Spectrum Allocation Policy Modeling for Elastic Optical Networks

Spectrum Allocation Policy Modeling for Elastic Optical Networks Adriana Rosa, Cicek Cavdar, Solon Carvalho, Joao Costa and Lena Wosinska

Abs tract-Today, optical transmission technologies are able to support 400Gbps over a single optical channel. However, this capacity cannot fit in the current fixed frequency grid optical spectrum. On the other hand, high rate optical channels have to co-exist with different ranges of line rates in order to serve heterogeneous

bandwidth

requests

from

variety

of

internet

applications. Today's fixed rate and rigid frequency grid optical transmission systems cause over provisioning, where usually more spectral resources are provided than necessary. Recently, the concept of elastic optical networks has been proposed in order to reduce this waste of resources. In networks with such feature enabled, modulation parameters and central frequencies are not fixed and the resources can be allocated with a fine granularity, in contrast to the traditional WDM networks. This flexibility makes it possible to adapt to the granularity of the requested bandwidth without over provisioning. However, this heterogeneous bandwidth allocation may on the other hand result in fragmentation of spectral resources under dynamic traffic. In this study we quantify the fragmentation in elastic optical networks and calculate the blocking probability

(BP)

together

with fragmentation on an elastic optical channel. In this regard, an analytical model based on a Markov Chain is developed under dynamic and flexible bandwidth traffic scenario. By using this analytical

model

different

spectrum

allocation

policies

are

compared. A novel spectrum allocation policy is proposed which has lower BP and fragmentation ratio compared to the existing strategies.

Index

Terms-

Physical

Impairments,

energy-efficient

networks, optical WDM networks.

I.

INTRODUCTION

ODAY, we are facing a paradigm shift in optical networks with the emerging flexible transmission technologies which are able to support 100 Gbps and even 400 Gbps [1] over a single wavelength [2]. Elastic optical networks (EON) are expected to support channels with different bandwidth demand without wasting of spectrum resources, and in this way accommodate ever-increasing bandwidth requirements of emerging heterogeneous applications. EON is a revolutionary solution to support different line rates, in a flexible grid for efficient usage of

Tbackbone

C. Cavdar ([email protected]) and L. Wosinska ([email protected]) are with the Royal Institute of Technology (KTH), Kista, Sweden. S. Carvalho ([email protected]) is with National Institute for Space Research, Sao Jose dos Campos, Brazil, J. Costa ([email protected]) and A. Rosa ([email protected]) are with Federal University of Para, Belem, Brazil. A. Rosa is currently visiting KTH, Kista, Sweden. The research leading to these results was supported by Optical Networking Systems (ONS) focus projects, part of ICT The Next Generation (TNG) Strategic Research Area (SRA) initiative at the Royallnstitute of Technology.

978-1-4673-2890-6/12/$31.00 ©2012

IEEE

spectral resources. EON has three dimensional agility that comes with the underlying technologies: (1) Coherent detection techniques enabling continuous optical carrier frequency, i.e., gridless; (2) Orthogonal Frequency Division Multiplexing (OFDM) [3] enabling variable numbers of subcarriers on a channel; (3) Different modulation formats on each OFDM subcarrier enabling the change of distance adaptive capacity contributed by each subcarrier [4]. There are different advantages of this agility. (1) Optical interfaces in EON can adapt/tune dynamically their data rate according to the amount of data to be transmitted [4]. Typically, the transmission rate of the interface can be precisely tuned to the required data rate instead of the static peak rate, enabling improved spectrum resource efficiency, especially when the traffic profile is dynamic; (2) EON can adapt modulation formats to support changing network conditions, e.g., optical signal quality degradations, (3) power savings, hence reduction in operational expenditure (OpEx), can be achieved. In EON, the optical spectrum is divided into a number of frequency slots, and the width of each slot corresponds to the spectrum width of an OFDM subcarrier [4]. According to the ongoing standardization efforts in ITU-T, the minimum frequency slot that can be allocated will be 12.5 GHz (which will correspond to the minimum granularity) [5][6]. In order to provision a spectrum path in an optical OFDM network, the traditional Routing and Wavelength Assignment (RWA) problem evolves towards a more challenging Routing and Spectrum Allocation (RSA) problem. Instead of a wavelength, a connection is now assigned one or more sub­ carrier slots, depending on whether the capacity requirement of a connection is larger than the OFDM sub-carrier capacity. If multiple slots are needed, they have to be contiguous which makes the routing and spectrum assignment problem more complicated than in fixed grid WDM networks. The traditional wavelength continuity constraint of the RWA problem becomes the spectrum continuity constraint in the RSA problem. The majority of the works available in the literature are investigated the possible advantages of using the flexible spectrum assignment concept in a static traffic scenario [7]. The objective of the static RSA problem is to minimize the number of sub-carrier slots that are necessary to provision the required number of connections. In [7], authors propose a heuristic and an integer linear programming (ILP) model fmding the optimum solution of the RSA problem taking into

242

account spectrum continuity and contiguity constraints with non-overlapping spectrum constraint. However ILP solution is not scalable to large networks, hence, some efficient meta­ heuristic solutions are proposed for the static problem [8] [9]. It is shown that efficient solutions can be achieved by ant colony optimization [8] and simulated annealing [9] based approaches respectively. So far, EON under dynamic traffic conditions, where the future bandwidth requests are not known in advance, are not widely investigated. In [lO] authors propose greedy heuristics to solve the problem without using any advanced optimization techniques. Under dynamic traffic conditions, fragmentation of the optical spectral resources is an important and an inevitable problem in EON. Fragmentation reduces the spectrum efficiency, and hence increases the blocking probability (BP) due to the gaps scattered around the spectrum, which are de­ allocated randomly by departing dynamic heterogeneous-rate connection requests. In [11] and [12] authors address the defragmentation problem under full spectrum retuning / wavelength conversion capability after the fragmentation occurs. However the defragmentation efforts can be quite expensive and disturb existing traffic. The main unsolved problem is to have an in depth analysis of spectrum assignment techniques in terms of spectrum fragmentation and to prevent fragmentation before it occurs. In [13], the authors presented a method to quantify the level of fragmentation called "utilization entropy" and in [14] another metric is presented called "spectrum compactness". However those quantifications are not precise and they don't consider the fragmentation in connection with the request bandwidth size. Fragmentation becomes a problem especially when the incoming connection requests have larger bandwidth than the available contiguous spectrum slots. If the connection requests are small enough, then the fragmentation might not be an issue. In this paper, we first propose methods to quantify the fragmentation in elastic optical networks and calculate the blocking probability (BP) together with fragmentation on an elastic optical channel. In this regard, analytical model based on Markov Chain is developed under dynamic and flexible bandwidth traffic scenario. By using this analytical model, BP and fragmentation in different spectrum allocation policies can be calculated. A novel spectrum allocation policy is proposed which has lower BP and fragmentation ratio compared to the existing strategies. II.

SPECTRUM ASSIGNMENT POLICIES

In an elastic optical channel, spectrum slots are assigned to the dynamically arriving connection requests with different granularities. In this work, we propose a spectrum allocation policy called Exact-Fit and compare it with three different existing spectrum allocation policies:

First-Fit (FF): the first-fit policy places the request in the first available frequency band fitting the spectrum

demand.

Smallest-Fit (SF): this policy allocates the smallest free block. This is done in order to fill-up the gaps, hence reducing fragmentation. Random-Fit (RND): the random allocation policy allocates incoming requests in any available block large enough to satisfy the requested bandwidth. This policy is considered for benchmarking purposes. The proposed spectrum allocation policy works in the following way:

Exact-Fit (EF): Starting from the beginning of the frequency channel EF searches for the exact available block in terms of the number of slots requested for the connection. If there is a block to match the exact size of requested resources, the algorithm allocates that spectrum. Otherwise, the spectrum is allocated in the first largest free block available. III.

FRAGMENTAnON PROBLEM

In networks with non-uniform bandwidth assignment, spectrum fragmentation is a problem, since the process of adding and terminating connections will soon lead to the interspersed free spectrum, which in turn results in many small noncontiguous spectral bands that cannot be used to satisfy requests of larger bandwidth. Hence, the spectrum efficiency gained by flexibility in the bandwidth allocation may be reduced due to this small noncontiguous free frequency bands scattered around the spectrum [15]. Note that fragmentation is not directly correlated with the spectrum utilization which is defmed as proportion of used over total spectral resources, it is a problem when free resources are broken into pieces smaller than the requested bandwidth.

A. Measures of fragmentation There are different alternatives to quantify the fragmentation. One of them is the external fragmentation, as denoted in Equation 1 [16].

largest free block

F""xt 1- -=----'�--=

(1)

total free

where the largest free block is the count of slots of the largest contiguous free space, and total free is the total number of free slots. In Equation 1, a fragmentation close to one (lOO%) means that the free space is all carved up into many small blocks. On the other hand, if all free memory is in a single block, fragmentation is 0%. This equation is valid under the assumption that there is always a free slot available in the system. Another measure of fragmentation takes into account the fact that the fragmentation is dependent on the bandwidth demand of connection requests, e.g., it is more severe when the connections require larger spectrum resources. Hence, the fragmentation can also be a function of the number of slots required by a connection request. This measure is expressed in Equation 2 [16].

243

F(c) 1=

c x Free(c) total free

(2)

In Equation 2 c is the number of slots required for a certain connection and Free(c) is a function that counts the number of simultaneous requests of size c that can be satisfied. Again, Equation 2 is valid under the assumption that there is always a free slot in the system. For Equation 2, every class of connection request, classified according to the number of requested slots, has its own measure of the fragmentation. Both formulations represented in Equations 1 and 2 are rather simple, but they capture the essentials of how much of the free space is not being used efficiently due to fragmentation. To give an example, suppose a frequency grid of 30 slots on the given states where one and zeros represent the busy and free slots respectively: Sj

=

S

(100110011010101110011000010101)2 (111111111111101010000000000000 )2

) By inspection, Sj is highly fragmented while S) is not. Hence, Sj can accept a wider variety of incoming connections (up to c = 13 slots) than S, (up to c = 4 slots), which certainly means that Sj may face higher blocking probability than S). By using the external fragmentation formula in Equation 1, this would result in FextC S,) = 1 - 4115 = 73.33% and Fex, (S) = 1 13115 = 13.33%. On the other hand, if one considers the formula in Equation 2, every type of request has its own measure of fragmentation. For instance, for connection requests of c = 2 slots: F2(S,) = 1 - (2 x 5113) = 23.07% and F2(Sj) = 1 - (2 x 6113) = 7.69%. =

Table 1 shows values of fragmentation in % for the sample states S, and Sj and for different number of requested slots calculated by Equation 2. It is important to note that the fragmentation is 0 for requests with c=1 in both cases according to Equation 2, considering the acceptance rate is the same due to the same number of free slots in both cases. Fext

F\

F2

F3

F4

Fs

Sj

73.33

0

23.07

76.92

76.92

100

Sj

13.33

0

7.69

7.69

7.69

100

Table 1 - Fragmentation (in %) according to Eqn. IV.

1

characterized by requested contiguous slots, c (J �c �C). Rc: Incoming connection request type ; Ac: arrival rate for Rc, according to a Poisson distribution; Ilc: service rate for Rc, according to an exponential distribution. The frequency spectrum occupied by one slot is equal to F GHz, and F represents the total system spectrum. In our model, in order to simplify the mathematical formulation, we neglect the guardbands. By using a Markov Chain to describe the stochastic process corresponding to the spectrum occupancy in the system, we obtain the probabilities of the system to be in given states of spectrum usage. We also calculate the average blocking probabilities and measure the fragmentation by taking M policies into consideration. In order to calculate the steady-state probabilities of being in a certain state in our Markov Chain (i.e. probabilities of certain occupancy of the available spectrum) we developed a spectrum allocation policy model, taken into account the spectrum fragmentation in an elastic optical grid. The objective is to analyze the steady-state behavior of an elastic optical link under different scenarios of spectrum assignment, which can calculate blocking probability and fragmentation.

B. Markov model We model our system by a Markov Chain, which consists of a set of states and its transition rates. The transition to the next state depends only on the current state and is independent from the previous states. To develop a model indepently of the spectrum assignment policy, we consider that every policy can be represented as a matrix M={mj) for i,j=O . . . 2N.I, where the elements m,,) are 1 (or true) if the transition from the state j to state i is possible, and zero (or false) otherwise, according to the formation law. The matrix Q shown in Equation 3 is known as the infmitesimal generator or transition-rate matrix as its elements are the instaneous rates of leaving a state for another state and is constructed from the allocation matrix M by using this strategy, we optimize the process of construction of the matrix Q, since it is a sparse matrix, and only the relevant elements, previously identified in the matrix M, are considered.

-L

j*o

qO,j

qO,1

qo,z

qO,ZN-1

and 2.

ELASTIC SPECTRUM ASSIGNMENT M ODEL

We propose a model based on a Markov Chain to analyze performance of different spectrum assignment policies discussed in Section II. For a future work, such specialized spectrum assignment policies can be combined with routing techniques to solve the entire RSA problem.

A. Problem definition As an input, we consider an elastic optical grid with N slots. The incoming connection requests are classified in C different types. Each type of incoming connection request Rc is

Q=

(3) qzN-1,O

qzN-1,1

L

j*ZN-1

qzN-1,j

The state space set can be described as a vector S = (Sl . . . sMJ and 71:, denotes the steady state probability of state Sj. Then, the T vector 71: = (71:1 . . . 71:MJ describes all the steady-state probabilities for a given policy. To obtain the steady-state probabilities, one has to solve the following linear system: As Q is highly sparse in Equation 4 and this system of linear equations is not square, we use the Sparse Equations and 244

Least Squares (LSQR) algorithm [17] to solve it efficiently.

(4) The average fragmentation can be calculated by F(S) X7r, where F(S) (F(s]) . . . F(sMJ) is a vector with a fragmentation measure, according to either Equation 1 or Equation 2, for every possible state. =

C.

Blocking probability calculation

For a given state s, Pls) denotes the blocking probability for each request type Rc It can be calculated based on the size of the largest free block (e.g. size m) in state s as in the following equation. p

c (s)

=

p, to,

i.f If

c

:::;

m

(5)

c > m

By summing up the blocking that can occur in each state and the probability being in that state, one can derive the blocking probability for a specific request type c by using Equation 6. ZN-1

Bc

=

L Pc(s)

X

rr(s)

(6)

Total blocking probability can be calculated by summing the BP of each request type where C denotes the number of customer types. C

=

L

c=l

(7)

Bc v.

B. Fragmentation rates analysis Figure 1 (c) shows the probability to have fragmentation higher than 50% by using Equation 1, for three policies: First­ Fit, Exact-Fit and the Random-Fit policy. For low loads, the difference between those policies is very significant, with more then 30% of difference between the two extremes: Exact-Fit and Random. For all loads, the Exact-Fit policy presents the lowest probability of high fragmentation. As the load increases, this probability gets lower. This fact is already expected, because it is more likely to have less free spaces and, therefore, less fragmented resources. Table 2 presents the fragmentation for the heterogeneous arrival rates for different request types according to Equation 1. One can note that the Exact-Fit policy shows, as expected, the least fragmentation for all types of loads, especially when small size requests have higher arrival rate, i.e. for A (3,2,1). It should be noticed that the First-Fit policy performs very close to Random-Fit policy when the arrival rates are heterogeneous, which shows the benefit of taking into account the sizes of requests during spectrum allocation especially when the rates are heterogeneous. =

s=o

B

Random-Fit showing the importance of using a smart approach instead of random spectrum allocation. Figure 1 (b) compares the three approaches, i.e. First-Fit, Smallest-Fit and Exact-Fit in terms of the BP reduction compared with the Random policy. It is shown that Exact-Fit outperforms both approaches. The reason is that it prevents the smallest fitting blocks if not exactly fitting hence avoiding the small leftovers after the smallest fit.

A

NUMERICAL RESULTS

In the elastic optical channel, average connection holding time 1111 is considered as one unit time following an exponential distribution. Connections arrive following a Poisson distribution with arrival rate of A nonnalized to the holding time. Results are presented for four different spectrum allocation policies taking into account three types of connection requests, i.e. with three different sizes: 1 slot, 2 slots or 3 slots, for a total system spectrum of 16 slots. The following vectors defme the arrival and service rates of corresponding requests: A (Ab A2, A3) and 11 (11" 112, 113)· Perfonnance of spectrum allocation policies is analyzed by calculating the blocking probability BP, BP reduction compared with the random allocation policy and fragmentation in the system. =

A A

=

=

=

FF

SF

EF

RND

(1,1,1)

42.40

33.34

25.63

47.16

(1,2,3)

43.00

35.06

27.74

42.21

(3,2,1)

34.08

23.68

16.66

33.06

Table 2 - Average fragmentation - Equation ] in % -for different SA policies and loads. The main lesson learned from our results in Table 2 is that the quality of an elastic optical channel, in terms of fragmentation gets worse with the increase of the arrival rate of large-size requests.

=

A. Blocking probability The average blocking probability for 4 different spectrum allocation policies is depicted in Figure 1 (a) which is defined as the weighted average BP for different type of requests. In this Figure, the arrival rates, in terms of arrivals per time unit, are homogeneous. Blocking probability increases exponentially with the increase of the load. Three policies have shown significantly better performance compared to

Table 3 shows the fragmentation according to Equation 2, for homogeneous arrival rates. Note that this alternative fragmentation calculation method is dependent on the number of slots requested, i.e. c. Therefore different fragmentation values are presented for each request type. We considered homogeneous rates for each request type to have a fair comparison of fragmentation for different request types. Note that the fragmentation value calculated for requests with c=1 is o. This is due to the fact that there is never wasted free space for connection requests of size c 1: they simply do not suffer from the fragmentation problem. If there is free space available, requests of size c ] will always be served. =

=

245

(ft

Random .� .. � .. First-Fit :0 B Sm a l i e s t Fi t � o 0.05 rL-_ E_x_a_c_t-F_ it_ ---' " '

" '

0 "0 c

o o

�

�

>

60

en Ol c

40

0

0) c

:i:

o o

C:i5

2

4

'> ctl (/) c... co

_ Exact-Fit D First-Fit _ Random

--- Exact-Fit '.

80

ctl a::

-

!l: en

0.5

10 0

E

•

0 '11

Smallest-Fit

.. � ..

LO

First-Fit

0 II 1\ Ol ctl

U: (['

·li .

' .. & .

20 0

.

.

.. . . . .. ..

0.3 0.2 0.1

.

0

4

2

Arrival Rate W

0.4

(1,1,1)(2,2,2)(3,3,3) Arrival Rate �

Arrival Rate (�

Figure J - (a) Average blocking probabilities for different loads; (b) T hroughput gain over random policy; (c) Probability of high fragmentation (> = 0.5) Ie = (3,3,3)

Ie = (2,2,2)

1e= (1,1,1)

[3]

c=2

c =3

c =2

c =3

c =2

c =3

FF

27.24

46.37

52.43

72.24

37.95

55.15

SF

30.33

51.99

57.30

76.99

46.51

64.29

S. Jansen, et aI., "Optical OFDM,a hype or is it for real?" Proc., ECOC,Sept. 2008.

EF

23.60

40.21

47.17

66.59

32.05

47.58

RND

36.40

58.07

57.80

76.73

47.38

64.03

[4]

M.

Jinno, et

aI., "Distance-Adaptive

Spectrum

Resource

Allocation In Spectrum-sliced Elastic Optical Path Network," IEEE Commun. Mag.,Vol. 48,No. 8,pp. 138-45,Aug. 2010. [5]

ITU-T CI284, "Proposal of subjects to be discussed regarding

[6]

ITU-T C1288, "Extension of Rec. G.694.1 by a new clause to

flexible grids," January 2011. address flexible frequency grids," January 2011.

Table 4 - Average fragmentation - Equation 2 in % -for different SA assignment policies and loads.

[7]

K. Christodoulopous, et aI., "Elastic Bandwidth Allocation in Flexible

OFDM-Based

Optical

Networks ",

IEEE/OSA

J.

Lightw. Technol.,Vol. 29,No. 9,2011.

VI.

CONCLUSIONS

[8]

Proc.,OFCINFOEC 2012.

stochastic process corresponding to the spectrum occupancy in an elastic optical channel to calculate the blocking probability and fragmentation for different spectrwn allocation policies by solving the steady state probabilities. We have shown that smart spectrwn allocation policies considering the size of the allocated block together with the size of the connection

Y. Wang, et aI., "Routing and Spectrum Assignment by Means of Ant Colony Optimization in Flexible Bandwidth Networks,"

In this paper we propose a Markov Chain illustrating the [9]

K. Christodoulopoulos, I. Tomkos, and E. A.

Varvarigos,

"Routing and Spectrum Allocation in OFDM-based Optical Networks with Elastic Bandwidth Allocation," Proc., GlobeCom 2010. [10] T.

Takagi, et aI., "Dynamic

Routing and Frequency Slot

Assignment for Elastic Optical Path Networks that Adopt

request performs better compared to random or sequential

Distance Adaptive Modulation," Proc.,OFCINFOEC 2011.

approaches. We have also shown that if it is not possible to

[11] D. 1. Geisler, et aI., "Demonstration of Spectral Defragmentation

find

an

exact

fitting

spectrum

block,

it

is

better

to

in Flexible Bandwidth Optical Networking by FWM," IEEE

accommodate the largest fitting block in order to not leave

Photonics Technology Letters, Vol. 23, No. 24, pp. 1893-1895,

behind small blocks that would lead to fragmentation. With

Dec. 2011.

this regard we have proposed a novel spectrum allocation policy called

Exact-Fit.

This study is the first attempt to

calculate blocking probability together with fragmentation ratio by presenting the preliminary results. In our future work we plan to include guard bands in our model and analyze the correlation between fragmentation and blocking probability under different conditions and find the critical value of fragmentation to avoid the unacceptable levels of blocking probability.

[12] Y. Yin, et aI., "Dynamic on-demand defragmentation in flexible bandwidth elastic optical networks," Opt Express., Vol. 20, No. 2,pp. 1798-804, Jan 16,2012. [13] X. Wang, et aI., "Utilization Entropy for Assessing Resource Fragmentation in Optical Networks," Proc.,OFCINFOEC 2012. [14] X. Yu, et aI., "Spectrum Compactness based Defragmentation in Flexible Bandwidth Optical Networks," Proc., OFCINFOFC 2012. [15] A. Patel, et aI., "Defragmentation of Transparent Flexible Optical WDM (FWDM) Networks," Proc.,OFCINFOEC 2011. [16] P. R. Wilson,et aI., "Dynamic Storage Allocation: A Survey and Critical Review," in Proceedings of the International Workshop

VII. [I]

REFERENCES

O. Gerstel, et aI., "Elastic Optical Networking: A New Dawn for the Optical Layer " IEEE Communications Magazine, Vol. 50, No. 2,pp. SI2-S20,February,2012.

[2]

B. Mukherjee,Optical WDM Networks,Springer,Feb. 2006.

on Memory Management, ser. IWMM '95. London, UK, UK: Springer- Verlag,1995,pp. 1-116. [17] C. C. Paige and M. A. Saunders, "LSQR: An algorithm for sparse linear equations and sparse least squares," TOMS, Vol. 8, No. 1,pp. 43-71,1982.

246