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Transparent Optical Network Design with Mixed Line Rates. Avishek Nag and Massimo Tornatore. University of California, Davis, USA. Email: {anag ...
Transparent Optical Network Design with Mixed Line Rates Avishek Nag and Massimo Tornatore University of California, Davis, USA Email: {anag, mtornatore}@ucdavis.edu Abstract—Future telecommunication networks are expected to be increasingly heterogeneous and support a wide variety of traffic demands. Based on the nature of the demands, it may be convenient to set up lightpaths with different bit rates. Then, the network design cost could be reduced because low-bit-rate services will need less grooming (i.e., less multiplexing with other low-bit-rate services onto high-capacity wavelengths) while highbit-rate services can be accommodated on a wavelength itself. Future optical networks may support mixed line rates (say over 10/40/100 Gbps). Since a lightpath may travel a long distance, for high bit rates, the effect of the physical impairments along a lightpath may become very significant (leading to high bit-error rate (BER)); and the signal’s maximum transmission range, which depends on the bit rate, will become limited. In this study, we propose a novel, cost-effective approach to design a mixed-linerate (MLR) network with transmission-range (TR) constraint. By intelligent assignment of channel rates to lightpaths, based on their TR constraint, the need for signal regeneration can be minimized, and a “transparent” optical network can be designed to support all-optical end-to-end lightpaths. The design problem is formulated as an integer linear program (ILP). Our results show that, with mixed line rates and maximum transmission range constraints, one can design a cost-effective network. Index Terms—Optical Network, WDM, Network Design, Mixed Line Rate, Signal Regeneration, Maximum Transmission Range, Bit-Error Rate.

I. I NTRODUCTION Traffic flowing through optical backbone networks – which typically employ wavelength-division multiplexing (WDM) – has been increasing steadily, and becoming more heterogeneous as well. As a result, a future-proof optical network needs to be designed which can support mixed line rates (MLR) over different wavelength channels. In such a network, a low-bit-rate service may need minimal or no grooming (i.e., less multiplexing with other low-bit-rate services onto highcapacity wavelengths), while a high-bit-rate service can be set up over a single wavelength [1]. Thus, a MLR network can be a cost-effective heterogeneous optical network design. 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 [2], the design of an opaque MLR network is proposed, where each node has electronic regeneration (which can also support wavelength conversion, grooming, etc.). This work also assumed that all wavelengths on a link run at same rate but different links have different rates. Based on the distance it needs to travel, a lightpath is routed in such a way that it requires minimum regeneration. In this work, (1) we consider a more general approach where a single link can have a combination of bit rates, and each

physical link in the network may support a combination of bit rates, each on a separate wavelength, and (2) our aim is to design a transparent MLR network that will significantly reduce the amount of electronic signal processing at the nodes. Note that the maximum transmission distance of a signal decreases with increasing bit rate based on a threshold bit-error rate (BER) [3]. If we know the network topology (including fiber link lengths) and the traffic demands that need to be carried by it, then we could determine the physical length of each lightpath based on a routing algorithm; then, based on the set of line rates available, we can choose only those paths whose maximum transmission distance is less than the physical length of the route. Hence, it may be beneficial to support different lightpaths at different rates, leading to a MLR network. Such a network is called “transparent” if its end-toend traffic demands flow over all-optical lightpaths with no electronic regeneration. In this study, we propose and investigate the characteristics of a method to design a transparent MLR network. We compare our design with single-line-rate (SLR) networks (where all wavelength channels run at the same bit rate), and we study the corresponding cost savings on network design, measured by the cost of line cards. In this context, the maximum transmission range (TR) could make some of the high-bit-rate paths infeasible and we may lose out on the volume discount that a high-bit-rate path provides over several low-bit-rate paths. Thus, placement of signal regenerators at a few nodes may improve the cost scenario1 . The analysis presented here can be a starting point for exploring the optimal regenerator placement problem in a MLR network. Section II presents our mathematical formulation of the design problem which turns out to be an integer linear programm (ILP). In Section III, illustrative results are presented. Section IV contains conclusion and future work. II. M ATHEMATICAL F ORMULATION Given a network topology (including number of wavelengths on each link), traffic demands, a set of available line rates (say 10/40/100 Gbps), and the cost of the associated transponders, we need to assign rates to the lightpaths such that the overall network design cost (measured in terms of the cost of line cards) is minimized. The constraints are: (1) a lightpath can be set at any rate that can be supported by the lightpath’s distance and the rate’s TR constraint, (2) the number of lightpaths on a link should be bounded by the 1 The concept of regenerator cards used in our model is similar to that discussed in [3].

number of wavelengths supported by the link, and (3) traffic between each source-destination pair should be supported. Our mathematical model, which turns out to be an ILP, is provided below. For sake of simplicity, this preliminary work considers shortest-path routing over the physical topology for the various traffic demands, and other routing approaches are currently being studied. A. Input Parameters •



• • • • •





• •

G(V, E): Physical topology of the network with V nodes and E links.  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 : Cost of a transponder with rate rk . Lij : Length of the lightpath between a s-d pair (in km). lmn : Physical link between nodes m-n. W : Maximum number of wavelengths supported on a link, λ ∈ {1, 2, . . . , W }. B: Threshold BER: a lightpath with a higher BER will be rejected. BERijkλ : BER for the lightpath between a s-d pair ij at rate rkand wavelength λ. 1 if BERijkλ ≤ B αijkλ = ∀ (i, j),k,λ 0 otherwise Pmn : Set of lightpaths passing through link lmn .

B. Variables •



receiver complexity among the advanced modulation formats [5]. The BER threshold is taken as B = 10−3 (worst possible value correctible using error-correcting codes) [5]. The value of W = 80. (For the traffic demands considered here, this is a high value of W which can support all the traffic demands.) Equation (2) sets a capacity constraint on the traffic demands routed over the lightpaths, considering only those lightpaths for which αijkλ = 1. The wavelength-continuity (i.e., optical “transparency”) constraint is taken care of by Eqn. (3), which implicitly also enforces a constraint on the available capacity (number of channels W ) over a physical link. Equation (4) satisfies the flow-conservation constraints. The output of this ILP is the number of lightpaths over different rates and wavelengths. This formulation can be downgraded for a SLR network by forcing the value of rk to a predefined bit rate. III. R ESULTS AND D ISCUSSION We present and discuss illustrative results obtained by our ILP for MLR design, and compare with SLR network design. The network topology used in our study is shown in Fig. 1, where all link lengths are in km. The traffic matrix that was used is given in Table I. It represents a total traffic of 1 Tbps, which is multiplied by different factors to represent a range of loads. The costs of 10G, 40G, and 100G transponders are, respectively, 1×, 2.5× and 4.5×. Thus, higher-rate transponders provide volume discount.

Xijkλ : Number of lightpaths at rate rk and wavelength λk between nodes ij on logical topology. fijsd : Traffic from source s to destination d routed on lightpath ij.

C. ILP Problem Formulation Minimize : such that

λ

XX λ

k

i,j∈Pmn

i

ij

rk · Xijkλ · αijkλ ≥

fijsd −

X i

(1)

Xijkλ · Dk

k

X

fijsd

∀ (i, j)

(2)

Fig. 1.

14-node NSF network (link lengths in km).

s,d

X X

X

XXX

Xijkλ · αijkλ ≤ 1

∀ (m, n), ∀ λ

TABLE I T RAFFIC M ATRIX .

(3)

k

sd fji

  Λsd −Λsd =  0

if s = j if d = j otherwise

∀ (i, j)

(4) The objective function in Eqn. (1) computes the overall cost due to transponders at various bit rates. The αijkλ ’s determine whether a lightpath between a pair of nodes is feasible over a particular wavelength and a bit rate (i.e., respects the BER threshold), and are calculated offline. BERijkλ is evaluated considering optical amplifier noise, crosstalk at intermediate nodes, chromatic dispersion, optical filter misalignment, and receiver noises [4]. The modulation scheme considered is optical duobinary modulation which has least transmitter and

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1 0 2 1 1 1 4 1 1 2 1 1 1 1 1

2 2 0 2 1 8 2 1 5 3 5 1 5 1 4

3 1 2 0 2 3 2 11 20 5 2 1 1 1 2

4 1 1 2 0 1 1 2 1 2 2 1 2 1 2

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6 4 2 2 1 3 0 2 1 2 2 1 1 1 2

7 1 1 11 2 3 2 0 9 4 20 1 8 1 4

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9 2 3 5 2 3 2 4 27 0 75 2 9 3 1

10 1 5 2 2 3 2 20 7 75 0 1 1 2 1

11 1 1 1 1 1 1 1 2 2 1 0 2 1 61

12 1 5 1 2 5 1 8 3 9 1 2 0 1 81

13 1 1 1 1 2 1 1 2 3 2 1 1 0 2

14 1 4 2 2 5 2 4 4 1 1 61 81 2 0

Figure 2 reports the cost of the network, in terms of line cards, for the following four scenarios: MLR network and three SLR networks, each equipped with either 10G, or

350 Mixed 100 G 40 G 10 G

Cost

250 200 150 100 50 0 0

Fig. 2.

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Comparison of transponder costs for SLR and MLR networks.

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the volume discount increases with bit rate: MLR is still the best choice, but now 100G is more cost-effective than 40G and 10G. But, if we use regenerators, their cost must also be counted. So we placed regenerators in the network according to the method proposed in [3] and we include their cost in the network design. The cost increase due to regenerators is very significant. Figure 4 shows the percentage savings in cost for designing networks without regenerators vs. with regenerators.

3.5

Fig. 3. Comparison of transponder costs for SLR and MLR networks without the BER constraints).

40G, or 100G line cards, considering the BER constraint. As expected, an MLR network with BER constraints has always the least cost (because all SLR solutions are part of the MLR solution space). For the SLR cases, interesting considerations arise: (1) at 10G, the cost increases almost linearly with traffic; (2) at 40G, the cost is less than 10G because of volume discount; and finally, (3) at 100G, due to the BER constraint, only a few 100G lightpaths can be used, so many more multihop paths have to be established2 . So the volume discount that 100G can provide, if all paths were feasible, is lost. Note also that there is a crossover in cost performance for 10G and 100G between traffic loads of 2 Tbps and 2.5 Tbps. This is because, for heavy traffic, 100G can support more grooming than 10G. Thus 100G SLR is a better option when the traffic is heavy. These results show that an MLR network is able to effectively support traffic heterogeneity as well as transparency. Now, for the SLR and MLR scenarios, let us assume that the network is equipped with regenerators so that all lightpaths over all rates become feasible [3]3 . For each node equipped with regenerators, we assume that dedicated regenerator cards for all wavelengths are placed and the cost of a regenerator card is 1.4× the cost of a transponder [3]. Figure 3 shows the same cost comparison as in Fig. 2, but considering the network is equipped with regenerators and no BER constraint on lighpath feasibility is needed. Now, the transponder costs will be reduced for 100G and 40G SLR networks and the MLR network (Fig. 3) compared to the costs in Fig. 2. (Note that, for the topology in Fig. 1, the lowest rate (10G) does not require any regeneration). With all paths feasible at all rates, 2 Based on our problem setting, 30% of connections can be set up over single-hop at 100G, 70% at 40G, and 100% at 10G. 3 Placement of regenerators at some nodes makes some of the α ijkλ values to go to 1 from 0 and this increases the number of possible Xijkλ , i.e., feasible paths. This also relaxes the wavelength-continuity constraint for some links, but we are not exploiting this advantage yet. Also the BER constraints will disappear if the link lengths of the network were appropriately reduced.

Percentage Savings in Cost

300

80 60 40 Mixed 40G 100G

20 0 0

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Fig. 4. Percentage cost savings for networks with and without BER constraint (with regenerators’ cost included).

Thus, without the BER constraint, one can gain on the network design cost through volume discount. But eliminating the BER constraint requires a lot of investment on regenerator cards. Thus, by placing regenerators at some selective nodes, we can obtain a more cost-effective design. So, the optimum placement of regenerator cards in an MLR network is an important open problem for future research. IV. C ONCLUSION

AND

F UTURE W ORK

We developed a novel approach to design a cost-effective mixed-line-rate (MLR) network. We showed how the MLR network’s cost evolved with increasing traffic compared to single-line-rate (SLR) networks. Our study showed that we can design a cost-effective MLR network by intelligent assignment of bit rates to the lightpaths while satisfying all the traffic demands. The ILP formulation takes several hours to return an optimum solution and heuristic algorithms need to be devised in future. We are also looking to extend this design for dynamic configurations. R EFERENCES [1] J. Berthold, A. A. M. Saleh, L. Blair, and J. M. Simmons, “Optical Networking: Past, Present, and Future,” IEEE/OSA J. Lightwave Technol., vol. 26, no. 9, pp. 1104–1118, May 2008. [2] M. Batayneh, D. A. Schupke, M. Hoffmann, A. Kirstdter, and B. Mukherjee, “Optical Network Design for a Multiline-Rate Carrier-Grade Ethernet Under Transmission-Range Constraints,” IEEE/OSA J. Lightwave Technol., vol. 26, no. 1, pp. 121–130, Jan. 2008. [3] J. M. Simmons, Optical Network Design and Planning, Springer, 2008. [4] B. Ramamurthy, D. Datta, H. Feng, J. Heritage, and B. Mukherjee, “Impact of Transmission Impairments on Teletraffic Performance of Wavelength-Routed Optical Networks,” IEEE Journal of Lightwave Technol., vol. 17, no. 10, pp. 1713–1723, Oct. 1999. [5] P. J. Winzer and R.-J. Essiambre, “Advanced Modulation Formats for High-Capacity Optical Transport Networks,” IEEE/OSA J. Lightwave Technol., vol. 24, no. 12, Dec 2006.