An Optimized Virtual Network Mapping Using PSO in Cloud Computing

An Optimized Virtual Network Mapping Using PSO in Cloud Computing Vahid Abedifar*, Mohammad Eshghi**, Seyedali Mirjalili***, S. Mohammad Mirjalili**** *ECE Department, Shahid Beheshti University, Tehran, Iran, [email protected] **ECE Department, Shahid Beheshti University, Tehran, Iran, [email protected] ***School of Information and Communication Technology, Griffith University, Brisbane, Australia, [email protected] ****ECE Department, Shahid Beheshti University, Tehran, Iran, [email protected]

Abstract: Virtualization of optical networks is key enabler of cloud computing. A main part of optical network virtualization is virtual network mapping on the physical infrastructure. One major issue in Routing and Wavelength Assignment, RWA, problem is optimized allocation of optical network resources. In this paper at first a background on Particle Swarm Optimization concept and formulation is presented. Then, an optimization scheme using PSO is proposed for virtual network mapping. Five different cost functions are formulated and a new encoding method for optical networks is proposed. The constraints for solutions of RWA problem are addressed and some heuristics are proposed to satisfy them. Proposed optimization scheme is simulated by finding the map of different virtual networks on a physical infrastructure in order to optimize five different cost functions. Results are presented and discussed for defined cost parameters.

Keywords: Cloud Computing, Optimization, PSO, RWA, Virtual Network Mapping. 1.

Introduction

According to increasing bandwidth demand by users in recent communication services, one major concern of the communication service providers is fast and reliable provisioning of connections. In optical fibre communication, DWDM technology [1] has an important role in supporting the users' on-demand requests. Furthermore, appearance of cloud computing concept which is nominated as the next revolution of the information technology has convinced the IT enterprises to develop cloud services. In cloud computing environment the CPU, storage and network resources are provided for end users or other enterprises as a utility and the pricing model is pay-per-use [2]. One bottleneck of cloud computing realization is communication networks. In the other hand, the communication networks, especially optical networks, are key enablers of cloud computing environment. Virtualization is an important technology in optical networks which enables the cloud services [3]. There are two types of virtualization, server virtualization and

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network virtualization. Virtualization of network resources is to run multiple logical networks over the same physical infrastructure at the same time [4]. For building a virtual network, mapping of the virtual nodes and links on the physical infrastructure, which is also named Routing and Wavelength Assignment, RWA, is an essential step [4]. The virtualization can make an abstraction between user and physical resources in which the user gets the illusion of direct interaction with physical resources [5]. In other word, virtualization can hide the specifications of the network infrastructure [6]. One major concern of optical infrastructure providers is optimized routing and wavelength assignment in virtual network mapping in order to use optimum physical network resources. The RWA problem is determined as a NP-complete case [7]. In other word, increasing the problem size will increase the computational time exponentially [8]. For optimization of the RWA, different methods have been investigated. Some of these methods are Integer Linear Programming, ILP, [9], simulated annealing [10], and Genetic Algorithms, GAs, [11]. In [8], the GA is used to optimize the path length and the number of common hops, jointly. In [12] the GA is used to maximize the throughput of the network. In [13], the objective of optimization is "to establish the maximum number of connections with the least number of wavelength converters." In this paper, Particle Swarm Optimization, PSO, method is used to find the optimized map of the virtual networks on a physical infrastructure. Different cost functions are defined. Then, encoding method and constraints are detailed. The rest of paper is organized as follows. In section 2, a background on PSO is stated. Proposed optimization scheme of virtual network mapping using PSO is presented in section 3. Section 4 includes the simulation results and discussion. Paper concludes in section 5.

2.

A Background on PSO

Particle Swarm Optimization is an evolutionary computation technique which is proposed by Kennedy and Eberhart [14, 15]. The PSO was inspired from social behaviour of bird flocking. It uses a number of particles (candidate solutions) which fly around in the search space to find best solution. Meanwhile, they all look at the best particle (best solution) in their paths. In other words, particles consider their own best solutions as well as the best solution so far [16]. The PSO algorithm was mathematically modelled as follows [17]. (1) (2) Where is the velocity of particle i at iteration t, w is is a weighting factor, rand is a a weighting function, is the current random number between 0 and 1, is the pbest of position of particle i at iteration t, agent i at iteration t, and gbest is the best solution so far. The PSO starts with randomly placing the particles in a problem space. The velocities of particles are calculated in each iteration, using Equation (1). After defining the velocities, the position of masses can be calculated using Equation (2). The process of changing particles’ position will continue until meeting an end criterion. In the continuous version of PSO, particles can move around the search space because of having position vectors with continuous real domain. Consequently, the concept of position updating can be easily implemented for particles by adding velocities to positions using Equation (2). However, the meaning of position updating is different in a discrete binary space [18]. In binary space, due to dealing with only two numbers, “0” and “1”, the position updating process cannot be done using Equation (2). Therefore, a way should be found to use velocities for changing agents’ positions from “0” to “1” or vice versa. The transfer function that has been used for the binary version of PSO in [17] is presented as Equations (3) and (4). (3) is the velocity of particle i at Where parameter iteration t in k-th dimension. 1

0

If

1

1

If

1

(4)

and indicates the position and Where velocity of particle i at iteration t in k-th dimension. The general steps of Binary PSO, BPSO, are as follows.

a) All particles are initialized with random values. b) Repeat steps c-e until the meeting of the end condition. c) For all particles, velocities are defined using Equation (8). d) Calculate probabilities for changing the elements of position vectors based on transfer function, Equation (3). e) Update the elements of position vectors with the rules in Equation (4). 3.

Proposed Optimized Virtual Network Mapping Using PSO

In this section at first, a novel formulation of RWA problem is presented in 3.1. Then, the proposed scheme for encoding the optical networks is investigated in 3.2. 3.1 Proposed Formulation of RWA Problem The virtual network mapping problem is to route the virtual links on the physical infrastructure and to assign wavelengths to the light paths. These light paths satisfy the desired connection between virtual nodes. In defining the RWA problem, we considered that and are the beginning and the end of a virtual link. The parameters and are the source and destination of a physical link. Physical infrastructure is corresponding to , , , where parameter is the physical a graph nodes set, is the physical links set and specifies the set of physical nodes and links constraints. Virtual network is corresponding to a graph , where , , determines the virtual network nodes set. Virtual links set is specified by , whereas represents the virtual resources constraints. The objective on the . is to map the In the proposed optimization algorithm, distinct wavelengths, called , in each link of a physical network are considered. These different wavelengths are classified based on different transmission capacities. The number of wavelengths per physical link is . Different wavelength groups of each physical link are determined with . The number of wavelengths , , , , , ,…, , belong to each group is considered , , , , , , … , , . Therefore, we can . Capacities of each wavelength say ∑ , group of each physical link are considered to be , , , , , ,…, , . The desired cost functions which are considered in the proposed optimization method are formulated as follows. The number of used nodes in the mapped network is considered to be _ , Equation (5). A binary , is '1' if the node k is parameter for each node, called in the mapped network , and is equal to '0', otherwise. In 1 if 1, 1, … , , otherwise other word, 0. Parameter has binary value. When the link ( , ) is in the mapped network, this parameter is equal to '1' and it is zero when the link , is not in the mapped network.

(5)

_

In Equation (5), parameter is the number of nodes in the physical infrastructure. The other objective in virtual network mapping is to minimize the total link cost of the mapped network, called as stated in Equation (6). (6)

represents the normalized length of each Parameter link ( , ) in physical infrastructure. It defined as Equation (7). ,

(7)

The number of used links in the mapped network of a virtual topology is named _ . It can be considered as Equation (8). _

(8)

The average number of used wavelengths per physical link is another important variable in a virtual network mapping. It is desirable to be minimized because it reduces the penalty between different wavelengths, according to physical impairments. The average of used wavelengths, _ , is shown in Equation (9). _

∑

_

∑

_ _

_

(9)

During the virtual network mapping, minimizing of the used wavelengths is a main goal. Therefore, cost of assigned wavelengths in a virtual network mapping, called _ , is stated in Equation (10). _

_

(10)

optimized subset physical network of an existing physical infrastructure to satisfy the desired virtual network. At first, each valid solution of virtual network mapping problem must be encoded as a string. This string is treated as inputs of the PSO. In the following, the proposed method of encoding is presented. In the proposed encoding method, some of the physical infrastructure constraints are taken into account to avoid invalid solutions, as much as possible. According to section 3.1, each network is corresponding to a graph and different wavelengths of a physical links are categorized in different groups, related to their transmission capacity. In adjacency matrix of a graph, some elements are zero which indicates that there is no link between those nodes. To encode the solutions of the virtual network mapping problem, we use the concatenation of the nonzero elements of the upper triangular matrix of the adjacency matrix to act as the segments of the string. But, it must be noted that instead of the aforementioned elements, we use a block of numbers indicating the number of used wavelengths of each group in physical links. The length of each string is equal to n * L where n is the number of different wavelength groups in physical link and L is the number of non-zero elements of the upper triangular part of the physical network adjacency matrix. The proposed encoding structure is depicted in Fig. 1.

Fig. 1: The Proposed Encoding Structure

With this encoding method, the search space of the PSO is smaller and the number of invalid solutions is limited. As an example of the proposed encoding scheme, consider a physical infrastructure as Fig. 2. The adjacency matrix of the example network is as follows.

is the number of used wavelengths Parameter _ in physical link ( , ). It is always less than or equal to , Equation (11). _

(11)

3.2 Proposed Encoding Scheme of Network If we have a precise look at the optimized virtual network mapping, there are two categories of constraints for the problem. One of them is the physical infrastructure and the other is the desired virtual network to be mapped on it. In other word, we want to find the

For encoding the subsets of the example network, the circled elements of the adjacency matrix are used.

Fig. 2: An Example Physical Infrastructure

Using the proposed encoding scheme, one possible solution, that is a subset of the physical network of Fig. 2, is encoded as:

102 | 542 | 000 | 013 where n=3 and L=4 and it means that 1 wavelength from the first group, no wavelength from the second group and 2 wavelength from the third group of the physical link between nodes 1 and 2 are used. The second and forth segments can be explained in the same way. The third segment of the example string means that no wavelengths from different groups are used. In other word, the link between nodes 2 and 4 does not exist in the subset network corresponding to the example string. Any physical network can be encoded using the proposed encoding method and any string is corresponding to a unique physical network. Recall that our purpose is to find the optimum map of a virtual network on the physical infrastructure. The valid strings must be distinguished in iterations of PSO. The constraints of created strings are addressed as follows. Each element of a string must be less than or equal to the maximum number of wavelengths in corresponding group. In other word, the element k of string where 1 ≤ k ≤ n , can have integer values between 0 to α k ,ij . If this constraint is met, the sum of elements of each segment is less than or equal to nλ . The physical networks corresponding to the string must satisfy the desired virtual network requirements. Therefore, sum of the virtual network traffic must be less than or equal to the sum of the produced physical topology traffic. It is worth mentioning that the number of the physical topology links is independent of the number of desired virtual topology links. Because it is possible that the map of some virtual links to have common parts in the physical infrastructure. The corresponding physical network of a string must be connected. To check the connectivity of a physical network, a heuristic is proposed, called Connected Graph Algorithm (CGA). The pseudo code of CGA is shown in TABLE I, in which Ap is the physical network adjacent matrix. The other constraint for physical networks is supporting of the virtual traffic. If the traffic of each virtual link can be routed in the physical network, it can be chosen as a solution of virtual network mapping problem. It means that if a physical network is valid, it must be able to route the virtual links traffic. In order to check this condition, a heuristic called Traffic Routing Algorithm (TRA) is proposed as Fig. 3. In TRA, the minimum path algorithm is executed to find a path as the map of each virtual link. But the cost of a physical edge is considered to be the available transmission capacity of physical link. It means that if a physical link has more free capacity, it has more chance to be selected as part of found path for virtual traffic routing.

TABLE I: Proposed Connected Graph Algorithm (CGA)

Array: Visited [1,…,n] ← False Stack: S Visited[1]←True Push (S,1) While not-empty(S) do X ← Pop (S) For i=1:n do If (Ap(X,i)=1 and Visited[i]=False) then Push (S,i) Visited[i]←True i←1 While (i≤n && Visited[i]=1) i++ If (i=n && Visited[n]=1) "Graph is connected" Else "Graph is not connected" end

Fig. 3: Proposed Traffic Routing Algorithm (TRA)

4. Simulation Results and Discussion Recall that in virtual network mapping optimization, the physical infrastructure acts as the constraint in finding the valid solutions. In order to simulate the performance of the proposed optimization scheme, physical infrastructure of Fig. 4 is considered. According to discussed is a formulation in section 3.1, we have 11 and set of 15 links. Eighty wavelengths per link are considered. In each physical link, three groups of wavelengths , , , , , are taken into account. In

Fig. 4: Considered physical infrastructure

Run Time of Optimized Mapping

600 Cost Function Cost Function Cost Function Cost Function Cost Function

550 500

1 2 3 4 5

450 400 350 300 250

Iteration=500 Particles=100

200 150

0

10

20

30

40

50

60

Fig. 5: Number of Virtual Links Run time of proposed optimization scheme versus virtual network size 1.1

Normalized Cost Value

other word, 3. The number of wavelengths in different groups is considered to be 16, 32, 32 and the transmission capacities of the wavelengths groups are supposed to be 100 Gbps, 40 Gbps and 10 Gbps, which are compatible with the real transponder bit rates. Five different cost functions are taken into account for simulation. According to section 3.1, they are Equations (5), (6), (8), (9) and (10) which are called 'Cost Function 1' to 'Cost Function 5', respectively. In simulations, 10 different virtual networks are created. Then, they are encoded using the proposed encoding scheme of section 3.2. Finally, the optimum maps of the virtual networks on the physical infrastructure of Fig. 4 are found using the binary version of PSO which is discussed in section 2. The BPSO is run 5 times for each cost function and the worst case results were picked up. As the virtual networks arrival time follows the Poisson process, which means that they may change dynamically, one major parameter in virtual network mapping optimization is the run time of the mapping algorithm. To show the performance of the proposed optimization scheme in terms of run time, a simulation is performed for five aforementioned cost functions. The relevance of the proposed optimization method with the virtual networks size for 500 iterations and 100 particles in BPSO is depicted in Fig. 5. As it can be seen in Fig. 5, run time increases with the growth of the virtual networks size and it is independent of the desired cost function. Variation of the normalized cost values of Cost Function 1 to Cost Function 3 with the virtual networks size is presented in Fig. 6. As it can be seen, the optimized value of cost functions is not dependent on the virtual network size. Because in process of finding the optimized map of a virtual link, the number of physical links which are the map of the desired virtual link may change from case to case. In other word, the number of physical links (map of virtual links) for a specific virtual network may be less than, equal to or more than the number of used physical links for other virtual network. As a result, firstly, the number of used physical links as the map of virtual links, secondly the number of used physical nodes and thirdly, the summation of the used physical links distance are not dependent on the desired virtual network size. The same scenario can be explained for Fig. 7. The value of virtual traffic and the mechanism of routing the traffic do not affect the value of Cost Functions 1, 2 and 3. Because according to formulation of section 3.1, these cost functions are only related to the physical topology and they are traffic-blind. The Cost Functions 4 and 5 are dependent on the virtual network traffic. The simulation result is shown in Fig. 8 in which the dependence of the Cost Function 5, the number of used wavelengths in found physical network, is more than the Cost Function 4, the average of used wavelengths for found physical links. Because in proposed TRA, Fig. 3, the shortest path algorithm is used and we assigned the free capacity of each found physical link as its cost. It means that if a found physical link has more free capacity, it has more chance to be chosen for

Cost Function 1 Cost Function 2 Cost Function 3

1.05

1

0.95

0.9 Iteration=500 Particles=100 0.85 0

10

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30

40

50

60

Number of Virtual Links Fig. 6: Normalized cost value for different number of virtual network link

on a physical infrastructure and results were discussed for five defined cost functions.

1.1 Cost Function 1 Cost Function 2 Cost Function 3

Normalized Cost Value

1.05

Acknowledgements This research is supported in part by Iran ICT Research Institute.

1

References 0.95

0.9 Iteration=500 Particles=100 0.85 0

0.5

1

1.5

2

Overall Virtual Traffic

4

x 10

Fig. 7: Normalized cost variation with different values of virtual network traffic 700 Cost Function 4 Cost Function 5

Optimized Cost Value

600

Iteration=500 Particles=100

500 400 300 200 100 0

0

0.5

1

1.5

Overall Virtual Traffic

2 4

x 10

Fig. 8: Optimized cost variation with different values of virtual network traffic

routing the virtual traffic. This idea can not affect the overall number of used wavelengths, Cost Function 5. As a result, the increment of Cost Function 4 with virtual traffic growth is less than the Cost Function 5. 4.

Conclusion

Optical networks play an important role in realization of cloud computing. Optimized allocation of optical network resources during virtual network mapping is a major issue in cloud environment. In this paper an optimization scheme using PSO was proposed for virtual network mapping. The RWA problem was formulated and five different cost functions were defined. A novel encoding method for optical networks was proposed to be used in PSO algorithm. The constraints for solutions of RWA problem are addressed and some heuristics were proposed to satisfy them. Proposed optimization scheme was simulated by mapping of different virtual networks

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