Photon Netw Commun DOI 10.1007/s11107-008-0113-6

Simulation-based SONET ADM optimization approach for dynamic traffic grooming in WDM optical networks Kuntal Roy · Mrinal Kanti Naskar

Received: 27 July 2006 / Accepted: 23 July 2007 © Springer Science+Business Media, LLC 2008

Abstract The article addresses a simulation-based optimization approach for allocation of ADMs in WDM optical networks with stochastic dynamic traffic. Since ADMs are expensive, it is desirable that if each node in WDM optical networks can use a minimum number of ADMs to achieve a near-ideal performance. In this article, first, the utilization statistics of ADMs are gathered by simulation. Then, ADMs are allocated based on the utilization statistics. In this respect, a simple sorting mechanism is used. The distinguished feature of the proposed approach is that it shows the way to allocate ADMs at the nodes of WDM optical networks with stochastic dynamic traffic. The experimental results ensure that the proposed approach can solve the problem of allocating ADMs in practical WDM optical networks considering stochastic dynamic traffic. Keywords WDM optical networks · SONET add-drop multiplexer · Dynamic traffic grooming · Sorting algorithm

1 Introduction Wavelength division multiplexing (WDM) [1,2] coupled with the synchronous optical network (SONET) [3,4] has emerged as a promising technology for use in backbone networks. Multiple signals distinguished by their wavelengths can be carried through a fiber using WDM technology [5–7]. The reason behind the bandwidth-division of a fiber is that its K. Roy (B) · M. K. Naskar Department of Electronics and Tele-Communication Engineering, Jadavpur University, Kolkata 700032, India e-mail: [email protected] M. K. Naskar e-mail: [email protected]

bandwidth is too high to carry a single signal. As the technology progresses, transmission-speed of fiber is also increasing from OC-48 (2.5 Gbps) to OC-192 (10 Gbps). As there are some constraints (e.g., power consumption) in increasing the number of wavelength channels without limit using WDM technology, the recent trend is to employ TDM slots within a wavelength channel itself. The resulting network configuration is known as WDM-TDM network or WDM grooming network [8–10]. At each node in the network, there are SONET add-drop multiplexers (ADM) for each wavelength to add or drop signal streams. An ADM has the capability to sum up lower-rate signals into a higher-rate signal. For example, four OC-48s can be multiplexed into an OC-192. But, the cost of ADMs dominates the total cost of designing WDM optical networks. As the nodes in a network increase, the number of ADMs required also increases by an amount equal to the number of wavelength channels in the network per node. Fortunately, it is not necessary for every node to be equipped with ADMs for all wavelengths. The ADM corresponding to a wavelength is required only to transmit or receive signals at that wavelength. Therefore, tremendous efforts have been exploited to minimize the number of ADMs in SONET/WDM networks.

1.1 Previous works There are different approaches found in the literature to optimize the performance of WDM networks on the basis of ADM minimization. The approaches proposed in [11–14] are the first-stage works on this field. In the next stage, there are some theoretical approaches to compute the lower-bound of ADMs for all-to-all uniform traffic and proof of NP-completeness as in [14,15]. Some good-illustrations of traffic grooming in optical networks have been presented in [16,17].

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In [18], greedy heuristic algorithms are proposed for arbitrary static traffic to minimize the number of ADMs. There are several other approaches for the same purpose [19–21]. In [22,23], Integer Linear Programming (ILP) and simulatedannealing are used as a optimization tools to solve the problem. In [23], there is a detailed comparison among greedy heuristic, ILP, and simulated annealing for different grooming-capabilities and for different types of traffic. All the aforesaid cases correspond to WDM networks with static traffic. In [24,25], the ADM optimization problem corresponding to deterministic dynamic traffic is studied. In very recent progress, the authors have proposed a genetic evolutionary approach [26] and a heuristic approach [27] to solve the same with static traffic. Although, lots of research have been performed to optimize the number of ADMs for WDM optical networks with static traffic and few for the same with deterministic dynamic traffic, i.e., the offered traffic is characterized by a set of traffic matrices, the same with stochastic dynamic traffic is hardly studied in the literature. 1.2 Proposed approach In recent years, minimization of ADMs in WDM optical networks have gained lots of attention in both the research and commercial arenas. The practical need is to allow stochastic dynamic traffic. This motivates the research presented in this article. The proposed approach is composed of two subsequent steps: (a) Gather utilization statistics of ADMs by simulation. (b) Optimize the allocation of ADMs depending on the utilization statistics. First, utilization statistics of ADMs at every node for different wavelength channels is recorded via computer simulation. It determines how many times a node requires a particular ADM during simulation. Simulation algorithm should be incorporated with the same Routing and Wavelength Assignment (RWA) algorithm that is used for the WDM optical networks in practice. In this article, shortest path routing and first-fit wavelength assignment have been assumed to make it simple. Furthermore, the same probability for each node to be source or destination has been assumed. It might happen that a node does not require an ADM corresponding to a certain wavelength. It largely depends on the network configuration. The utilization statistics efficiently include all such information. During the simulation, the endeavor is to reduce the number of overall required ADMs. Since, a simulation-based optimization approach has been adopted in this article, the proposed approach is not restricted to a specific network model or traffic characteristics. Thus, the number of required ADMs can be determined to achieve a certain given blocking probability for WDM optical networks.

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The article is organized as follows. Section 2 presents the problem statement. In Sect. 3, the steps of the proposed algorithm are described in subsequent sub-sections. The timecomplexity analysis of the proposed algorithm is performed in Sect. 4. Experimental results are presented in Sect. 5. Finally, Sect. 6 concludes the article.

2 Problem statement The following notations and conventions are used. N = Number of nodes in the WDM optical network. W = Number of different wavelength channels in the network. T = Total number of available ADMs. U = Utilization matrix (of order N × W ), in which the (i, j)th entry (where, 1≤ i ≤ N, 1≤ j ≤W ) denotes the percentage of time that an ADM corresponding to the jth wavelength is utilized at node i. Here, it is considered that T < N * W. Otherwise, the optimization problem becomes simple as it only requires to allocate ADMs at every nodes for every wavelengths. x = ADM allocation matrix (of order N × W ) where, ⎧ ⎨ 1 if ADM corresponding to thej th x(i, j ) = wavelength is allocated to node i ⎩ 0 otherwise So, the total utilization for all ADMs at node i is jW=1 U (i, j ) × x(i, j ). Correspondingly, the total utilization for all nodes due to the jth wavelength is N 

U (i, j ) × x(i, j ).

i=1

Consequently, the objective function can be formulated as follows, N Maximize i=1 jW=1 U (i, j ) × x(i, j ) subjected to the following constraints (i)

W N   i=1 j =1

x(i, j ) = T

(ii) x(i, j ) ∈ {0, 1}. But, further enhancement over the aforesaid objective function has been proposed due to some critical situation that might arise as described below. The aforesaid objective function remains as the prime criteria. If there is any conflict during the allocation of ADMs due to similar entries in different position of the utilization matrix, we choose the position (m1, n1) over (m2, n2) if the following condition holds.

Photon Netw Commun

⎧ ⎪ ⎨UNn1 > UNn2

for m1 = m2, n1 = n2 or m1 = m2, n1 = n2

⎪ ⎩ UADMm1 > UADMm2 for m1 = m2, n1 = n2

(1) (2)

where, the total utilization for all nodes due to the n-th wavelength is UNn =

N 

U (m, n) × x(m, n)

(3)

m=1

and the total utilization for all ADMs at node m is UADMm =

W 

U (m, n) × x(m, n).

source and destination nodes. The corresponding pseudocode is given in Appendix A.

(4)

n=1

The rationale behind this approach is to efficiently exploit the trend of utilizing a particular ADM specific to a wavelength. It also takes care of the fact that a connection has to be established between a node-pair through a particular wavelength channel, and it requires an ADM at both the source and destination nodes for that particular wavelength. Even if, some conflict occurs due to the same UN/UADM, the proposed algorithm selects the positions arbitrarily. Since the experiments are to be performed off-line, we can sacrifice some computation time to achieve better blocking probability by careful handling of the critical situations as described above. 3 Proposed algorithm The proposed algorithm works with three consecutive steps: A. Collect utilization statistics of ADMs. B. Allocate ADMs depending on utilization statistics. C. Simulation with the allocated ADMs. The steps are described below. 3.1 Collect utilization statistics of ADMs In this step, we perform a simulation to collect the utilization statistics for the ADMs. We have assumed that every node has ADMs corresponding to all wavelengths. As the simulation proceeds, the proposed algorithm tries to minimize the number of ADMs required and in this way the utilization of the ADMs is determined. For the Routing and Wavelength Assignment Algorithm (RWA), the shortest path routing and first-fit wavelength assignment algorithm have been used to make it simple. During the simulation, the algorithm first tries to establish a new call with the ADMs already allocated to both the source-destination node-pair. If a lightpath cannot be set for the call in this way, the algorithm selects any opportunity by using one additional ADM only. Even if the call cannot be established, the algorithm has no other opportunity but to provide two more ADMs corresponding to the

3.2 Allocate ADMs Depending on the utilization statistics received from the previous step and the number of available ADMs, allocation of the ADMs needs to be done. In this context, we have used the standard Quick sort algorithm to sort all the entries of the utilization matrix in descending order and then allocated the available ADMs from top to bottom. If there occurs any conflict during the allocation of ADMs due to similar entries in the utilization matrix, it is resolved according to the intuitive based reasoning described in Sect. 2. The pseudocode is given in Appendix B. 3.3 Simulation with allocated ADMs In this step, we assess the blocking performance of the network with the allocated ADMs as done in the previous step. The same Routing and Wavelength Assignment (RWA) algorithm i.e., the shortest path routing and first-fit wavelength assignment have been used. A call is blocked if ADMs corresponding to both the source and destination nodes cannot be found after route and wavelength channel for the lightpath are fixed, i.e., after fixing the route, a continuous wavelength channel throughout the route corresponding to the set of common ADMs for the source and destination nodes has to be found. If it cannot be established in this way, the call is blocked. The corresponding pseudocode is provided in Appendix C.

4 Time-complexity analysis To analyze the time-complexity, the following notations have been used. N = Number of nodes in the WDM optical network. W = Number of wavelength channels in the network. C = Number of TDM slots in a wavelength channel. T = Number of available ADMs. P = Number of hops from a source node to a destination node. F = Number of conflicting positions in a simulation (described as critical situation in Sect. 2). Time required: • To search WADM wavelength channels for free TDM slots is O(P × WADM × C). • To sort the entries of utilization matrix in descending manner is O(N × W × log(N × W )). • To check conflicting situation is O(F).

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• To sort the array corresponding to conflicting positions is O(F 2 ). • To allocate the ADMs is O(T ). So, the total time required to allocate the ADMs at the nodes of WDM optical networks depending on utilization statistics is O(N × W × log(N × W ) + F + F 2 + T ). If no conflicting situation arises during the allocation of ADMs, i.e., F = 0, the total time required is O(N × W × log(N × W ) + T ).

5 Results The well-known NSFNET model (shown in Fig. 1) has been used in the simulation. It has 14 nodes and 21 duplex links. It is assumed that all the links between the nodes have same number of wavelength channels (W = 8) and each wavelength channel has equal number of TDM slots (C = 3). The request arrival rate is assumed to follow a Poisson distribution with rate, λ = 10. The connection duration time follows a negative exponential distribution with mean of 1 time unit. For a large number of calls (≈ 100,000), the simulation has been performed. In this context, every node is assumed to have equal probability to be source or destination. As stated, shortest path routing and first-fit wavelength assignment has been incorporated. It is also assumed that every node has ADMs for all wavelength channels whether required or not. Table 1 shows the percentage utilization of the ADMs for a certain experiment with the configuration stated above. The rows denoting the corresponding nodes and the columns denote the percentage utilizations of the ADMs corresponding to the wavelength channels.

Fig. 1 NSFNET T1 backbone Network (not drawn to scale)

From Table 1, it can be observed that the sum of all the entries is 200 as a lightpath between a node-pair corresponding to a certain call needs two ADMs (corresponding to source and destination nodes). Furthermore, it can be noticed that there are some zero entries even if in the first or second column. It signifies that for those wavelengths, the corresponding nodes have not transmitted/received any call that is intended to reduce the number of required ADMs. For this particular experiment, the number of ADMs required is 91 that can be verified by counting the number of non-zero entries in Table 1. To maintain accuracy, we have performed similar experiments as above 30 times and averaged it in Table 2. The next step is to allocate ADMs depending on the utilization statistics (Table 2) and the number of available ADMs. In this regard, a different number of available ADMs is considered with the same utilization statistics. Tables 3– 5 show the allocation of 56, 75, and 90 ADMs, respectively, for the utilization statistics of Table 2. Next, with different assignment of ADMs, the blocking performance of the NSFNET network with the same

Table 1 Percentage Utilization (for a certain experiment) of ADMs in NSFNET WDM network with W = 8 and C = 3 W1

W2

W3

W4

W5

W6

W7

W8

Node 1

3.80

0.00

3.20

0.65

0.00

0.35

0.10

0.00

Node 2

6.95

3.80

2.45

1.35

0.50

0.40

0.00

0.10

Node 3

7.15

4.15

2.05

1.75

0.90

0.20

0.00

0.00

Node 4

7.55

4.10

1.70

0.90

0.55

0.20

0.05

0.00

Node 5

7.95

3.85

1.70

0.80

0.55

0.10

0.00

0.05

Node 6

8.45

2.80

1.70

1.25

0.00

0.45

0.15

0.00

Node 7

7.05

4.15

1.80

1.00

0.35

0.25

0.10

0.05

Node 8

0.00

10.2

1.35

2.20

0.55

0.15

0.05

0.00

Node 9

7.15

3.65

1.85

0.35

1.70

0.35

0.05

0.00

Node 10

7.75

3.80

2.60

1.10

0.60

0.15

0.10

0.00

Node 11

7.15

4.60

2.45

1.30

0.80

0.40

0.05

0.00

Node 12

8.10

3.55

2.10

0.75

0.30

0.15

0.00

0.10

Node 13

0.00

9.10

3.95

1.55

0.80

0.25

0.15

0.00

Node 14

3.95

1.65

0.80

0.65

0.20

0.00

0.00

0.00

123

Photon Netw Commun Table 2 Average percentage utilization of ADMs in NSFNET WDM network with W = 8 and C = 3 3.912347

1.170702

1.390835

0.750450

0.35021

0.150090

0.030018

0.000000

5.833500

5.143086

2.531519

1.170702

0.620372

0.120072

0.110066

0.030018

6.353812

4.302582

2.131279

1.210726

0.740444

0.250150

0.110066

0.060036

8.284971

3.832299

1.390835

1.600961

0.510306

0.250150

0.110066

0.030018

8.915349

2.781669

1.350810

1.340804

0.800480

0.080048

0.090054

0.020012

8.535121

3.271963

1.620973

1.050630

0.290174

0.180108

0.150090

0.000000

7.324395

3.602161

2.081249

0.690414

0.600360

0.200120

0.100060

0.030018

6.633980

4.222534

1.280768

1.961177

0.540324

0.340204

0.080048

0.020012

7.694617

3.352011

1.600961

1.080648

0.730438

0.140084

0.130078

0.040024

7.984791

3.762257

2.021213

1.080648

0.420252

0.240144

0.080048

0.020012

7.514509

4.122473

2.091255

1.290774

0.630378

0.350210

0.070042

0.020012

8.475085

3.482089

1.991195

0.860516

0.420252

0.200120

0.060036

0.030018

6.033620

4.742846

2.471483

0.990594

0.610366

0.240144

0.190114

0.020012

4.182510

1.500901

1.180708

0.470282

0.580348

0.100060

0.030018

0.000000

Table 3 Allocation of 56 ADMs for the utilization statistics of Table 2 1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

Table 4 Allocation of 75 ADMs for the utilization statistics of Table 2 1

1

1

1

1

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

0

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

0

0

0

123

Photon Netw Commun Table 5 Allocation of 90 ADMs for the utilization statistics of Table 2 1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

0

0

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

0

0

1

1

1

1

1

1

1

0

1

1

1

1

1

1

0

0

configuration has been simulated. The corresponding curve is shown in Fig. 2. The curve in Fig. 2 signifies the trend of reduced blocking probability with increased number of ADMs. Accordingly, the number of required ADMs can be determined to achieve a certain blocking probability. Now, handling of the critical situation that might arise during the allocation ADMs due to similar entries in the utilization statistics as described in Sect. 2 will be highlighted. Even if there are similar entries in the utilization statistics of Table 2, a modified one (Table 6) has been chosen to present the conflict and the proposed solution in a more directive manner. In Table 6, it can be observed that there are similar entries for the positions U(3, 4), U(3, 5) and U(5, 5) and the corresponding values, 0.917217 are shown in bold. Let us assume that the given number of ADMs is 52, i.e., there is only one ADM for the aforesaid three conflicting places. The corresponding allocation is shown in Table 7. It can be observed from Table 7 that the proposed algorithm has allocated the last ADM to location (3, 4) instead of (3, 5) or (5, 5). The reason according to Sect. 2 is described below. First, let us compare positions (3, 4) and (3, 5) in this respect. Rule (1) in Sect. 2 will be applicable in this case as the row indices for the positions are same. According to Eq. 3 in Sect. 2, UN4 = (1.170702 + 1.600961 + 1.340804 + 1.05063 + 1.961177 + 1.080648 + 1.080648 + 1.290774 + 0.990594) = 11.56694. UN5 = 0. So, UN4 > UN5 . Subsequently, position (3, 4) has preference over position (3, 5).

123

Fig. 2 Number of ADMs versus Blocking Probability for W = 8, C = 3 in the NSFNET Network

Now, positions (3, 4) and (5, 5) are compared. Also, for this case, rule (1) is applicable. Similarly as above, according to Eq. 3 in Sect. 2, UN4 = 11.56694. UN5 = 0. Apparently, UN4 > UN5 and position (3, 4) has preference over position (5, 5). So, position (3, 4) has greater preference over positions (3, 5) and (5, 5). But, positions (3, 5) and (5, 5) would be compared in case one more ADM is provided. For comparison between positions (3, 5) and (5, 5), rule (2) in Sect. 2 will be applicable. Accordingly, from Eq. 4 in Sect. 2, UADM3 = (6.353812 + 4.302582 + 2.131279 +0.917217) = 13.70489.

Photon Netw Commun Table 6 A modified utilization statistics corresponding to that of Table 2 3.912347

1.170702

1.390835

0.75045

0.35021

0.150090

0.030018

0.000000

5.833500

5.143086

2.531519

1.170702

0.620372

0.120072

0.110066

0.030018

6.353812

4.302582

2.131279

0.917217

0.917217

0.250150

0.110066

0.060036

8.284971

3.832299

1.390835

1.600961

0.510306

0.250150

0.110066

0.030018

8.915349

2.781669

1.350810

1.340804

0.917217

0.080048

0.090054

0.020012

8.535121

3.271963

1.620973

1.050630

0.290174

0.180108

0.150090

0.000000

7.324395

3.602161

2.081249

0.690414

0.600360

0.200120

0.10006

0.030018

6.633980

4.222534

1.280768

1.961177

0.540324

0.340204

0.080048

0.020012

7.694617

3.352011

1.600961

1.080648

0.730438

0.140084

0.130078

0.040024

7.984791

3.762257

2.021213

1.080648

0.420252

0.240144

0.080048

0.020012

7.514509

4.122473

2.091255

1.290774

0.630378

0.350210

0.070042

0.020012

8.475085

3.482089

1.991195

0.860516

0.420252

0.200120

0.060036

0.030018

6.033620

4.742846

2.471483

0.990594

0.610366

0.240144

0.190114

0.020012

4.182510

1.500901

1.180708

0.470282

0.580348

0.100060

0.030018

0.000000

Table 7 Allocation of 52 ADMs for the utilization statistics of Table 6 1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

Table 8 Allocation of 53 ADMs for the utilization statistics as in Table 6 1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

1

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

1

1

1

1

0

0

0

0

1

1

1

0

0

0

0

0

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Photon Netw Commun

UADM5 =

(8.915349 + 2.781669 + 1.340804) = 14.38863.

+

1.350810

So, UADM5 > UADM3 and accordingly, position (5, 5) has preference over position (3, 5). Subsequently, the allocation of 53 ADMs for the same is tabulated in Table 8.

6 Conclusions In this article, a simulation-based optimization approach is proposed for allocation of a limited number of ADMs in WDM optical networks with stochastic dynamic traffic. The well-known NSFNET network has been used for experiment. The number of wavelength channels and the number of TDM slots in a wavelength channel are assumed as 8 and 3, respectively, to test the prototype. Also in this context, shortest path routing and first-fit wavelength assignment have been incorporated. Advanced Routing and Wavelength Assignment (RWA) algorithms along with the required number of wavelength channels and TDM slots can be used as needed. The critical situation that may arise during allocation of ADMs is presented with examples and solved intuitively rather than arbitrarily. It is ultimately intended to obtain a better blocking probability for WDM optical networks. The prototype result shown is of great significance as it determines the number of ADMs required to achieve a certain blocking probability. It is well expected that there is a tradeoff between the number of ADMs and blocking probability for WDM optical networks but the proposed approach navigates the problem and provides a way to have a quantitative solution for the same with stochastic dynamic traffic.

Appendix A: Gathering utilization statistics After a route (path) has been fixed for a call between a source node (S) and a destination node (D), the pseudocode below describes the algorithm used in this article to determine the utilization statistics of ADMs.

If sourceADM and destinationADM both are empty then Assign a wavelength channel and consequent slot along ‘path’. Also, assign two ADMs corresponding to source node S and destination node D. Else // may have some common ADMs // commonADM ← the intersection of the sets sourceADM and destinationADM. If commonADM is not empty then Search for a free wavelength and consequent slot for the wavelengths corresponding to commonADM along ‘path’. If free wavelength and slot found then goto UpdateAll. End End If noSourceADM > noDestinationADM then Search for a free wavelength and consequent slot for the wavelengths corresponding to sourceADM along ‘path’. If free wavelength and slot found then Assign one ADM to destination node D. goto UpdateAll. End Search for a free wavelength and consequent slot for the wavelengths corresponding to destinationADM along ‘path’. If free wavelength and slot found then Assign one ADM to source node S. goto UpdateAll. End Else Search for a free wavelength and consequent slot for the wavelengths corresponding to destinationADM along ‘path’. If free wavelength and slot found then Assign one ADM to source node S. goto UpdateAll. End Search for a free wavelength and consequent slot for the wavelengths corresponding to sourceADM along ‘path’. If free wavelength and slot found then Assign one ADM to destination node D. goto UpdateAll. End End Assign a wavelength channel and consequent slot along ‘path’. Also, assign two ADMs corresponding to source node S and destination node D. End UpdateAll: Update all the network information.

Appendix B: Allocate ADMs

sourceADM ← Set of ADMs already allocated to source node, S.

This algorithm allocates ADMs at the nodes of WDM optical networks depending on the utilization statistics. The procedure in this regard with pseudocode is given below.

destinationADM ← Set of ADMs already allocated to destination node, D.

Procedure allocate ADMs(U, N, W, T, x) // inputs: U, N, W, T

noSourceADM ← number of entries in sourceADM. noDestinationADM ← number of entries in destination ADM.

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U ← It is an N × W boolean matrix in which (i, j)-th entry denotes the number of involvements of the ADM (in percentage) corresponding to j-th wavelength for i-th node. N ← number of nodes in the WDM optical network.

Photon Netw Commun

W ← number of different wavelength channels in the network. T ← number of available ADMs. This algorithm assumes N * W > T, i.e., supply (of ADMs) is less than the requirement. output: x x ← It is an N × W boolean matrix in which a ‘1’ in (i, j)-th entry denotes the assignment of an ADM at i-th node for j-th wavelength. //

If not (UNi > UNj ) then Swap values of the indices i and j in similarInd. End End //end if-else End //end for End //end for . For i = 1 to (T - simRequired) x(sortedUM(i, 2), sortedUM(i, 3)) = 1 End Allocate ADMs at the positions corresponding to the topmost simRequired number of elements in similarInd. End //end if-else End //end procedure

UM ← Construct a matrix of order N*M × 3 where, entries in each row for the three columns denote utilization value, rows and columns of U, respectively.

Procedure checkConflict(sortedUM, N, W, T) simB ← 0 simA ← 0 // The following ‘for’ loop calculates the number of duplicate entries before index T // sortedUM ← sort rows of UM in descending manner with For i = T-1 to 1 (decrement 1 each step) respect to its first column. // standard Quick sort If sortedUM (i, 1) = sortedUM (T, 1) then algorithm is used in this respect // simB ← simB +1 indexSimilar(simB) ← i [similarInd, simRequired ] ← checkConflict (sortedUM, N, Else break W,T) // The procedure ‘checkConEnd //end if-else flict’ is given below. // End //end for Add the value T to indexSimilar. //since it is also a part of conflict // // similarInd ← An array of indices corresponding to the simRequired ← simB + 1 ‘sortedUM’ matrix for those conflict has occurred // We need to allocate ‘simRequired’ number of ADMs among the conflicting positions // due to similar utilization values. // The following ‘for’ loop calculates the number of duplicate entries after index T // nSimInd ← number of entries in similarInd. For i = T + 1 to N*W If sortedUM(i, 1) = sortedUM (T, 1) then simRequired ← Number of ADMs to be allocated among simA ← simA + 1 the conflicting positions. indexSimilar(simA + simRequired) ← i Else break. Obviously, simRequired < nSimInd. // End //end if-else End //end for return indexSimilar, simRequired. End //end procedure If number of entries in similarInd = 1 then // No conflict // For i = 1 to T x(sortedUM(i, 2), sortedUM(i, 3)) = 1 End Appendix C: Simulation with allocated ADMs Else // Conflict // For i = 1 to nSimInd For j = i+1 to nSimInd This pseudocode below determines if a call (between source If sortedUM(similarInd(i), 3) = sortedUM(similarInd(j), 3) node, S and destination node, D along the route, ‘path’) will then be blocked due to non-availability of ADMs. UADMi ← current total utilization at node sortedUM(similarInd(i), 2) for all wavelengths. UADMj ← current total utilization at node sortedUM(sisourceADM ← Set of ADMs allocated to source node S. milarInd(j), 2) for all wavelengths. If not (UADMi > UADMj ) then Swap values of the indices i and j in similarInd. destinationADM ← Set of ADMs allocated to destination End node D. Else UNi ← current total utilization due to wavelength sortedUM(similarInd(i), 3) for all nodes. UNj ← current total utilization due to wavelength sortecommonADM ← Intersection of the sets sourceADM and dUM(similarInd(j), 3) for all nodes.

destinationADM.

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Photon Netw Commun If commonADM is not empty then Search for a free wavelength and consequent slot for the wavelengths corresponding to commonADM along ‘path’. If free wavelength and slot not found then Call is blocked. End Else Call is blocked. End

References [1] Mukherjee, B.: Optical Communication Networks. McGrawHill, New York (1997) [2] Ramaswami, R., Sivarajan, K.N.: Optical Networks: A Practical Perspective. Morgan Kaufman Publishers (1998) [3] Black, U., Waters, S.: SONET and T1 Architectures for Digital Transport Networks. Prentice Hall, New Jersey (1997) [4] Kartalopoulos, S.V.: Understanding SONET/SDH and ATM Communications Networks for the Next Millennium. IEEE press, New York (1999) [5] Biswas, U., Naskar, M.K., Mukhopadhyay, A., Maulik, U.: A heuristic algorithm for static wavelength assignment in WDM optical networks. IETE Tech. Rev. 22(3), 199–204 (2005) [6] Mukhopadhyay, A., Biswas, U., Naskar, M.K.: Distributed Routing and Wavelength Assignment Algorithms for Dynamic WDM All-Optical Networks. International Conference PHOTONICS— 2004 (Cochin, India, Dec. 2004), pp. NET P.2 (2004) [7] Naskar, M.K., Sarkar, T., Biswas, U., Sarkar, S.K.: An Efficient Heuristic for Static Wavelength Assignment in WDM Optical Networks. Conference HOT 2003 (Calcutta, India, Feb. 2003), pp. 83 (2003) [8] Mukhopadhyay, A., Biswas, U., Naskar, M.K.: A Genetic Algorithm for Traffic Grooming in Unidirectional SONET/WDM Rings. IEEE India Annual Conference INDICON, 2004 (IIT, Kharagpur, 20–22 Dec. 2004), pp. 252–255 (2004) [9] Mukhopadhyay, A., Singh, J.K., Biswas, U., Naskar, M.K.: Distributed Approaches for Dynamic Traffic Grooming in WDM Optical Networks. International Conference CODEC-04 (Calcutta, India, Jan. 2004), pp. P-55 (2004) [10] Mukhopadhyay, A., Singh, J.K., Biswas, U., Naskar, M.K.: Improved Distributed Approaches for Dynamic Traffic Grooming in WDM Optical Networks. DPN’04 (IIT Kharagpur, India, 11–13 June 2004), pp. 92–96 (2004) [11] Gerstel, O., Sasaki, G.: Cost effective traffic grooming in WDM rings. Proceedings of IEEE INFOCOM ’98 (San Francisco, CA, USA, March 1998), vol. 1, pp. 69–77 (1998) [12] Gerstel, O., Lin, P., Sasaki, G.: Wavelength Assignment in a WDM Ring to Minimize Cost of Embedded SONET Rings. Proceedings of IEEE INFOCOM ’98 (San Francisco, CA, USA, March 1998), vol. 1, pp. 94–101 (1998) [13] Gerstel, O., Lin, P., Sasaki, G.: Combined WDM and SONET Network Design. Proceedings of IEEE INFOCOM ’99 (New York, NY, USA, March 1999), vol. 2, pp. 734–743 (1999) [14] Chiu, A., Modiano, E.: Reducing Electronic Multiplexing Costs in Unidirectional SONET/WDM Ring Networks via Efficient Traffic Grooming. IEEE/IEICE Global Telecommunication Conference (Sydney, Australia, Nov. 1998), vol. 1, pp. 332–327 (1998) [15] Chiu, A., Modiano, E.: Traffic grooming algorithms for reducing electronic multiplexing costs in WDM ring networks. IEEE/OSA J. Lightwave Technol. 18(1), 2–12 (2000) [16] Modiano, E., Lin, P.J.: Traffic grooming in WDM networks. IEEE Commun. Mag. 39(7), 124–129 (2001)

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[17] Modiano, E., Narula-Tam, A.: Mechanisms for providing optical bypass in WDM-based networks. SPIE Opt. Networks Magaz. 9–16 (2000), [18] Zhang, X., Qiao, C.: An effective and comprehensive solution to traffic grooming and wavelength assignment in SONET/WDM rings. Proceedings of SPIE, vol. 3531, pp. 221–232 (1998) [19] Liu, L., Li, X., Wan, P., Frieder, O.: Wavelength Assignment in WDM Rings to Minimize SONET ADMs. Proceedings of IEEE INFOCOM ’00 (Tel Aviv, Israel, March 2000), vol. 2, pp. 1020– 1025 (2000) [20] Sridharan, M., Somani, A.K.: Revenue Maximization in Survivable WDM Networks, Optical Networking and Communications. Proceeding of SPIE, vol. 4233, pp. 291–302 (Oct. 2000) [21] Wan, P., Liu, L., Frieder, O.: Grooming of Arbitrary Traffic in SONET/WDM Rings. IEEE/IEICE Global Telecommunication Conference , vol. 1B, pp. 1012–1016 (1999) [22] Cho, W., Wang, J., Mukherjee, B.: Improved approaches for costeffective traffic grooming in WDM ring networks: Uniform-traffic case. Photon. Network Commun. 3(2), 245–254 (2001) [23] Wang, J., Cho, W., Rao Vemuri, V., Mukherjee, B.: Improved approaches for cost-effective traffic grooming in WDM ring networks: ILP formulations and single-hop and multihop connections. IEEE/OSA J. Lightwave Technol. 19(11), 1645– 1653 (2001) [24] Hu, J.: Traffic grooming in wavelength-division-multiplexing ring networks: a linear programming solution. J. Opt. Network. 1(11), 397–408 (2002) [25] Berry, R., Modiano, E.: Reducing electronic multiplexing costs in SNET/WDM rings with dynamically changing traffic. IEEE J. Select. Areas Commun. 18(10), 1961–1971 (2000) [26] Roy, K., Naskar, M.K.: Evolutionary approach for static traffic grooming to SONET over WDM optical networks. Comput. Commun. 30(17), 3392–3402 (2007). doi:10.1016/j.comcom.2007. 06.009 [27] Roy, K., Naskar, M.K.: A heuristic solution to SONET ADM minimization for static traffic grooming in WDM uni-directional ring networks. Photon. Network Commun. 12(2), 153–160 (2006)

Author Biographies Kuntal Roy received his B.E. (Hons) from Electronics and Tele-Communication Engineering Department, Jadavpur University, Kolkata, India in the year 2003. He held several technical positions of application programmer in Interra IT, TCS (RFID center of excellence), and IBM during 2003–2006. From September, 2006, he is pursuing Master of Science in Embedded Systems Design at Advanced Learning and Research Institute (ALaRI), University of Lugano, Switzerland. His research interests include WDM optical networks, microelectronics, VLSI circuit design, nanotechnology, low power design, and embedded systems design. He is an author/co-author of the following published/accepted articles in WDM optical networking field—“Adaptive Dynamic Wavelength Routing for WDM Optical Networks” [WOCN, 2006], “A Heuristic Solution to SADM minimization for Static Trafffic Grooming in WDM uni-directional Ring Networks” [Photonic Network Communi-

Photon Netw Commun cations, 2006], “A Simple Approach for Optimal Allocation of Wavelength Converters in WDM Optical Networks” [WOCN, 2007], “Genetic Evolutionary Approach for Static Traffic Grooming to SONET over WDM Optical Networks” [Computer Communication, Elsevier, 2007], and “Genetic Evolutionary Algorithm for Optimal Allocation of Wavelength Converters in WDM Optical Networks” [Photonic Network Communications, 2008]. Mrinal Kanti Naskar received his B. Tech. (Hons) and M. Tech from E&ECE Department, IIT Kharagpur, India in 1987 and 1989, respectively and PhD from Jadavpur University, India in 2006. He served as a faculty member in NIT, Jamshedpur and NIT, Durgapur during 1991–1996 and 1996–1999, respectively. Currently, he is a professor in the Department of Electronics and Tele-Communication Engineering, Jadavpur

University, Kolkata, India where he is in charge of the Advanced Digital and Embedded Systems Lab. His research interests include ad-hoc networks, wireless sensor networks, optical networks, and embedded systems. He is an author/co-author of the several published/accepted articles in WDM optical networking field that include “Adaptive Dynamic Wavelength Routing for WDM Optical Networks” [WOCN, 2006], “A Heuristic Solution to SADM minimization for Static Traffic Grooming in WDM uni-directional Ring Networks” [Photonic Network Communications, 2006], “Genetic Evolutionary Approach for Static Traffic Grooming to SONET over WDM Optical Networks” [Computer Communication, Elsevier, 2007], and “Genetic Evolutionary Algorithm for Optimal Allocation of Wavelength Converters in WDM Optical Networks” [Photonic Network Communications, 2008].

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Simulation-based SONET ADM optimization approach ...

Since ADMs are expensive, it is desirable that if each node in WDM optical networks can use a minimum number of ADMs to achieve a near-ideal performance.

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