Cost-Optimized Reservation and Routing for Scheduled ... - IEEE Xplore

Ding et al.

VOL. 5, NO. 11/NOVEMBER 2013/J. OPT. COMMUN. NETW. 1215

Cost-Optimized Reservation and Routing for Scheduled Traffic in Optical Networks Hui Ding, Pan Yi, and Byrav Ramamurthy

Abstract—Connection requests for data-intensive applications can require a specific start time and end time/ duration when they are submitted. With the additional time domain information, cost-efficient connections can be established. In this paper, we propose two capital expenditure (CapEx) optimized approaches: the multilayer (ML) approach and a transponder/regenerator reuse (TRR) approach. Integer linear programming (ILP) is used to formulate the routing, wavelength assignment, and regenerator/multiplexer placement problem in a complex multilayer optical network to provide lower bounds for the optimized CapEx value. Due to the time and space complexity of ILP when it deals with large networks and traffic demands, we also propose a greedy heuristic and a tabusearch (TS) heuristic to solve the same problem in a less time- and resource-consuming manner. Finally, we compare the results in terms of computing time and optimized CapEx value across the ILP, greedy heuristic, and TS heuristic methods with the ML approaches for the Internet2 topology and a six-node ring topology. The performance of all three methods with the TRR approach is also tested with the same input traffic, which is composed of a mix of 10, 40, and 100 Gbps demands. The results show 30%–40% less CapEx when comparing ML with TRR. Further, our TS heuristic performs better than the greedy heuristic, and it can achieve near-optimal results compared to the ILPs. Index Terms—Cost optimization; Integer linear programming (ILP); Multilayer scheduling.

I. INTRODUCTION

T

he ever-increasing growth in bandwidth demand in communication networks has stimulated the deployment of high-capacity optical backbone networks. These demands, such as e-Science, cloud computing, datacenter backup, etc., often require large bandwidth only for a certain period of time to satisfy the scheduled traffic. Network operators are expected to provide connections for the specified time duration, and they try to minimize the capital Manuscript received May 1, 2013; revised July 27, 2013; accepted August 16, 2013; published October 23, 2013 (Doc. ID 189819). H. Ding (e-mail: [email protected]) is with the State Key Laboratory of Information Photonics and Optical Communications, BUPT, Beijing 100876, China, and the School of Electronic & Electrical Engineering, University of Leeds, Leeds LS2 9JT, UK. P. Yi and B. Ramamurthy are with the Department of Computer and Science Engineering, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, USA. http://dx.doi.org/10.1364/JOCN.5.001215

1943-0620/13/111215-12$15.00/0

expenditure (CapEx) for providing these connections as much as possible. There are several ways to lower the soaring CapEx, including developing low-cost network devices and exploring cost-efficient resource allocation schemes. To solve the CapEx-optimized bandwidth allocation problem for scheduled traffic, we propose two integer linear programming (ILP) formulations: multilayer ILP (ML-ILP) and transponder/regenerator reuse ILP (TRRILP) with the objective of minimizing the total CapEx. ML-ILP optimizes CapEx at the reconfigurable optical add/drop multiplexer (ROADM) layer, the express link layer, and the multiplex link layer. TRR-ILP additionally includes the transponder/regenerator reuse. Scheduled traffic demands (STDs) are fed to the ILP solvers to solve the multilayer routing problem. We also propose a corresponding greedy heuristic and tabu-search (TS) heuristic to solve the same problem in order to overcome the limitations due to the complexity of the ILP-based approach. With the objective of minimizing the CapEx, our work formally defines the multilayer routing problem and optimizes the CapEx for satisfying scheduled traffic demands. Setting up or tearing down a lightpath in an optical network requires several steps and involves the configuration of multiple optical and electrical devices. Typically, when a client submits a request through some interfaces, IP routers send it through the Ethernet layer/synchronous digital hierarchy (SDH) layer to the wavelength division multiplexing (WDM) layer where the connection request is translated to a lightpath request between two ROADM nodes. To set up a point-to-point dense wavelength division multiplexing (DWDM) connection, from the source node to the destination node, a pair of optical transponders is needed for transmitting and receiving optical signals. Other elements such as optical amplifiers and fibers are necessary to maintain the quality of the optical signal, as shown in Fig. 1. Regenerators, which are also needed when a signal travels beyond its optical reach, are often colocated with ROADMs [1]. Optical reach is a parameter provided by the system vendor via complicated measurement and computation according to different physical characteristics of the system. Assume a DWDM system with 100 Gbps capacity per wavelength; when accommodating lower rate demands, such as 10 and 40 Gbps demands, muxponders are deployed to multiplex ten 10 Gbps demands or two 40 Gbps demands to a higher rate signal of 100 Gbps in order to use the wavelength resources efficiently. © 2013 Optical Society of America

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Fig. 1. Establishment of a connection in an optical network.

Fig. 2. Multilayer optical network.

Figure 2 presents the multilayer optical network model employed in this paper. It consists of four layers: the fiber span layer, the ROADM (DWDM) layer, the express link layer, and the traffic demand layer. Vertices in these layers from bottom to top represent fiber joints, ROADM nodes, regenerators, and client access routers. We assume that the ROADM in this model is fully flexible, colorless, directionless, and nonblocking based on previous works on design and demonstration of such ROADM architecture [2–7]. The traffic demands can be generated by optical transport network (OTN) and wide-area Internet services [8]. In this paper, we define the cost-optimization problem for routing scheduled traffic in the multilayer OTN, formulate it, and solve it first with two ILP methods. Then we propose two heuristics to solve it more efficiently. Section II includes some related work in the field of multilayer routing and traffic scheduling. Section III formally defines the cost optimization of the multilayer routing problem, and we propose two ILPs to solve the problem. In Section IV, we develop a greedy heuristic and a TS-based heuristic to solve the same problem. Results obtained by applying all the ILP and heuristics with the two methods, ML and TRR, in two topologies are given in Section V along with analysis. Section VI concludes the paper.

II. RELATED WORKS

AND

MOTIVATION

Cost optimization for the routing and wavelength assignment (RWA) problem has been the subject of both academic and industry research. Xu et al. [9] proposed a cost-efficient physically diverse routing in a complex multilayer heterogeneous core network and used a carrier

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network to validate their solution. Their solution includes an ILP to compute diverse routes and a postprocessing procedure to determine the transponder/regenerator location and wavelength assignment. Patel et al. [10] discussed the cost-optimization problem for traffic grooming and regenerator placement with physical-impairment information. They analyzed the detailed ROADM cost model and proposed three policies to solve the problem. The results showed the lowest cost is obtained by employing both traffic grooming cards and transponder cards properly. Shen et al. optimized the cost with four multiplexing policies [11] in DWDM networks, and their emphasis was on the impact on the investment cost across the four policies without scheduling. Hou et al. [12] addressed the power and port-cost-efficient design for multigranularity robust IP over WDM networks. They defined a key parameter, multigranularity power ratio (MGPR), to evaluate the proposed grooming algorithm, and results showed the hybrid grooming methods achieved both energy efficiency and port savings. Traffic grooming is also extensively discussed in [13, 14]. The optimization problem is also discussed in recently emerging orthogonal frequency division multiplexing (OFDM)-based elastic optical networks. Vizcíano et al. [15] investigated the routing and spectrum allocation (RSA) problem with the objective of maximizing energy efficiency in both elastic OFDM-based networks and conventional WDM (single line rate and mixed line rate) for static and dynamic service provision. The results obtained from evaluating the proposed heuristics in different network settings, different topologies, and varied traffic loads with realistic unit energy consumption show that the elastic OFDM-based network provides the benefit of lower energy efficiency as well as lower network blocking probability compared to WDM networks. Castro et al. addressed the dynamic RSA problem in flexgrid optical networks [16]. They studied the relation between slot width and traffic rates and proposed a spectrum (re)allocation algorithm for better resource utilization. The problem of scheduling traffic was also discussed extensively in many previous works. Palkopoulou et al. proposed multilayer, multiperiod network planning using ILP to gain cost reduction [17]. The results showed that with the knowledge of upcoming traffic, more cost savings can be obtained compared to successive optimization within one time slot. The main cost saving was received at the IP layer. However, the authors did not explore different optical layers for cost minimization. Angu and Ramamurthy [18] proposed a continuous and parallel algorithm to route scheduling demands with the objective of accepting as many demands as possible. A framework for solving the scheduling problem in hybrid IP-WDM networks is proposed in [19]. There are also novel heuristics and algorithms to tackle the scheduling problem with the optimization goal of minimizing the required resources or reducing the blocking rate or both [20,21]. For a comprehensive survey and more papers on the scheduling problem in wavelength-routed WDM networks, please refer to [22]. Recently, Lu and Zhu analyzed the RSA problem for scheduling traffic and proposed both ILP and heuristics to solve the

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problem [23]. The objective of their work is to minimize blocking. Different from previous works, the objective of this paper is to minimize the overall CapEx for accommodating scheduled traffic demands during their requested time periods. We consider an optical network composed of four layers, namely, the fiber span layer, the DWDM layer, the express link layer, and the multiplex link layer. CapEx optimization is performed at each layer along with RWA and regenerator and muxponder placement. We also utilize the time information that the demands specified to explore further CapEx reduction. In an earlier work [24], we defined the cost-optimization problem, formulated it, and solved it with the ILP method. In this paper, we modify the ILPs and the heuristics to accommodate traffic with three data rates rather than two. We also provide a detailed description of the heuristics, complexity analysis, and more results.

III. PROBLEM DESCRIPTION The multilayer routing problem is defined as follows: given a network configuration including fiber span information, link capacity, DWDM system reachability, multiplexing ability, and a set of STDs, find the routes and the regenerator/muxponder location for each demand during the specified time period in this multilayer optical network, satisfying all the requirements with the least CapEx.

A. Multilayer Optical Network Detailed descriptions of the network architectures are given in [9]. The multilayer network topology is made of a set of vertices V and a set of bidirectional weighted edges E connecting them; the weight of each edge is denoted as αe
e ∈ E, and each edge has the same number of L wavelengths. In our model, V has two subsets V d , which are DWDM (ROADM) nodes, and V f , the fiber joint nodes. V  V d ∪ V f . E, constituted by several subsets as well, is a union of edges on different layers, which are the direct links Ed on the DWDM layer, the express links Ep on the express link layer, and the multiplex links Em on the multiplexing link layer. How to multiplex 10 and 40 Gbps traffic into a wavelength channel is shown in Fig. 3. E  Ed ∪ Ep ∪ Em . L defines the constant capacity (in Gbps) across all links in the network. We assume that 10 lower rate demands (10 Gbps traffic) or two 40 Gbps traffic demands can be multiplexed to transport in a 100 Gbps rate optical channel. We also assume that each multiplex link at the same wavelength channel has the same cost so as to bundle up to 10 lower rate traffic demands to one high rate channel. As mentioned in previous sections, a lightpath may pass through one ROADM node in our model besides its terminal nodes. Also, optical reach constraints are applied for node bypass, meaning that a node bypass happens only when the physical distance of the two nodes is within

Fig. 3. Multiplexing different data rates into a wavelength channel.

the optical reach to prevent unrecoverable signal degradation. Figure 4 illustrates the node bypass conditions. Please refer to [1] and [25] for more information on the optical reachability and node bypass conditions. To simplify this example, we assume that the bypassing conditions are 1) a lightpath can bypass at most one ROADM node and 2) the distance of the bypass link is less than 1500 km. So bypass link A–C can exist and it bypasses node B; however, B–D cannot exist because the distance exceeds 1500 km as shown in Fig. 4.

B. Scheduled Traffic Demands A STD is defined as a tuple (s; d; n; ts ; te ), and the parameters represent the source-destination node, the data rate, the start time, and the end time of a demand, respectively. The time domain, in which the scheduling is performed, is divided into fixed 1 h long time slots as shown in Fig. 5. A schedule time (ST) can be 6∕12∕24 time slots long. Before

Fig. 4. Node bypass condition.

Fig. 5. Schedule illustration.

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the ST, the solver collects STDs. After the traffic-collecting period, the optimization takes place. After the ST, the second round of collecting STDs and performing optimization begins. Our solver rejects demands that will begin after an ST cycle, and an STD should last at least 1 h, 1 ≤ te − ts ≤ ST. For simplicity purposes, we assume that there are three different line rates in traffic demands, 10, 40, and 100 Gbps [26], which extends the traffic rates in [24]. Traffic demands can be divided into three data rate groups, D10 , D40 , and D100 .

TABLE II PARAMETERS Ed Ep Em E Vd Vf V L D D10 D40 D100 CCt

C. Cost Model The cost model is composed of fixed CapEx and incremental CapEx. In the multilayer optical network we considered, the fixed CapEx is the cost of predeployed system components in the optical part, including optical amplifiers, fibers, and optical switches (ROADM), etc. We use the per kilometer cost Cdis to quantify the fixed cost. The incremental CapEx is associated with the incoming STDs, including optical transponders, muxponders, and regenerators. The CapEx for network elements is based on the normalized cost [27] as shown in Table I. We make some changes from our previous cost model in [24]. The cost model does not include the revenue and profit. A 10 Gbps, 750 km transponder is set as 1 unit cost. The cost for 10, 40, and 100 Gbps transponders is 1×, 2.5×, and 3.75× according to [28]. We denote Cot;10 , Cot;40 , and Cot;100 as 10, 40, and 100 Gbps WDM transponders, and Creg;10 , Creg;40 , and Creg;100 as 10, 40, and 100 Gbps regenerators, Cmux for 100G muxponders. The common cost of the system, denoted as Cdis , is 0.0001 in our model, and it is of the same magnitude as that in the cost model derived from commercial networks [11].

D. ILP Formulations The static traffic RWA problem known as the static lightpath establishment (SLE) is proved to be NP-complete [29]. In this work, time constraints are added to the SLE problem. Every solution in our scheduling problem is a solution in the SLE problem; hence scheduling < SLE and the reduction can be completed in polynomial time. Thus, our scheduling problem is also NP-complete.

We propose two ILPs, namely, ML-ILP and TRRILP. ML-ILP optimizes the total cost in a multilayer setting. TRR-ILP, adding transponder/regenerator reuse strategy to ML-ILP, shares the same constraints as ML-ILP but with a different CapEx computation formulation. Using the parameters provided in Table II as input, the two ILPs try to solve the following decision variables shown in Table III: 1) Pr
i; j is a binary variable; it equals 1 when the working path of demand r traverses link
i; j and 0 otherwise. 2) T r
i; j;t is a binary variable; it equals 1 when some path of demand r traverses link
i; j at time slot t and 0 otherwise. 3) W r
i; j;t;w is a binary variable; it equals 1 when some path of demand r traverses link
i; j at time slot t and uses wavelength w, and is 0 if otherwise. 4) M r
i; j;t;w;m is a binary variable; it equals 1 when some path of lower rate demand r traverses link
i; j at time slot t and uses multiplex link m on wavelength w, and is 0 if otherwise. ML-ILP optimizes CapEx in a multilayer scenario. The objective function is minimize

10G transponder 40G transponder 100G transponder 10G regenerator 40G regenerator 100G regenerator 10G × 10 muxponder ROADMs, OAs, fiber, etc.

X cr : r∈D

TABLE I COST MODEL Cot;10 Cot;40 Cot;100 Creg;10 Creg;40 Creg;100 Cmux;100 Cdis

Set of direct edges, DWDM links Set of express edges Set of multiplex edges Full set of edges Set of DWDM nodes Set of fiber joint nodes Full set of nodes Number of wavelengths on each link Set of scheduled traffic demands Set of 10 Gbps data rate STDs Set of 40 Gbps data rate STDs Set of 100 Gbps data rate STDs Number of concurrent connections at time slot t

TABLE III DECISION VARIABLES 1.00 2.50 3.75 1.40 3.50 5.25 11.25 0.0001

Pr
i;j T r
i;j;t W r
i;j;t;w M r
i;j;t;w;m cr

If edge (i; j) on the path of demand r If edge (i; j) on the path of demand r at time slot t If edge (i; t) on the path of demand r at time slot t uses wavelength w If edge (i; t) on the path of low data rate demand r at time slot t uses wavelength w and subchannel m Cost of accommodating STD r

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Constraints:

CapEx computation in ML-ILP:

Flow conservation: X Pr
sr ;o  1;

Pr
o;sr 


sr ;o∈E

 0;

(1)

cr  2 × Cot  

X
i;j∈E

X
i;j∈Ed

Pr
i;j −

X
j;k∈Ed



Pr
j;k  0;

∀
i; j ∈ E; tsr ≤ t ≤ ter :

(3)

Wavelength assignment:

W r
i;j;t;w  T r
i;j;t ;

w1

∀
i; j ∈ E; tsr ≤ t ≤ ter :

(4)

Multiplex link assignment for lower rate demands: 10 X

M r
i;j;t;w;m  W r
i;j;t;w ;

ch1

∀ r ∈ D10 ∪D40 :

(5)

Wavelength continuity constraints in the time domain: W r
i;j;t;w  W r
i;j;t1;w ; tsr ≤ t ≤ ter − 1:

(6)

Multiplex link continuity constraints in the time domain: M r
i;j;t;w;m  W r
i;j;t1;w;m ;

tsr ≤ t ≤ ter − 1;

∀ r ∈ D10 ∪D40 :

(7)

Express link mapping to direct links: T r
i;j;t  T r
l;k;t ;

Pr
i;j × αe × Cdis


Pr
i;j − 1 × Creg

L X Time XX

M r
i;j;t;w;m × Cmux :

∀
i; j ∈ Ep ;

∀
l; k ∈ Ed :

Constraints (1) and (2) compute a single path from source node sr to destination node dr . Constraint (3) guarantees that the path of demand r is active during its specified time duration. An available wavelength is assigned to each link along the path for demand r by constraint (4). The ML-ILP includes an express link and multiplex link so a lower data rate STD (r ∈ D10 ∪ D40 ) can be multiplexed to a higher data rate channel. So while each 10 or 40 Gbps STD is multiplexed into a subchannel, it needs to be assigned a subwavelength as realized by constraints (5). Though wavelength continuity constraints are not necessary with the presence of regenerators in the network, using the same wavelength/subwavelength through the service time is required. Constraints (6) and (7) ensure the wavelength continuity and subwavelength continuity in the time domain, respectively. In the multilayer network setting, the routes on the express link layer are essentially set up at the physical fiber span layer. Since in our model, the fiber span layer only adds fiber joints based on the ROADM layer, to reduce the size of the problem, we only map the express links to their corresponding direct links (express link layer to ROADM layer), which is enforced by constraints (8). The multiplexing factor is assumed to be 10 for 10 Gbps STDs and 2 for 40 Gbps STDs as in constraints (9). This is because we consider the line rate in the network to be 100 Gbps. The multilayer setting also leads to different CapEx computation formulation as shown in Eq. (10). It includes the cost of the muxponder when the multiplex link is constructed. Now, we present the TRR-ILP. Solving the same costoptimization problem in the multilayer scenario as ML-ILP, TRR-ILP is a variant of the same problem, which includes the transponder/regenerator reuse strategy. Note that in TRR-ILP, only transponders/regenerators are reused. They are plugged into the ports when the connections are active and unplugged when the connections are torn down. Muxponders are not reused since they create multiplex links that will be used for lower rate demands in the future. The objective function of TRR-ILP is the same as ML-ILP:

(8) minimize

Capacity constraints in ML-ILP: X r∈D100

T r
i;j;t  2 ×

X r∈D40

(10)

(2)

Service time is satisfied:

L X


i;j∈E


i;j∈E t1 w1

j ∈ V d ;
j ≠ sr ; tr :

Pr
i;j  T r
i;j;t ;

X

T r
i;j;t  10 ×

X cr : r∈D

X r∈D10

T r
i;j;t ≤ L:

(9)

And it shares the same constraints (1)–(9) in ML-ILP. But the TRR-ILP differentiates from ML-ILP in the CapEx computation equation.

1220 J. OPT. COMMUN. NETW./VOL. 5, NO. 11/NOVEMBER 2013 t (hour)

CCt

1

2

3

4

5

6

7

8

9

10

11

12

2

1

0

1

2

3

2

1

1

1

2

1

STD1

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in the real network, we propose two practical heuristics: the greedy algorithm and the TS algorithm.

A. Greedy Algorithm

start time

STD2 STD3 STD4 STD5 STD6

Fig. 6. Illustration of computing max CC.

CapEx computation in TRR-ILP: max XCC X X cr  max CC × 2 × Cot 
Pr
i;j − 1 × Creg 1

r∈D



L X Time XX
i;j∈E t1 w1


i;j∈E

M r
i;j;t;w;m × Cmux ;

max CC  max CCt : 1≤t≤Time

(11)

(12)

The CapEx computation equation for TRR-ILP (11) is more complex than the previous one in Eq. (10). Figure 6 presents an example of computing CCt and max CC. CCt represents the number of concurrent STDs at time slot t, and max CC is the maximum of CCt in the time period considered. In the example shown in Fig. 6, max CC  3. TRR exploits the time information provided by STD, finds the concurrent connections, and computes the number of transponders necessary in the whole network. TRR-ILP can share muxponders by establishing connections based on previous or active connections with lower data traffic. We assume there is a bank of regenerators/transponders at each location and sharing is possible only within the location. Our approach will compute the maximum number at each location. The ML-ILP and its variant with TRR-ILP share the same variables and constraints, so the calculations for variables and constraints in them are the same. The number of variables is calculated by jDj  jVj2 
2  ST  ST  L, while the number of constraints is calculated by jDj  jVj2 
2  ST  13  ST  L  jEd j  jDj. When ST is 6, the number of requests is 50; for the two topologies we studied, the number of variables is 2,352,000 (Internet2) and 108,000 (6-node). The number of constraints is 24,776,050 and 1,127,316, respectively. Thus, for large-size networks, efficient heuristics are required for a fast solution. Next, we will present two effective heuristics for the problem.

Algorithm 1: Greedy Algorithm Input and Initializations: G 
V; E; D  STD1 ; …; STDM , where STDr 
sr ; dr ; nr ; tsr ; ter , r  1; …; M; //the set of STDs K; //number of K-shortest paths cr ; //total CapEx of STDr L; //number of wavelengths on each link Cot ; //transponder cost Creg ; //regenerator cost Cdis ; //fraction of per kilometer cost Cmux ; //muxponder cost Output: P minimized r∈D cr ; 1: Sort STDs as D  fSTD1 ; …; STDM g according to: earliest start time first; shortest duration first; low data rate first; //Following is to compute the K-shortest paths for the demands r in D list, as P1
r; …; Pk
r. 2: for r  1; r ≤ M; r   do 3: j  1; 4: while NextPath  NULLj and j < K do 5: Pj
r  Next
; //Get next shortest path for r 6: if (Pj
r available and t ∈ ter − tsr ) then 7: PCr  Insert
Pj
r; //put Pj
r in candidate path list for r; 8: j  ; 9: else 10: Delete path Pj
r; 11: end if 12: end while 13: for j  1; j ≤ k; j   do 14: Crj  Cost
Pj
r; //compute cost of path Pj
r 15: end for 16: cr  min1≤j≤K fCrjg; //min-cost path for r 17: r  ; 18: Update resource; 19: end forP 20: return r∈D cr ;

IV. HEURISTICS

The greedy algorithm is an intuitive and straightforward algorithm with the method of stepwise construction of the optimal solution. That is, it always makes a local optimal choice in the hope that this choice will lead to a globally optimal solution [30]. In our problem, to implement the CapEx-optimized routing for scheduled traffic, we exploit the greedy algorithm to obtain a routing path with the minimum cost, which is seen as a local optimal solution.

The ILPs in Subsection III.D have the limitations of requiring a large amount of computing resources and they also take a long time to return optimal or near-optimal results when dealing with real network topologies and a large number of STDs. To solve the multilayer routing problem

Our greedy algorithm processes STDs according to their position in the list D. To acquire the shortest path of each demand STDi in the list, several short paths will be produced first for one demand. Yen’s K-shortest-paths algorithm [31] is invoked to generate K-shortest paths for a given source-destination pair. Yen’s algorithm is an

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algorithm for ranking the K-shortest paths between a pair of nodes. It always searches the shortest paths in a “pseudo”tree containing K-shortest loopless paths. The very shortest one is obtained in the first place, and the second shortest path is always explored on the basis of the shortest paths that are shorter. For demand r, the generated K-shortest paths are noted as fP1
r; …; Pk
rg. Then the greedy algorithm computes the cost of each path Pj
r; j  1; …; k, denoted as Crj. Finally, the path out of K paths with minimum cost is chosen for demand r. Demand r will be removed from the STDs list after processing; the network resource, such as the available wavelength capacity on each link at every time slot, will be updated. The algorithm repeats the loop to process P every demand in the STDs list, and returns the total cost r∈D cr . The pseudocode of our greedy algorithm is shown in Algorithm 1.

solutions. So we propose a TS-based heuristic to resolve our routing problem for scheduled traffic in multilayer optical networks.

B. Tabu-Search Heuristic

With graph and traffic demands as two inputs of our TS heuristic, we still need some other initialized elements. We set K as the upper bound of path numbers that we need to compute for each demand; set L to represent the number of wavelengths on each link between the pair of nodes; set several cost variables as transponder cost Cot , regenerator cost Creg , muxponder cost Cmux , and fraction of per mile cost Cdis ; and also set the cost of each demand r as cr .

Algorithm 2: Tabu-Search Algorithm Input and Initializations: Same as in Algorithm 1 Output: P minimized r∈D cr ; 1: Compute K-shortest paths for each demand in D; 2: Initial solution: Randomly choose a shortest path for each demand in D; 3: while i < iteration do 4: if 100 Gbps STD then 5: Solution for STD :
11; 0; …; 0, where K − 1 zeros; 6: if is Available
 then 7: C100 : 2  Cot  Creg 
mn Length − 2 Cdis  md Weight; 8: Update resource; 9: else 10: Neighbor solution  rand
%K; 11: Continue(); //next iteration 12: end if 13: else 14: Solution for STD :
ch; 0; 0…0, where ch  1; …; 10, K − 1 zeros; 15: if is Available
 then 16: C10 : C10  Cmux ; 17: C40 : C40  Cmux ; 18: Update resource; 19: else 20: Neighbor solution  rand
%K; 21: Continue(); 22: end if 23: end if 24: SolutionCost  C100  C40  C10 ; 25: Update tabu list; 26: i  ; 27: Neighbor Solution  rand
%K; //random choose solution 28: end while 29: return solution; The greedy heuristic always makes the choice that looks best at the moment and does not always yield optimal

TS, developed by Glover and McMillan [32], is a local search method that can be used for solving combinational optimization. TS has been used to solve optimization problems in optical WDM networks [33,34]. Three essential problem-specific elements must be taken into account in the algorithm design: 1) an initial solution, 2) a cost function to evaluate the solutions generated by the algorithm, and 3) a procedure to generate neighborhood solutions from the current solution. According to the above considerations, the TS algorithm designed to solve our RWA problem is shown in Algorithm 2. Several important concepts such as move, tabu list, and tabu length will be discussed next along with our heuristic.

In our heuristic, the “K-shortest-paths” heuristic is invoked first to obtain the K-shortest paths for each demand as Line 3 illustrates. Then we feed the solution of the greedy heuristic as the initial solution to the TS heuristic. In our heuristic an iteration number is defined as the stopping condition of the TS loop. We decrease this iteration number by 1 when one round of the TS procedure is completed. This parameter in general is larger than the number of demands and can be changed when needed. In the following, Lines 4 to 23 are the main process of the heuristic. Here, we have STDs with three different data rates: 100, 40, and 10 Gbps. We use different equations to compute the cost of setting up connections for these three different demands (denoted as C100 , C40 , and C10 , respectively), which is described in detail in Subsection III.C. Here we would like to emphasize again the whole bandwidth of a channel is 100 Gbps, and it can be divided into 10 subchannels with 10 Gbps bandwidth each. For a 100 Gbps demand, the solution is recorded as
11; 0; …; 0 with K − 1 zeros. The number 11 means the entire wavelength is occupied by the chosen path for this request. Thus the solution means the position noted with a number 11 is the path we choose among K paths; the positions noted with zeros are other unchosen K − 1 paths. For a 40 Gbps demand, the solution is recorded as
ch; 0; …; 0, where there are K − 1 zeros and ch  1; 2; 3; 4. For a 10 Gbps demand, the solution is recorded as
ch; 0; …; 0, where there are K − 1 zeros and ch  1; …; 4. The numbers 1; 2; …; 10 represent subchannels 1 through 10 within one channel. Thus the solution means the position noted with ch is the path we choose, and the subchannel number is indicated, as well. The positions noted with zeros are other unchosen K − 1 paths. In our heuristic, we use a random function, as Line 10 shows, to realize the move operation to generate the neighborhood solution. For 100 Gbps STDs, the move is to change a path; for 40 and 10 Gbps STD, the

1222 J. OPT. COMMUN. NETW./VOL. 5, NO. 11/NOVEMBER 2013

move is to change a path or a subchannel or both. When a solution is obtained, we need to update the tabu list. Here, the tabu length is set in the beginning and will be changed when needed. We will insert the new solution in the tabu list before the list is full. When the list is full, we only replace the solutions in the list with our newly discovered better solutions to update the tabu list. Our TS heuristic stops when it reaches the iteration number and returns the final solution.

C. Time Complexity Analysis To obtain better insights into our solution approaches, we analyze the time complexity of greedy and TS algorithms. Both algorithms use Yen’s K-shortest-paths heuristic to compute K-shortest paths. Given a graph G 
V; E, where n  jVj and m  jEj, and a STD set, D  fSTD1 ; …; STDM g. The time complexity of Yen’s K-shortest-paths heuristic is O
Kn
m  n log n [31]. 1) Time Complexity of the Greedy Heuristic: • The outer loop: O
M. • While the loop is called the K-shortest-paths to compute the top-K paths for one demand, the time complexity is mentioned above, which is O
Kn
m  n log n. • Compute the cost loop: O
K. Total time complexity: O
M
Kn
m  n log n  K  O
MKn
m  n log n. 2) Time Complexity of the TS Heuristic: • Compute the top-K paths for r demands: O
M
Kn
m  n log n. • Choose the initial solution: O
M. • Store the solution: O
MK. • Compute the cost: O
n2  M
mn  n2 T; T is the time duration. • Update the tabu list: O
KM.

Ding et al.

• GenerateSolutions(): O
M. • The total time complexity of the TS heuristic is O
M
Kn
m  n log n  O
M  O
MK  O
Iteration

n2  M
mn  n2 T  KM  M  O
M×
Kn
m  n log n  O
Iteration
Mn2 T  Mmn. Here we can see the time complexity of the TS is also related to the number of iterations.

V. NUMERICAL RESULTS

AND

ANALYSIS

In our case studies we investigate two network topologies: a six-node ring topology and an Internet2 topology [35]. The ILP model is implemented using an IBM ILOG CPLEX solver [36], which runs on a desktop with 4 G RAM and a 3.10 GHz Intel Core CPU. We investigate CapEx optimization with the multilayer scenario and transponder/regenerator reuse approaches. The scheduling traffic demands are generated by a traffic generator, which randomly chooses the source and destination nodes, the traffic rate, and the ST in the network. For each scenario, the computing time and optimized CapEx for different lengths of ST are compared across the two topologies. The Internet2 network provides multilayer topologies including IP layer and WDM layer. In Fig. 7(a), the vertices represent the ROADMs and the solid edges represent the direct links in the Internet2 network. And the numbers at the direct link represent the physical distance between two ROADM nodes. Here we only considered the optical layer (WDM layer), which has 28 DWDM nodes located at major cities in the US and 33 DWDM links with an average length of 516.7 km. The mean node degree is 2.32. The sixnode ring topology is an arbitrary topology as shown in Fig. 7(b). It has six nodes and six links. We assume that the vertices represent the ROADMs and the solid edges represent the direct links. The distance between each pair of adjacent nodes is the same 10 km. The mean node degree is 2. We assume the reachability for the 100 Gbps WDM system is 1500 km in the Internet2 network and is the same in

Fig. 7. Auxiliary graphs for multilayer topologies of the two networks investigated. (a) Auxiliary graph of Internet2. (b) Auxiliary graph of 6-node ring.

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the six-node ring network. Also, for simplicity, the express link can only bypass at most one node in the ROADM layer. We add one virtual edge [dashed lines in Figs. 7(a) and 7(b)] to represent an express link between two ROADMs, while the length of the edge is the summation of the lengths of the two direct links it actually traverses as in Fig. 2. Based on the above ROADM layer topology and assumptions, we construct an auxiliary graph by adding an express link layer to represent the multilayer optical network. The number of express links is 35 in the Internet2 topology and six in the six-node ring topology. This graph is configured to solve the routing problem for scheduled 100 Gbps traffic demands. For lower data rate 10 and 40 Gbps traffic, besides the fiber span layer, the ROADM layer, and the express link layer, the multiplex link layer is included. The multiplex link layer, with the goal of minimizing the total cost, 10 and 40 Gpbs demands, should be efficiently bundled up into one wavelength link. To fulfill that, one wavelength link is split into 10 subwavelength channels with different costs, which are different proportions of the multiplexing cost, such as 10% of the total multiplexing cost for using each of the subchannels to encourage upcoming demands to use existing multiplex links.

A. Computing Time Performance Tables IV–VI show the computing time in the Internet2 topology in the multilayer scenario with three different approaches, namely, ILP, greedy heuristic, and TS heuristic, with different schedule lengths. We can see from the results that with less than 20 STDs, the computing times of ML-ILP, ML-Greedy, and ML-TS are comparable. As the number of STDs increases, the computing time of ILP starts to increase drastically, but the computing time of both heuristics increases steadily. Note that the number of iterations of the TS heuristic in all three cases is 20. We set the termination time for ILP to 2 h. The asterisks in the tables mean that ILP cannot return an optimal result within 2 h due to the size of the problem. As expected, the number of asterisks in the tables increases with the length of ST. When the length of ST doubles from 6 to 12 (or 12 to 24), the size of time domain matrix TABLE IV COMPUTING TIME (S) OF RUNNING ML-ILP, ML-GREEDY, AND ML-TS WITH ST  6 No. of STDs 10 20 30 40 50 60 70 80 90 100

ML-ILP

ML-Greedy

ML-TS (20)

0.06 2.11 13.35 28.06 57.23 87.1 111.98 184.32 355.12 

0.858 1.778 2.635 3.658 4.177 4.947 5.524 6.404 7.113 7.909

0.889 1.654 2.842 3.715 4.242 5.02 5.605 6.497 7.213 8.015

TABLE V COMPUTING TIME (S) OF RUNNING ML-ILP, ML-GREEDY, AND ML-TS WITH ST  12 No. of STDs 10 20 30 40 50 60 70 80 90 100

ML-ILP

ML-Greedy

ML-TS (20)

0.39 1.51 8.97 18.95 46.94 242.8 340.18   

0.808 1.69 2.571 3.394 4.234 5.023 5.943 6.645 7.425 8.205

1.208 1.742 2.576 3.471 4.336 5.123 6.052 7.425 7.456 8.236

TABLE VI COMPUTING TIME (S) OF RUNNING ML-ILP, ML-GREEDY, AND ML-TS WITH ST  24 No. of STDs

ML-ILP

ML-Greedy

ML-TS (20)

10 20 30 40 50 60 70 80 90 100

0.87 2.26 15.83 192.63 245.86 1506.43    

0.936 1.84 2.636 3.572 4.305 5.054 5.803 6.723 7.456 8.268

0.982 1.903 2.683 3.603 4.352 5.101 5.85 6.754 7.503 8.299

doubles as well. A similar trend can be observed when the transponder/regenerator reuse approach is applied.

B. CapEx Optimization Performance First, we present the cost performance in six-node ring topology with the schedule length ST  6 across the ILP, greedy, and TS heuristics under two CapEx computing methods in Fig. 8. It is observed that our TS heuristic can return the optimal CapEx value when the number of STDs is less than 50 using both multilayer and transponder/ regenerator reuse methods. CapEx savings of 10%–50% is achieved when the TRR approach is used. We can also see from Fig. 8 that the TS heuristic has better performance than the greedy heuristic in all cases. The performance of ILP, the greedy heuristic, and the TS heuristic using the multilayer approach in Internet2 topology with ST  12 is shown in Fig. 9. Figure 10 shows the results of the transponder/regenerator reuse approach with the same topology and ST. It is shown that with more complex topology, both MLtabu and TRR-tabu cannot return the optimal CapEx as ILP, but TS still obtains better results than the greedy heuristic. It is worth mentioning that when the number of STDs is 40, the greedy heuristic almost returns the same CapEx as the TS, whereas when the number of STDs is 100, the greatest gap between greedy and TS is shown. When the number of STDs increases, the TS heuristic maintains good performance. However, the greedy heuristic cannot return reliable

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results because of its local optimal feature. ILP runs out of memory when it tries to find the optimal solution for 100 STDs (marked with hash signs), which is also shown in Table V. The performance of the ML and TRR approaches in six-node ring topology is similar (not shown).

6 node ring topology ST=6 ML-ILP ML-Greedy ML-Tabu TRR-ILP TRR-Greedy TRR-Tabu

Optimized CapEx value

1000

800

Figure 11 shows the optimized CapEx value obtained by the ML and TRR approaches in the Internet2 topology when the schedule length is 24 h. Similar to in the six-node topology, TS has better cost performance compared to the greedy heuristic. One of the differences between Fig. 11 and Fig. 8 is that ILP cannot return optimal results when there are more than 60 STDs in the complex Internet2 topology.

600

400

200

0 10

20

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30

40

50

60

70

80

Number of STDs

Fig. 8. Optimized CapEx using ML and TRR in six-node ring topology and ST  6.

The optimized CapEx with different scheduling length is presented in Fig. 12. It is obvious that the ILP returns the lowest CapEx and the greedy heuristic returns the highest one in the same set. However, the cost difference between ST  6 and ST  12 in the same set is barely seen, which 3000

Internet2 topology with ST=12 ML-ILP ML-Greedy ML-Tabu # out of memory

2500

Optimized CapEx value

Optimized CapEx value

2000

1500

1000

2000

ML-ILP ML-Greedy ML-Tabu TRR-ILP TRR-Greedy TRR-Tabu # out of memory

Internet2 topology with ST=24

1500

1000

500

500

20

40

60

80

# # # # # # # #

0

#

0

10

20

30

40

50

60

70

80

90

100

Number of STDs

100

Number of STDs

Fig. 9. Optimized CapEx using ML-ILP, ML-greedy, and ML-TS.

Fig. 11. Optimized CapEx using ML and TRR in Internet2 topology and ST  24. Internet2 topology ST=6 vs ST=12

Internet2 topology with ST=12 TRR-ILP TRR-Greedy TRR-Tabu # out of memory

2000

Optimized CapEx value

Optimized CapEx value

1500

1000

500

#

0 10

20

30

40

50

60

70

80

90

100

Number of STDs

Fig. 10. Optimized CapEx using TRR-ILP, TRR-greedy, and TRR-TS.

1500

ML-ILP ST=6 ML-Greedy ST=6 ML-Tabu ST=6 ML-ILP ST=12 ML-Greedy ST=12 ML-Tabu ST=12 # out of memory

1000

500

#

0 10

20

30

40

50

60

70

80

90

100

Number of STDs

Fig. 12. Optimized CapEx in Internet2 topology with different scheduling length.

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implies that the CapEx is mostly based on routing but not the scheduling length. In the case studies we have two topologies, multilayer and transponder/regenerator reuse approaches and 6∕12∕24 time slots for ST; we investigate all those different combinations with ILP, the greedy heuristic, and the TS heuristic.

VI. CONCLUSION In this paper, we propose and implement two ILPs (ML-ILP and TRR-ILP) to optimally perform multilayer routing with the objective of minimizing overall CapEx cost in the multilayer optical network. Obtaining the results from the two ILPs as a lower bound, we also propose the greedy heuristic and the TS heuristic to solve the same problem. We analyze the computing time and optimized CapEx results after performing different combinations of approaches for two topologies, Internet 2 topology and six-node ring topology. The computing time results show that ILP, the greedy heuristic, and the TS heuristic return results within comparable short times with small numbers of STDs. However, as the number of STDs increases, ILP starts to slow down drastically, while the two heuristics can still generate results in several seconds. And the computing time of the heuristics only increases steadily with the growing STDs. We also find that the longer the ST is, the larger the problem size becomes, which leads to the 2 h ILP termination criterion being met with less than 100 STDs. The CapEx optimization results demonstrate that the transponder/regenerator reuse approach has 10%–50% (30%–40%) CapEx savings compared to the multilayer approach in six-node ring topology (Internet2 topology) due to including the transponder/regenerator reuse strategy. The results also show that our greedy heuristic can achieve optimal or near-optimal results compared to the lower bound (ILP results). Our TS heuristic performs better than greedy since it uses the greedy solution as the starting point. One of the possible future works involves applying other meta-heuristics, such as the genetic heuristic and the stimulated annealing heuristic, to solve this problem. We could also investigate energy-efficient scheduling in the future.

ACKNOWLEDGMENTS This work was supported in part by an NSF FIA grant (CNS-1040765). This work was performed while H. Ding was a Visiting Researcher at the University of Nebraska-Lincoln on a China Scholarship Council fellowship. This study is partly supported by China 863 Project No. 2012AA011302. An earlier version of this work was presented at the IEEE LANMAN 2013 workshop [24].

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Hui Ding is a Ph.D. candidate in the Institution of Photonics and Optical Communications at Beijing University of Posts and Telecommunications. She received her B.S. degree from the Department of Electronics and Information Engineering, Huazhong University of Science and Technology, in 2008. She is also a Postdoctoral Research Fellow in the Faculty of Electronics and Electrical Engineering at the University of Leeds starting April 2013. Her research interests include energy optimization, control, and management in future optical networks.

Pan Yi received the B.S. degree from the Department of Computer Science, Xi’an Jiaotong University, China, in 2007, and the M.S. degree from the Department of Electrical Engineering, Xi’an Jiaotong University, China, in 2010. She is currently working toward the Ph.D. degree in the Department of Computer Science and Engineering, University of Nebraska-Lincoln. Her research interests include cloud computing, network survivability, and the future Internet. Her current focus is on resource management and scheduling in grid/cloud computing using optimization theory.

Byrav Ramamurthy is currently a Professor and Graduate Chair in the Department of Computer Science and Engineering at the University of Nebraska-Lincoln (UNL). He is the author of the book Design of Optical WDM Networks—LAN, MAN and WAN Architectures and a co-author of the book Secure Group Communications Over Data Networks published by Kluwer Academic Publishers/Springer in 2000 and 2004, respectively. He served as the Chair of the IEEE Communication Society’s Optical Networking Technical Committee (ONTC) during 2009–2011. He served as the IEEE INFOCOM 2011 TPC Co-Chair. He is currently an Editor-in-Chief for the Springer Photonic Network Communications (PNET) journal. His research areas include optical and wireless networks, peer-topeer networks for multimedia streaming, network security, and telecommunications.