Routing and Spectrum Assignment in Spectrum Sliced Elastic Optical ...

JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007

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Routing and Spectrum Assignment in Spectrum Sliced Elastic Optical Path Network Mirosław Klinkowski and Krzysztof Walkowiak

Abstract—A spectrum-sliced elastic optical path network (SLICE) architecture has been recently proposed as an efficient solution for a flexible bandwidth allocation in optical networks. In SLICE, the problem of Routing and Spectrum Assignment (RSA) emerges. In this letter, we both formulate RSA as an Integer Linear Programming (ILP) problem and propose an effective heuristic to be used if the solution of ILP is not attainable. Index Terms—Elastic Optical Path Network, ILP, RSA.

I. I NTRODUCTION

T

HE SLICE architecture is a novel and very promising solution for 100 Gb/s and beyond connection provisioning in optical networks [1]. SLICE can provide, at the same time, sub-wavelength granularity for low-rate transmission and super-channel provisioning for accommodating ultra-high capacity client signals. As an analogy to the Routing and Wavelength Assignment (RWA) problem in DWDM optical networks [2], the Routing and Spectrum Assignment/Allocation (RSA) problem emerges in SLICE [3]. RSA concerns assigning a contiguous fraction of frequency spectrum to a connection request subject to the constraint of no frequency overlapping in network links. The objective of RSA is to minimize the spectrum used to serve the demand matrix. An heuristic approach initially proposed to solve the problem makes use of the Fixed-Alternate routing and First-Fit frequency assignment (FA-FF) algorithm [3]. As the authors of [3] noticed, FA-FF is not very efficient because it tends to produce unstaffed spectrum occupancy. Indeed, although the FA-FF strategy results in low overall frequency resources usage since it favors shorter routing paths, still the spectrum of frequencies used in the network is wide. The RSA problem is novel to the community and, to the best of our knowledge, there is little work that addresses it in the literature. In the very recent work by Christodoulopoulos et al. [4], the RSA is formulated as an ILP problem. The authors present and examine greedy heuristic algorithms that process demands one-by-one according to selected ordering criteria. In this letter, we introduce an ILP formulation which, on the contrary to the one presented in [4], makes use of variables Manuscript received February 09, 2011; revised May 24, 2011. This work was supported by the Polish Ministry of Science and Higher Education. M. Klinkowski is with the Department of Transmission and Optical Technologies, National Institute of Telecommunications, ul. Swojczycka 38, 51-501 Wrocław, Poland (e-mail: [email protected]). K. Walkowiak is with the Department of Systems and Computer Networks, Wroclaw University of Technology, Wrocław, Poland (e-mail: [email protected]). Copyright (c) 2011 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected].

and constraints that depend on the frequency resources. The problem objective is to minimize the width of the frequency spectrum allocated in the network. RSA is N P-hard and, as our results show, it is computationally difficult even for small network scenarios. Anticipating large problem instances in real networks due to the high resource granularity, we propose a novel heuristic algorithm called AFA-CA (Adaptive Frequency Assignment - Collision Avoidance). The main idea behind the method is to adaptively select the sequence of processed demands in order to minimize the spectrum used in the network. An additional criterion applied in AFA-CA is a metric indicating potential collision of links, i.e., we want to select paths that do not include links which are likely to be congested. Numerical experiments show that AFA-CA outperforms other heuristics as well as it provides results close to the optimal ones.

II. N ETWORK S CENARIO AND P ROBLEM D EFINITION SLICE allows to allocate flexibly appropriate-sized optical bandwidth, by means of contiguous concatenation of optical spectrum, to an end-to-end optical path and according to traffic demand. To provide the elastic multiple-rate data traffic accommodation the network should be equipped with bandwidth-variable transponders (BV-Ts) and bandwidthvariable wavelength cross-connects (BV-WXCs) [1]. BV-T may operate with either single-carrier or multicarrier advanced modulation formats (QAM, QPSK, O-OFDM) [3]. Concurrently, BV-WXCs can be built with the existing technology, such as the WaveShaper programmable optical processor [5]. In order to represent spectral resources, the concept of frequency slots (FSs) has been proposed in [3] as an extension to the current ITU-T DWDM rigid frequency grid [6]. In the proposal, the ITU-T frequency grid is further divided into a number of narrow spectrum segments (i.e., FSs). Each FS represents optical channel and an optical path can be allocated by assigning a number of contiguous FSs according to the requested bandwidth and the modulation format [3]. In this letter, we assume a static (off-line) RSA problem, where traffic demands are known in advance. We assume that the volume of traffic can be translated into a number of requested FSs (as discussed in [3]). The RSA problem objective is to find, for a given set of demands, the end-to-end optical paths and assign the requested FSs in a contiguous way with a constraint to avoid FS overlapping in network links. We consider the network which has capacity sufficient to serve all offered demands, i.e., there is no connection blocking.

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III. RSA P ROBLEM F ORMULATION

xpf , ypf , xef , xf ∈ {0, 1} , F ∈ Z+ ,

We formulate RSA as an ILP problem. For the sake of simplicity, we make use of so-called path-link approach [2] for the network flow representation of RSA. In such a formulation, a set of paths is predefined between network nodes and each path is identified by a subset of network links. A. Notation We use G = (V, E) to denote the graph of the network; the set of nodes is denoted as V, and the set of unidirectional links is denoted as E. In each link an ordered set F = f1 , f2 , . . . , f|F | of frequency slots is given. Let D denote the set of demands, where each demand corresponds to a connection request. Demand d is determined by a triple (sd , td , nd ), where sd and td are source and termination nodes, and nd ∈ Z+ is the number of FSs requested by the connection. Let Pd denote the (non-empty) set of predefined candidate paths for demand d ∈ D. Each set Pd comprises paths that have the origin in sd and the termination in td . Let S P denote the set of all paths, i.e., P = d∈D Pd . Each path p ∈ P is identified with a subset p ⊆ E. Adequately, subset Pe ⊆ P identifies all paths that go through link e. Remark: Without loss of generality, we consider nd to be independent on the path length (see [3] for more discussion). B. ILP formulation We introduce a set of problem variables: xpf ∈ {0, 1} - equal to 1 if FS f ∈ F on path p ∈ P is selected to be the lowest indexed slot that is assigned to a demand, and equal to 0 otherwise, ypf ∈ {0, 1} - equal to 1 if FS f ∈ F on path p ∈ P is assigned to a demand, and equal to 0 otherwise, xef ∈ {0, 1} - equal to 1 if FS f ∈ F is occupied in link e ∈ E, and equal to 0 otherwise, xf ∈ {0, 1} - equal to 1 if FS f ∈ F is assigned to at least one demand in the network, and equal to 0 otherwise, F ∈ Z+ - number of FSs in the frequency spectrum that are assigned to at least one demand in the network. We formulate RSA as an ILP optimization problem: minimize

F

subject to P P

xpf = 1,

(ILP1) ∀d ∈ D,

(1a)

p∈Pd f ∈F

∀d ∈ D, ∀p ∈ Pd , ∀fi , fj ∈ F, where i = 1, . . . , |F| − nd + 1, and j = i, . . . , i + nd − 1, (1b)

xpfi − ypfj ≤ 0,

xpfi = 0,

∀d ∈ D, ∀p ∈ Pd , ∀fi ∈ F, where i = |F| − nd + 2, . . . , |F| , (1c)

P

ypf − xef = 0,

∀e ∈ E, ∀f ∈ F,

(1d)

p∈Pe

P

xef − |E| xf ≤ 0,

∀f ∈ F,

(1e)

e∈E

P f ∈F

xf − F = 0,

(1f)

∀p ∈ P, ∀f ∈ F, ∀e ∈ E. (1g)

The problem objective is to minimize the number of FSs in the frequency spectrum that are assigned to at least one demand in the network. Constraints (1a) are the path and FS selection constraints. For each demand a path is selected from the set of candidate paths and, concurrently, a FS is selected on this path as the lowest indexed slot assigned to this demand. Constraints (1b) are the contiguous FS assignment constraints. Whenever there is a FS fi selected as the lowest indexed slot for demand d, the consecutive slots fj , where j = i, . . . , i + nd − 1, should be assigned to this demand. The spectrum continuity constraint along a route is imposed implicitly since the assignment of a FS concerns the entire path and, therefore, each link on the path. Constraints (1c) aim to exclude such FS selection options for which there is no enough space for the FS assignment in the frequency spectrum. Constraints (1d) are the capacity constraints and they say that each FS in each network link can be assigned to at most one demand, what is guaranteed by the binarity of xef . Constraints (1e) force variable xf to be equal to 1 if FS f is used in at least one link. Constraint (1f) counts the total number of such active FSs. Finally, (1g) are the variable range constraints. Remark: The main difficulty of formulation ILP1 comes from the large number of FSs (equal to |F|) in some network scenarios. As a result, there is a huge number of constraints (1b), which is of the order of O (|P| |F| Xn ), where Xn = −1 P |D| d∈D nd is the mean number of slots requested by a demand. Indeed, the presence of the contiguous FS assignment constraints (1b) is the main difference between RSA and RWA. In fact, the special case of RSA, in which nd = 1, ∀d ∈ D, is equivalent with the RWA problem. As a consequence, the RSA optimization problem is N P-hard in general. IV. AFA-CA A LGORITHM Here, we present a novel heuristic method called Adaptive Frequency Assignment - Collision Avoidance (AFA-CA). Let Dn denote a set including all demands with requested FSs equal to n, i.e., Dn = {d : d ∈ D, nd =Pn}. For P each link e, we calculate a collision metric ce = d∈D p∈(Pd ∩Pe ) nd and this metric estimates the number of FSs that might be allocated to link e taking into account all candidate paths. Note that the bigger is value of ce the more FSs might be potentially allocated to the particular link. Consequently, if we select shorter paths (in terms of metric ce ), less congested links are selected and thusP the objective function F is likely to be decreased. Let lp = e∈p ce denote the length of path p ∈ P calculated according to metric ce . Using metric lp , we −1 P compute metric ld = |Pd | p∈Pd lp that defines the average length of candidate paths of demand d in terms of metric ce . In AFA-CA we assume that demands are processed in decreasing order of requested FSs (denoted by nd ). We start with demands Dn that require the highest number of FSs, i.e., for n = max {nd : d ∈ D}. Let function MinFS(d) return the lowest indexed and accessible FS for demand d. In details, MinFS(d) analyzes all candidate paths p ∈ Pd of the

JOURNAL OF LATEX CLASS FILES, VOL. 6, NO. 1, JANUARY 2007

considered demand d and searches for the lowest indexed FS that can be selected for demand d under the assumption all model constraints and previously allocated demands are taken into account. Using MinFS(d), we select demand d∗ ∈ Dn with the lowest index of FS. If more than one demand included in set Dn returns the same index of FS, we use additional selection criterion defined by metric ld . Now, let function MinFSPath(d) return the index of a candidate path selected to allocate demand d in order to minimize the index of allocated FS. Using a similar idea as above, all candidate paths p ∈ Pd are examined. If more than one candidate path yields the minimum index of FS, we select a path with a lower value of the lp metric. Recall that the lp metric estimates congestion on path p calculated using the collision link metric ce . The already processed demand d∗ is allocated to path p =MinFSPath(d∗ ) and is removed from set Dn . We continue the procedure until set Dn is empty. Next, we decrement n and process the next set of demands Dn until all values of n are examined and, consequently, all demands are allocated in the network. Below we present a pseudocode of AFA-CA. Algorithm 1 AFA-CA 1: n ← max nd d∈D

Dn ← {d : d ∈ D, nd = n} for each demand d ∈ Dn do fd ← MinFS(d) d∗ ← arg min(fd ); if more than one demand yields the minimum value of fd , use metric ld as additional criteria. 5: Allocate demand d∗ to path p ←MinFSPath(d∗ ) 6: Dn ← Dn \ {d∗ }; if Dn = ∅, go to step 7, otherwise, go to step 3. 7: n ← n − 1; if n < 1, terminate, otherwise, go to step 2.

2: 3: 4:

The computation complexity of AFA-CA is bounded by O (|D| |P| |F | |E|), where |D| is the number of demands to be processed, |P| is an upper bound on the number of paths analysed by MinFS(·) (per iteration), and |F| |E| corresponds to the (worst-case) complexity of the FS search in MinFS(·). The main difference between our algorithm AFA-CA and reference algorithms proposed in earlier works (i.e., FA-FF [3], MSF [4]) consists in the way demands are processed. Previous algorithms analyze demands according to a fixed order (e.g., the MSF algorithm assumes that demands are processed in decreasing order of the number of their requested FSs). Our method works in an adaptive way and – according to previously allocated demands as well as the current usage of FSs in the network – selects the next demand to be processed. V. N UMERICAL R ESULTS AND D ISCUSSION Here we compare RSA performance results obtained with ILP, AFA-CA, and two reference algorithms, namely, FAFF [3] and MSF [4]. We evaluate the number of FSs of the occupied frequency spectrum (F ) and the computation time (T ). We use IBM ILOG C PLEX v.12.2 [8] on an Intel i3 2.27GHz 2GB computer to solve ILP. The results are obtained for three mesh network topologies [7]. We assume |Pd | = 3, ∀d ∈ D and the paths are the shortest paths. The demand pairs (sd , td ) are generated randomly and the number

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of requested FSs nd is uniformly distributed on {1, . . . , S}, where S ∈ {5, 15, 30, 45}. TABLE I O PTIMALITY GAP (SIMPLE NETWORK , 6 NODES / 16 LINKS ). Scenario S |D| 5 30 5 60 5 90 15 30 15 45 30 15

F 14.25 28.30 40.20 43.85 66.50 43.55

ILP T [sec] 13 145 1146 1233 7313 12747

FA-FF G [%] 33.22 32.02 29.70 32.33 29.11 32.29

MSF G [%] 13.59 10.10 9.45 14.35 9.15 14.93

AFA-CA G [%] 7.02 3.29 2.49 6.96 3.51 5.22

In Table I, we focus on a small network and evaluate the optimality gap for heuristic solutions with respect to the ILP optimal results (G). The results are averaged over 20 randomly generated demand sets. We can see that AFA-CA offers better performance (approx. 7.5%) than MSF. Processing times are in the milliseconds range for all heuristics. TABLE II C OMPARISON OF ALGORITHMS ; (T IN MILLISECONDS ). Scenario Network S NSFNET 5 15 nodes / 15 46 links 30 45 UBN24 5 24 nodes / 15 86 links 30 45

|D| 420 420 420 420 552 552 552 552

FA-FF F 134.5 374.0 723.6 1075.1 179.3 483.8 939.0 1394.1

T 2 3 4 7 3 5 9 15

MSF F 104.0 286.9 564.5 836.1 121.8 329.3 635.2 959.9

T 5 11 22 38 8 17 36 64

AFA-CA F T 96.1 217 261.9 262 511.7 350 762.3 468 118.8 421 319.3 517 618.2 717 937.7 977

In Table II, we compare algorithms in larger networks. We show results averaged over 100 randomly generated demand sets. We can see that in all reported cases, our method AFACA provides better results than the reference algorithms. The average distance between AFA-CA and MSF for NSFNET and UBN24 is 9.4% and 2.7%, respectively. The percentage distance between algorithms generally does not depend on S. Algorithm AFA-CA needs more time to find the solution comparing to FA-FF and MSF. However, the execution time of AFA-CA is less than 1 second even for most demanding case (UBN24 network with 552 demands and S = 45). R EFERENCES [1] M. Jinno et al., ”Spectrum-efficient and scalable elastic optical path network: Architecture, benefits, and enabling technologies”, IEEE Comm. Mag., vol. 47, no. 11, pp. 66-73, Nov. 2009. [2] M. Pi´oro and D. Medhi, Routing, Flow, and Capacity Design in Communication and Computer Networks, Morgan Kaufmann, 2004. [3] M. Jinno et al., ”Distance-Adaptive spectrum resource allocation in spectrum-sliced elastic optical path network”, IEEE Comm. Mag., vol. 48, no. 9, pp. 138-145, Aug. 2010. [4] K. Christodoulopoulos et al., “Routing and Spectrum Allocation in OFDM-based Optical Networks with Elastic Bandwidth Allocation”, IEEE Globecom 2010, Miami, FL, US, Dec. 2010. [5] Finisar: Programmable narrow-band filtering using the WaveShaper 1000E and WaveShaper 4000E, White Paper, http://www.finisar.com. [6] ITU-T G.694.1, “Spectral grids for WDM applications: DWDM frequency grid,” May 2002. [7] M. Klinkowski et al., “An Overview of Routing Methods in Optical Burst Switching Networks”, Opt. Switch. Net., vol. 7, no. 2, pp. 41-53, Apr. 2010.

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[8] “IBM ILOG CPLEX: High-performance mathematical programming engine.”, http://www.ibm.com/, 2010.

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