) (12); (5) Calculate using (3) (4) and using (7) (8); (6) Calculate using (6) and using (1); (7) Find by (13). If 1, then stop; otherwise, set t=t+1 and go to Step 3. IV. RESULTS AND PERFORMANCE ANALYSES e evaluate the lightpath blocking performance for colorless and directionless ROADM with intra-node add/drop contention using both simulations and the analytical model presented in the previous Section. All the degree links are considered equivalent and so are all the auxiliary links. Lightpath requests are assumed to follow a Poisson arrival process and the holding time of each lightpath is assumed to follow a negative exponential distribution. For simplicity, we normalize the time such that the average holding time of each established lightpath is unity (i.e., ). The offered lightpath traffic load per nodal degree is assumed to be the same. Each fiber link maximally carries 16 wavelengths in a 3-degree node and 4 wavelengths in a 4-degree node. 1 6 lightpath arrival requests are simulated to find each lightpath blocking probability point. Figs. 3 and 4 show the results of the analytical model and the simulations for different numbers of add/drop ports per bank,. Each nodal degree is assumed to have a fixed 6.- Erlang offered traffic load in Fig. 3 and 22.-Erlang offered traffic load in Fig. 4. The dashed curves correspond to the results of the analytical model and the solid curves are the results of the simulations. According to the results, we can see that for the ROADM node with intra-node contention, the analytical results are in good agreement with the results of the simulations. In addition, we can see that increasing the number of add/drop ports per bank can significantly improve the node lightpath blocking performance. It is also reasonable to expect that with an increasing number of add/drop banks C, the lightpath blocking performance can be significantly improved. This is because a larger C corresponds to a larger number of add/drop ports at the node and a larger number of optical channels that are allowed to use the same wavelength added/dropped at the node. However, it should be noted that when the add/drop contention factor C is larger than the number of node degrees, there will be no performance effect even if C is further increased because compared to the number of nodal degrees there are more than enough add/drop ports that can use the same wavelength. 1.E Number of add/drop ports per bank Fig. 3: Node lightpath blocking probability versus limited number of add/drop ports per bank (3-degree; offered load: 6. Erlang per degree) 1.E-3 Ana(C=3) Sim(C=3) Number of add/drop ports per bank Fig. 4: Node lightpath blocking probability versus limited number of add/drop ports per bank (4-degree; offered load: 22. Erlang per degree) Figs. 5 and 6 show similar results from the perspective of a fixed number of add/drop ports per bank (i.e., 16 for the 3- degree node and 4 for the 4-degree node) and variable 1

5 offered traffic loads per nodal degree. e can see that the lightpath blocking probability increases with the increase of offered traffic load per degree and decreases significantly with an increasing add/drop contention factor C. e also see that the analytical model is effective in predicting the simulation results. 1.E Fig. 5: Node lightpath blocking probability versus offered load (in Erlang) per degree (3-degree; 16 add/drop ports per bank) Offered load per degree (in Erlang) 1.E-3 Ana(C=3) Sim(C=3) Offered load per degree (in Erlang) Fig. 6: Node lightpath blocking probability versus offered load (in Erlang) per degree (4-degree; 4 add/drop ports per bank) V. CONCLUSION This paper analyzed the impact of the ROADM intra-node contention constraint on node lightpath blocking performance based on the analytical model and the simulations. The results showed that the analytical model can effectively predict the node lightpath blocking performance under different combinations of contention factor C, the number of add/drop ports per bank, and offered traffic load per nodal degree. e also observed that properly raising the contention factor C can significantly improve node lightpath blocking performance. [2] P. Roorda and B. Collings, Evolution to colorless and directionless ROADM architectures, in Proc. OFC/NFOEC 28, pp. 1-3, San Diego, US, Feb. 28. [3] R. Jensen, A. Lord, and N. Parsons, Highly scalable OXC-based contentionless ROADM architecture with reduced network implementation costs, in Proc. OFC/NFOEC 212, pp. 1-3, Los Angeles, US, Mar [4] S. L. oodward, M. D. Feuer, P. Palacharla, X. ang, I. Kim, and D. Bihon, Intra-node contention in a dynamic, colorless, non-directional ROADM, in Proc. OFC/NFOEC 21, pp. 1-3, San Diego, US, Mar. 21. [5] M. D. Feuer, S. L. oodward, P. Palacharla, X. ang, I. Kim, and D. Bihon, Intra-node contention in dynamic photonic networks, IEEE/OSA Journal of Lightwave Technology, vol. 29, no. 4, pp , Feb [6] G. Shen, S. K. Bose, T. H. Cheng, C. Lu, and T. Y. Chai, Performance analysis under dynamic loading of wavelength continuous and noncontinuous DM networks with shortest-path routing, International Journal of Communication Systems, vol. 14, no. 4, pp , May 21. [7] G. Shen, T. H. Cheng, S. K. Bose, C. Lu, T. Y. Chai, and H. M. M. Hosseini, Approximate analysis of limited-range wavelength conversion all-optical DM networks, Computer Communications, vol. 4, no. 1, pp , May 21. [8] Y. Li, L. Gao, G. Shen, and L. Peng, Impact of ROADM colorless, directionless, and contentionless (CDC) features on optical network performance [Invited], IEEE/OSA Journal of Optical Communications and Networking, vol. 4, no. 11, pp. B58-B67, Nov [9] A. Birman, Computing approximate blocking probabilities for a class of all-optical networks, IEEE Journal on Selected Areas in Communications, vol. 14, no. 5, pp , Jun [1] S. Subramaniam, M. Azizoglu, and A. K. Somani, All-optical networks with sparse wavelength conversion, IEEE/ACM Transactions on Networking, vol. 4, no. 4, pp , Aug [11] R. A. Barry and P. A. Humblet, Models of blocking probability in alloptical networks with and without wavelength changers, IEEE Journal on Selected Areas in Communications, vol. 14, no. 5, pp , Jun [12] G. Shen, T. H. Cheng, S. K. Bose, C. Lu, T. Y. Chai, and H. M. M. Hosseini, Approximate analysis of limited-range wavelength conversion all-optical DM networks, Computer Communications, vol. 4, no. 1, pp , May 21. [13] L. Gao, Y. Li, and G. Shen, Modeling the impact of ROADM intra-node add/drop contention on optical network performance, in Proc. ACP 213, pp. 1-3, Beijing, China, Nov [14] P. Pavon-Marino and M. V. Bueno-Delgado, Dimensioning the add/drop contention factor of directionless ROADMs, IEEE/OSA Journal of Lightwave Technology, vol. 29, no. 21, pp , Nov ACKNOLEDGMENTS This work was jointly supported by the National 863 Plans Project of China (212AA1132), National Natural Science Foundation of China (NSFC) ( , ), and Research Fund for the Doctoral Program of Higher Education of China ( ), and Natural Science Foundation of Jiangsu Province (BK212179, BK2133). REFERENCES [1] S. Gringeri, B. Basch, V. Shukla, R. Egorov, and T. J. Xia, Flexible architectures for optical transport nodes and networks, IEEE Communications Magazine, vol. 48, no. 7, pp. 4-5, Aug