Abstract: We propose new design models for mixed-line-rate (MLR) optical ... between transponder cost and regenerator card cost using mixed line rates.
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Transparent vs. Translucent Optical etwork Design with Mixed Line Rates Avishek ag1 and Massimo Tornatore2 1
Department of Electrical and Computer Engineering, University of California Davis 2 Department of Computer Science, University of California Davis {anag,mtornatore}@ucdavis.edu
Abstract: We propose new design models for mixed-line-rate (MLR) optical networks with no regeneration (transparent) and selective regeneration (translucent). Our results show the interplay between transponder cost and regenerator card cost using mixed line rates. © 2009 Optical Society of America OCIS codes: 060.4250
1. Introduction The traffic in today’s backbone networks is increasing and becoming more heterogeneous. Different types of new applications (IPTV, VoD, VoIP, etc.) are associated with different bandwidth granularities of the traffic demands that converge on the optical backbone network. Hence, a next-generation backbone network will be versatile if it can support mixed line rates (MLR) over its links, e.g., 10/40/100 Gbps. MLR provides a lot of flexibility in assigning line rates to a particular demand. In such a network, a low-bit-rate service may need minimal or no grooming (i.e., multiplexing with other low-bit-rate services onto high capacity wavelengths), while a high-bit-rate service can be set up directly over a single wavelength [1]. In optical WDM backbone networks, MLR can be facilitated by having different sets of wavelengths that can support different rates. Thus, the routing and wavelength assignment (RWA) problem modifies to routing, wavelength, and rate assignment (RWRA). In the design of such a network, the tradeoffs are as follows: (1) there should be reasonable number of high bit-rate paths (i.e., the ones with 40G and 100G line rates), as they provide volume discount; and (2) the more high-bit-rate paths are used, more is the investment on regenerator cards, as the high-bit-rate paths have limited optical reach (note that physical signal impairments vary with line rates). In this paper, we propose a cost-effective design of an MLR network with due consideration to regeneration (translucent architecture). This approach is compared with a transparent design proposed in [2]. Our results show that an effective placement of regenerators for paths with higher bit rates, combined with cost optimization, can further reduce the overall cost in a translucent network compared to a transparent network. In Section 2, we present our mathematical model. In Section 3, illustrative results are presented. 2. Mathematical Formulation for the MLR Design Problem with Regenerator Placement The mathematical formulation for our design problem turns out to be a two-step integer linear program (ILP). In the first step, an optimal regenerator placement problem is solved for the MLR scenario. Regenerators are needed since long paths, especially with higher bit-rates (40/100 Gbps) may not be utilizable in a transparent network, due to excessive physical impairments (i.e., they do not respect a BER threshold). The BER is calculated using an analytical model which considers accumulated optical noise and crosstalk, fiber chromatic dispersion, optical filter and laser center frequency misalignment and receiver beat noises [2]. Then, our focus is to enable as many highbit-rate paths as possible, with a given upper bound on the total number of regenerator cards. With this information as input we solve another optimization problem which minimizes the total network cost comprising of the cost of transponders and regenerator cards of various line rates. The ILPs are presented below. Input Parameters: −G(V , E) : Physical topology −T = [ Λsd ] :Traffic Matrix with aggregate demands Λsd (in Gbps) between a s-d pair −R = {r1, r2 ,...., rk }:Set of available channel rates −Dk (Ck ) : Cost of a transponder (regenerator) with rate rk −lijk : lightpath between a node pair i-j on rate k −Pmn : Set of lightpaths passing through physical link m-n −B : Threshold bit-error rate (BER)
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−BERijk : Denotes the BER for the lightpath lijk 1 , if BERijk ≤ B −αijk = ∀ (i, j),k 0 , otherwise (denotes whether a lightpath lijk is feasible or not based on threshold BER) −L = {lijk | αijk =0, ∀ijk} (denotes the set of unfeasible lijk 's based on threshold BER) −W : Maximum number of wavelengths supported on a link, λ ∈{1,2,....,W} −K : Maximum number of regenerators that can be placed in the network
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Variables (1st Step): − X ijk
1, if lightpath lijk is feasible due to = regenerator placement 0, otherwise
−Yek ( ij )
− Z ek (ij )
1, if an intermediate node e along the path connecting end-nodes ij enables = regeneration for rate rk 0, otherwise
Maximize
∑
X ijk
1, if an intermediate node e for lijk exists, where lijk can be fragmented into two feasible = lightpaths 0, otherwise
1, if both Yek (ij ) and Z ek ( ij ) takes value 1 −Wek ( ij ) = 0, otherwise − . ek = number of regenerators at node e of line rate rk
(1)
i, j ,k
Such that : Z ek ( ij ) ≥ α iek + α ejk − 1
(2a)
Z ek ( ij ) ≤ α iek
(2b)
Z ek ( ij ) ≤ α ejk
(2c)
X ijk ≤ Wek ( ij )
(4)
Wek ( ij ) ≥ Z ek ( ij ) + Yek ( ij ) − 1
(3a)
Wek ( ij ) ≤ Z ek ( ij )
(3b)
Wek ( ij ) ≤ Yek ( ij )
(3c)
. ek ≥ ∑ Yek ( ij ) ∀ k
∑.
(5)
i, j
≤K
ek
(6)
e,k
In the first step, our aim is to identify a set of candidate regenerators, so that they can support effectively long and high-bit-rate paths in the network. The objective function (1) maximizes the number of paths which were infeasible according to the threshold BER requirement but become feasible due to the regenerator placement. Equation (2a), (2b), and (2c) assign value equal to 1 to variable Z, on a node e and rate k, if the placement of a regenerator in e would allow to enable the lightpath lijk (i.e., if the two fragments liek and lejk are feasible). Equations (3a) (3b) and (3c) assign value equal to 1 to variable W, on a node e and rate k, if Z=1 and Y=1 (Y assumes value equal to 1 when a regenerator is actually deployed in node). Equation (4) allows discovering the newly-enabled lightpaths according to the regenerator placement. Equation (5) evaluates the number of regenerators placed in each node e for each link-rate k. Equations (6) imposes a maximal value on the expenditure for regenerators. Let Q= {lijk:| Xijk=1}, which become feasible after solving the first step and let Se be the set of lightpaths passing through node e. With the solution of the 1st step as input we solve the 2nd step of the problem. Variables (2nd Step): xijk λ : Denotes the number of lightpaths at rate rk and wavelength λ between nodes i -j on the logical topology f ijsd : Denotes traffic from source s to destination d on lightpath i -j
Minimize
x ∑∑∑ λ
ijkλ
i, j
k
Dk + ∑∑∑xijkλCk
(7)
λ i , j∈Q k
Such that : Λsd , if s = j sd sd ∑i fij − ∑i f ji = −Λsd , if d = j ∀ (i, j) 0, otherwise
rx ∑∑ λ
α ≥ ∑ fijsd ,∀ (i, j)
k ijkλ ijk
k
(10)
(8)
s,d
∑ ∑x
α ≤ 1 ,∀ (m, n),∀λ
ijkλ ijk
(9)
(i, j )∈Pmn k
∑ ∑x
ijkλ
≤ .ek ∀e, k
(11)
i , j∈Q∩Se λ
The second step gives the total optimized cost of the network in terms of the transponders and regenerator cards. Equations (8)-(10) signify the capacity, wavelength-continuity, and flow constraint respectively, while Eqn. (11) signifies the limit on the number of bypass lightpaths that can be regenerated at a node. 3. Results and Discussion Our formulation is applied on the network topology shown in Fig. 1 (where all link lengths are in km) and with line rates of 10 Gbps, 40 Gbps, and 100 Gbps. The costs of 10G, 40G, and 100G transponders are, respectively, 1x, 2.5x and 4.5x. Thus, higher-rate transponders provide volume discount. The analysis is presented for both a uniform and a non-uniform traffic matrix: the non-uniform traffic matrix is given in Table I. It represents a total traffic of 1 Tbps, which is then multiplied by different factors to represent a range of loads. First, we present the result for a transparent MLR network, where there is no intermediate fragmentation of lightpaths due to regeneration. In such a case, the constraint denoted by Eqn. (11) will be absent and, in the cost function, the cost of
© 2009 OSA/OFC/NFOEC 2009
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transponders is optimized only. Moreover, the first step (i.e., the regenerator placement routine) is not required for transparent design: in this context, it is worth mentioning that the 10G line rate does not require any regeneration considering the present problem setting. In the transparent scenario, the volume discount that high-bit-rate paths provide over several low-bit-rate paths can not be exploited as longer paths are constrained to take lower bit-rates. So, in the attempt to exploit these volume discounts, we put regenerators, over the different line rates, in the network (translucent cases). According to the previous formulation, we first consider the maximal number of regenerators K and set it to 10, 20, and 40 (after 40, results show a saturation effect), and find an effective distribution of the same over the network. Table 1 shows the distribution of regenerators. As a second step, we evaluate the optimum cost of the network in the translucent and transparent cases, and how it evolves for increasing traffic and K. Tables 2 and 3 show our results for the case of non-uniform and uniform traffic, respectively. Costs for translucent cases are always less than the costs for the transparent case. So, using MLR, the total network cost can be minimized if one chooses translucent design with effective regenerator placement. This is because regeneration increases the possibility of more high-bit-rate paths and lowers the transponder costs through volume discount. The extra cost of regenerators is compensated by this decrease in the transponder cost. Moreover, we can observe that, with uniform traffic, the savings in cost is more pronounced. This is because, in our non-uniform traffic matrix, most of the bulky demands are along short distances, so that most of the traffic can be served without regeneration. It follows that the network cost savings achievable by using regenerators is significantly dependent on the type of traffic matrix: note that the future network will be more likely to support geographical-distance-uncorrelated data-type of traffic (as in the uniform traffic matrix case), so the role of regeneration in MLR network cost optimization is likely to increase in the years to come.
Fig.1 Network Topology and Traffic Matrix
K=10
1 -
2 -
3 40G=1
4 40G=2
K=20
-
K=40
-
40G=1 100G=2 40G=3 100G=2
40G=1 100G=1 40G=1 100G=1
40G=4 100G=2 40G=6 100G=4
Node
Table 1: Distribution of Regenerators 6 7 8 40G=2 40G=2 100G=1 40G=2 40G=5 100G=1 100G=3 40G=2 40G=1 40G=5 100G=2 100G=5 100G=1
5 -
Table 2: Normalized Network Cost for Non-uniform Traffic Total 1Tbps 2Tbps 3Tbps 4Tbps 5Tbps 6Tbps Traffic Transparent 58 115 173 231 289 347 K=10 57 114 172 229 286 343 K=20 57 114 172 229 285 342 K=40 57 114 172 229 285 341
9 -
10 -
11 -
12 -
13 -
14 -
-
-
-
-
40G=1
-
100G=2
-
-
-
40G=1
100G=1
Table 3: Normalized Network Cost for Uniform Traffic Total Traffic 2Tbps 4Tbps 6Tbps Transparent 137 274 411 K=10 134 269 403 K=20 134 268 402 K=40 134 267 401
To conclude, in this work we have applied our model to a specific setting, i.e., a case-study network with realistic cost parameters and under this scenario; we have discussed the transponder vs. regenerator tradeoffs in designing a cost-effective MLR network. As a next step, we aim to analyze this problem considering a more general traffic and network model and exploring a wider range for the input parameters. Heuristic design methods also have to be devised to obtain scalable solution to this problem. 4. References [1] J. Berthold, A. A. M. Saleh, L. Blair, and J. M. Simmons, “Optical Networking: Past, Present, and Future,” IEEE/OSA Journal of Lightwave Technol., vol. 26, no. 9, pp. 1104.1118, May 2008. [2] A. Nag and M. Tornatore, “Transparent Optical Network with Mixed Line Rates,” accepted in 2nd International Symposium on Advanced .etworks and Telecommunication Systems (A.TS), Dec. 15-17, 2008, Mumbai, India. [3] J. M. Simmons, Optical .etwork Design and Planning, Springer, 2008.
