Multi-core shared tree based MP2MP RWA algorithms in large scale and multi-domain optical networks

The increasing demands of bandwidth-intensive parallel computing and collaborative applications, efficient service provisioning to support multipoint to multipoint (MP2MP) communications have attracted increasing attention. However, with the development of larger-scale and multi-domain optical networks, MP2MP RWA are introduced optimal domain sequence selection and core nodes belong to which domains problems which cannot be tackled by the conventional algorithms proposed aim at a signal domain. In this paper, we proposed a multi-core node shared multicast tree heuristic algorithm (MCSMT) which calculation could be parallelized, delay and minimal cost constrained for multi-domain optical networks. It could realize the accurate calculation of minimum number of cores and the hosted domains of the cores. The source and destination nodes were added in different shared trees respectively with delay constrained algorithms according to specific QoS selection strategy. At the same time, according to more complicated MP2MP algorithms we propose a PCE-cloud based control architecture for optical networks by applying the cloud computing technology (e.g. virtualization and parallel computing) to reform the control plane for improving system reliability, intelligence and maximizing resource utilization. The performances of the proposed heuristic with regard to the number of multi-core nodes, wavelength channel occupied and MP2MP setup latency are compared. In addition, the performance about path computing latency for PCE-cloud control architecture is compared with conversional control architecture.


Introduction
It has been found that optical networks are the most suitable option for handling the ever-increasing global traffic growth of 50%-60% every year [1].The increasing demands of bandwidth-intensive datacenter-based parallel computing and collaborative applications have attracted increasing research attention [2,3].They urge optical networks could offer efficient support for multi-point to multi-point (MP2MP) communication services..The growing need for bandwidth-intensive parallel computing and collaborative applications is driving the increasing popularity of multiparty communication in optical networks.Many bandwidthintensive network applications, including network-based parallel computing (e.g., cloud computing and grid computing) and collaborative visualization, adhere to the multiparty communication paradigm [1,2].The increasing demands of such applications have led to a growing focus on efficient service delivery to support multi-point to multi-point (MP2MP) multicast in optical networks [3].
MP2MP is a special type of multiparty communication paradigm.In MP2MP, any node can be the traffic source and traffic sent by any node is delivered to all others.The MP2MP RWA problem involves finding an RWA scheme for a given MP2MP session, with the objective of minimizing the utilization of network resources (e.g., wavelength channels) and satisfying the constraints (e.g., delay) specified by users and the network [4], while ensuring that the traffic stream from each node is delivered to all other nodes in the group.
Jeong et al propose a multicast scheme called tree-shared multicasting (TS-MCAST) which solve the MP2MP routing problems make all members shared one or several forwarding trees [5][6][7].The algorithm should as much as possible minimize the number of shared tree for reducing the network resources utilization.However, there are instances where a single shared multicast tree cannot meet the various constraints imposed by the application, yet multiple shared trees can.It is evident that as the number of shared trees increases, so does the overall overhead for managing the session.Consequently, it is expected that the number of centers should be kept to a minimum [8].This paper takes the multi-domain, delay constrained and minimal cost into consideration for MP2MP algorithms.
However, as optical networking evolves towards larger scales, wider coverage and more multi-user access, the routing computing capacity of conventional MP2MP RWA algorithms become insufficient to meet the QoS requirements of these services [9][10][11][12][13].Consequently, there are two main challenges, on one hand, design multiple QoS constrained MP2MP RWA algorithms have always been technically challenging, as many of these algorithms are NP-hard [14].On the other hand, the MP2MP RWA problems in current optical environmental put forward higher requirements for optical networks which should provide powerful and elastic computing resources.
In this paper, we focus on the MP2MP RWA problem in multiple domains GMPLS optical networks.For the first challenge, we take into consideration of the multiple constraints of services and cost of networks for designing the MP2MP RWA algorithms.We mathematically formulate the MP2MP RWA using integer linear programming (ILP) and introduce a multiple domains delay constrained minimal cost multi-core node shared multicast tree-construction heuristic algorithm to efficiently solve the MP2MP RWA problems in larger-scale, multi-region and multi-layer GMPLS optical networks.For the second challenge, we take into consideration of maximize the computing resources utilization from applying the cloud computing technology (e.g.virtualization and parallel computing) to reform the GMPLS control plane.
The paper is structured as follows: In Section 2, we describe previous related works.Section 3 presents the problem statement of MP2MP RWA.Section 4 provides the proposed SPC architecture.Section 5 presents the mathematical formulation of the MP2MP RWA problem using ILP.The paper's proposed heuristics are presented in Section 6, followed by a comprehensive presentation of simulation results and analyses in Section 7. Finally, Section 8 concludes the paper.

Related works
In recent years, much prior work has focused on the technology of multicast routing problem in optical networks [14][15][16][17][18].However, multicasting was not deployed over wide-area and multi-domain networks until recently.Moreover, with the advent of multiparty communication applications, it is no longer enough to simply minimise the overall cost of the multicast tree.What is required now is an algorithm that, taken into account a set of QoS requirement specifications and current status of the network links, finds multi-core node shared multicast trees that meets the QoS specification of the services.Accordingly, the focus of MP2MP routing research has shifted to finding multi-core node shared multicast trees which support the quality of service requirements of multiparty communication applications as well [8,17].
It should be noted that while MP2MP has been extensively studied in other research areas, optical MP2MP RWA is a relatively new research topic.The only relevant work in this area pertains to MP2MP in multiple domains GMPLS optical networks.It has been studied extensively.There are four solutions proposed by Salama for the delay constrained multiple-shared multicast tree which are GREEDY, NAÏ VE, MAXD and AVGD [18].Moh also proposed three improved algorithms which are MN, MNmedian and MN-linear median [17].
The main difference between the problem addressed in this paper and the work in [14][15][16][17][18] is that our work considers the case in which any node in the multicast session could be the source that can provide the data stream.Moreover, this paper not only considers the multiple constrains and minimal cost but also the cross domain MP2MP RWA problems.

Problem statement
MP2MP is a kind of multipoint-to-multipoint commun-ication which can be established by using light path, light tree or light forest among all group members.In general, a MP2MP communication session involves multiple sources transmitting to multiple destinations.A node in a MP2MP session it could be a source or a destination.However, it could not be a source and also a destination.The MP2MP RWA problem in multi-domain GMPLS optical networks can be defined as follows: given a set of MP2MP calls and a certain number of wavelengths, the objective is to maximize the number of admitted MP2MP sessions while minimizing the resources used and the call blocking probability.The task involves identifying an RWA scheme for a given MP2MP session and assigning a wavelength channel to each link along the selected route.This is subject to wavelength continuity constraints to ensure that the traffic stream from each source node can be delivered to all other member nodes in the group.
To help understand the multiple domains MP2MP RWA problem, we provide an illustrative example depicted in Fig. 6.The example involves eight nodes, specifically Nodes 1, 2, 7, and 8, participating in MP2MP communication.The network has a simple topology with eight nodes via eleven bidirectional optical fiber links.The identifier of each traffic stream is identified by i T , where i represents the node from which the traffic i T originates.The MP2MP traffic can be accommodated by using the wavelength channels that are denoted as the directional arcs.Figure 1(a) shows the MP2MP with light forest in multi-domain GMPLS optical networks occupied seven links and two wavelength channels.However, the MP2MP with shared tree, which is shown in figure 1(b), occupied five links and one wavelength channel.Consequently, the MP2MP with shared tree save 50% resources of links and 40% resources of wavelength channels.

Mathematical formulation of MP2MP RWA problem
The MP2MP problem can be formally described as follows.
{ , ,..., } = ,..., , ,..., ,..., ,..., Border/gateway nodes connect different domains.Define Assume that a path from node 1 v to k v is defined as a sequence of nodes and links ( , ) , , ,..., Define a lightpath of multidomain optical networks as expression (2).(a) (b) where the link between any two nodes is 1 ( , ) The cost of a path i G which is the max time that a message from the source reaches any of the destinations and c is the shared center node of the shared tree.Therefore, the cost and latency of a path are defined as equations ( 3) and ( 4).
Assuming there are totally Z MP2MP sessions, denoted as X1, X2, ..., XZ, let i M represent the set of member nodes for a given MP2MP session (1   ) represent the number of nodes of Xi.Let () j i ts represent the traffic stream from node ( 1 ) s M j n     .The total cost and the latency of setting up the MP2MP connection can be expressed as ( 5) and ( 6).

Delay
Delay P s D de de de A. Variable The decision variables are described as follows.The objective of constructing a MP2MP communication connection consists of maximizing the number of MP2MP sessions admitted and minimizing the link and wavelength resources occupied.Therefore, base on these analyses, we take dual optimisation objectives to minimise both network resources, i.e. link and wavelength cost, and lightpath setup latency.We consider the RWA problem in optical networks with wavelength consistency constraints.The optimisation objective function is given by equation (7).
where  is the maximum lightpath setup latency of the optical networks and The constraint of ( 8) is the topology connectivity.The constraint of ( 9) is the wavelength capacity.
2) Wavelength-Utilization constraints ,, ( , ) , ( ) ; , ,, ; , ,, ; , ,, ; , ; , , Constrains (10) and (11) indicate that if any wavelength channel carries the traffic () is a large constant which is used for enhanced constrain.Constrain (12) ensures that there should be at least one outgoing channel if the traffic is present at a nonmember node.Constrain (13) ensures that there should be one incoming channel to carries the traffic () j i ts if it presents at node n.The constrain of ( 14) ensures that the traffic () j i ts should be feedback to its source where it from j i s .The equation of ( 15) is used for constrain the traffic is present at all of the MP2MP session of i X .
3) Flow-Conservation constraints Flow-Conservation Constraints: The constraints are as follows: ,, ,, ( ) , , ;, The equations of ( 16) and (17) indicate the constraints between commodity flow and wavelength channel utilization.The commodity flow of () j i ts should be more than 1 if the any wavelength channel carries the traffic () j i ts .Where ( ), ( ), {0, 1}

Proposed MP2MP RWA heuristics algorithm
The MP2MP RWA problem is a NP-complete problem [17].Therefore, solving the optimization problem formulated in the previous ILP model can be computationally intractable.To address this challenge, in this section, we present a polynomial-time heuristic algorithm to solve the MP2MP RWA problem efficiently.The proposed algorithm is a multi-core node shared multicast tree (MCSMT) heuristic algorithm whose calculation could be parallelized, delay and minimum cost constrained for multi-domain optical networks.It enables the accurate calculation of minimum number of cores and the hosted domains of the cores.The source and destination nodes are assigned to different shared trees using delayconstrained algorithms based on a specific QoS selection strategy.The detailed description of the algorithm is shown in table 1 and get the nodes which cannot satisfy the delay constrain and remove this nodes from the tree.At the same time , we get the nodes list which meet the delay constraint { , ,..., } which don't contain in the multicast forest.

Step 7
Select node ' ( 1, ) to be the new center node which contains the max number nodes of set rem V .Then delete corresponding nodes from set rem V .Select the multicast tree which is rooted with ' i c and delete the nodes which is out of the rang of rem V .

Step 8
If the set rem V is empty, go to Step 8 , otherwise go to Step 6.

Step 9
Combine the forest from delete the duplicate edge in different trees.Consequently, the multiple shared-trees composed by the disjoint light tree and the root nodes of the trees compose the set of center nodes.
Step 10 Return light-forest F to wavelength assignment function.
Step 11 Choose the one shared multicast tree of light forest F by order and find a free wavelength j  , ( 1) jw  with first-fit approach algorithm, where W is the total number of wavelengths per fiber in the network.Then mark the wavelength j  .
Step 12 Repeat Step 11 for all elements of F.

PCE-cloud architecture based GMPLS optical networks
The PCE cloud consists of the Control Plane Manager (CPM), the Path Computing Element Manager (PCEM), the Task Tracker (PCETT) and the Centralized Shared Database (CSD).The CPM is the foundation of the SPC.The hardware and software resources are pooled by CPM to serve multiple users, with different physical and virtual resources dynamically allocated and reallocated according to user requirements.

Figure 2. Task process flow chart of PCEM
As shown in Figure 2, PCEM manages the tasks from users, conducts map-reduce operation for parallel computing based on specified routing policy, and assigns computing tasks to PCETTs.Moreover, the PCEM is responsible for maintaining synchronization the TED and LSPD between the PCCs and the SPC.The PCETT is the actual path computation unit.PCETTs work together to process the path computation request using parallel computing technology.PCEM and PCETT run on the VMs.
The core idea of PCE-cloud is to integrate PCE in multiple fields to form a PCE cloud computing data center with centralized computing and storage capabilities.In addition, we apply cloud computing technologies (such as virtualization and parallel computing) in the configuration of PCE Cloud to improve the reliability of the GMPLS control plane and maximize resource utilization.The path calculation requests of multi-domain users will be submitted and completed centrally by the PCE cloud data center.Meanwhile, the PCE-cloud not only could realize the traditional function of path computing, but also could achieve function expansion for flexible network control and management easily.

Simulation results and analysis
To evaluate the performance of the MP2MP RWA algorithm MCSMT in multi-domain GMPLS optical networks, we developed an SPC-based GMPLS optical network using the distributed event simulation tool OMNet++.As shown in Figure .3,the simulated network topology is based on the European IST project framework, which contains 6 domains and 46 nodes.To simplify the problem, we assume that the intra-domain link length between any two nodes is 20 kilometers and the inter-domain link length between any two nodes is 200 kilometers.The definition of network link delay is the link transmission delay, ignoring queuing delay and sending delay.The transmission speed is 2/3 of the speed of light.Therefore, the propagation delay is equal to the cable length times 0.005ms/km.

Figure 3. MUPBED network topology
To evaluate the performance of the heuristic algorithm proposed in this study, we mainly verify the networks resources cost and routing success ratio under the same simulation scenarios.Four typical heuristic algorithms are selected in the comparison, GREED, AVGD, NAIVE and MCSMT.
In the first simulation, we verify the networks resources cost based on the center node assigned and wavelength occupied number for M-DCMSMT problem.We assume the MP2MP routing delay constant range is from 3 to 10ms.Three simulations were performed with different numbers of MP2MP groups, 5, 10, and 15 groups, respectively.In each type delay constraint we compare the center node assigned between the four heuristic algorithms with the same MP2MP sessions which is randomly generated.Simulations in different delay constants are all conducted 1000 times.
From figure 4 it can be observed that the center node number decreases with the relaxation of delay constraint for all simulation scenarios which is due to there will more routing path could be selected

GEANT2
when the delay constraints more relaxation.It could be easy to find a single shared tree when the delay constraints reach a certain limitation in all different heuristic algorithms.In addition, we could observe that the average center number of MCSMT is minimal in all the compared four heuristic algorithms.In addition, the advantage of average center number of MCSMT is not obvious than the other three heuristic algorithms which can be seen from Figure 4 (a).The advantage is more obvious along with the MP2MP group size increasing.This is because, on one hand, that the algorithm of MCSMT updates and merges the center nodes cycle repeated for optimization center nodes.On the other hand, the control plane based SPC could get optimization domain sequence which also contributes to the optimization center nodes selection.We assume the MP2MP routing delay constraint is 5ms.We compared and analyzed 1000 times with the same group size between different heuristic algorithms.From Figure .5 it can be observed that the occupied wavelength number increases with the increase of group size for all four heuristic algorithms which means MP2MP routing will cost much more networks resources when the group size is large.In addition, we could observe that the MCSMT saves more wavelength resources than the other three algorithms.This is assigned with MCSMT is first-fit, the wavelength occupied number is determined by the center node number.
In the third simulation, we compare the MP2MP based success ratio between the four heuristic algorithms under the same networks resources provision.We assume each link contains 16 wavelengths.The delay constraint rang is 5ms.There are three type MP2MP request randomly generated which group sizes are 5, 10 and 15.To examine the proposed heuristic algorithm for multi-core shared trees we simulated each light-forest size 50,000 times in turn.We set 25% of the arriving calls to be MP2MP.
As can be seen from Figure .6,the average success rate of MP2MP increases with increasing traffic load among all four heuristics.This is because the limitation of wavelength number in each link.In addition, the performance of MCMSMT is much better than the other three heuristic algorithms which with because the center node assigned and wavelength occupied are all much little than the other algorithms.
In order to verify the ability of path computing and elastic resources providing performance of the SPC architecture, We selected four typical PCE architectures through comparison, distributed individual domain PCE architecture (DPA), improved hierarchical PCE architecture model (HPA), DRE and SPC.The simulation assumes that requests arrive according to a Poisson distribution.The arrival rate is equal to λ(s,d) and the connection duration per call follows an exponential distribution with mean equal to 1. Unicast calls are routed using the shortest path first (SPF) algorithm, and wavelength allocation is done using the first-fit method.The MP2MP calls used the light-forest based heuristic proposed by [], while the wavelength distribution also adopts the first fitting method.We assume the MP2MP group size is a random number between 3-6.
We first evaluate the average connection establishment time, and the change in MP2MP session ratio among total route requests.The connection setup time is consisted by path computing and RSVP-TE signal transmission time consuming.The network load was 100 Erlangs.We simulated 10,000 calls for each MP2MP sessions ratio.
As can be seen from Figure .7, in all three architectures, as the MP2MP session ratio increases, the connection establishment time also increases.This is because MP2MP path computing takes much more time than P2P, the more MP2MP sessions require more path computing time.In addition, the SPC using virtualization and parallel computing technology can better complete computing-intensive cross-domain path computing tasks.Consequently, this exhibits that the SPC significantly outperforms the other architectures with larger scale inter-domain routing and can realize fast routing and path establishment which is more suitable for complicated and more computing resources needed routing calculation tasks such as MP2MP.
The second simulation we evaluate is the average connection setup time and the addition of traffic load for the tree architectures.We assume the MP2MP group size is a random number between 3-6.The MP2MP sessions ratio in total routing request is set to 15%.
As can be seen from Figure .8,the average connection establishment time increases with increasing traffic load for all three architectures.At the same time, we can observe that the performance of average connection setup time based SPC has a great improvement than the other two architectures.The reason is same as the Figure.

Conclusions
This study discusses the challenges of MP2MP RWA problems in large-scale optical networks.We analyze the problems of MP2MP RWA in multi-domain optical networks which include optimal MP2MP domain sequence and core nodes belong to which domains.The mathematical expression of MP2MP RWA is proposed via integer linear programming (ILP), and a multi-core node shared multicast tree based delay and minimal cost constrained heuristic algorithm is presented for multi-domain and largescale optical networks.The performances of the proposed heuristic with regarding to network resource occupied and routing success probability are compared.These results illustrate that the MCSMT is a promising approach to routing in multi-domain optical networks which could effectively reduce network resources occupied, increase the MP2MP success probability and reduce algorithm perform latency.Moreover, a novel control architecture based on PCE-cloud for larger-scale and multi-domain optical networks is proposed which is used for tackle the more complicated MP2MP algorithms.The performance of this control architecture with regarding to MP2MP setup latency is compared.The result illustrates that the PCE-cloud is a promising solution for complicated algorithm in larger scale and multidomain optical networks.

Figure 1 .
figure 1(b), occupied five links and one wavelength channel.Consequently, the MP2MP with shared tree save 50% resources of links and 40% resources of wavelength channels.Figure 1.Illustrative example of MP2MP.(a) light forest-based.(b) shared tree-based

2 |.
of m directed optical links connecting them.Let W represent the number of wavelength channels in each link, and let C denote the bandwidth of each wavelength channel.From a basic result of Graph Theory, we have The optical networks are divided into multi-domain, denoted by 12 { , ,..., } n D D D .Each domain comprises a set of nodes, represented by (1).
is a link from node m to node n; otherwise, .Denote () Nm as the set of neighborhood of node m , i.e., , . The cost of a path is the sum of cost of the links 1 ( , ) k P v v and the wavelength assigned to the routing from node 1 the delay of the MP2MP

F
Indicate the number of destinations of () j i ts reached by ( , ) link m n , which is the Commodity-flow value.( , ) () mn Lw Indicates the wavelength-channel occupation status.If wavelength w on ( , ) link m n is occupied by any traffic, ( , ) () mn Lw equals 1, otherwise 0. , ( , ) () ij mn Lw Indicates the wavelength-channel usage status.If ()

F
is the commodity flow which indicates total number of the destinations.The constraint (18) ensures that the wavelength indicator ( , ) () mn Lw should be 1 if any traffic occupies the wavelength channel , w mn l .The constraint of (19) indicates that if the traffic () j i ts go through anyone destination node the commodity flow of the traffic will minus 1. Equation (20) ensures that if the traffic () j i ts go through anyone node which is not the destination the commodity flow will not change.The constraint (21) indicates that traffic should be from the sources node group.The equation of (22) constrains that the source and destination number of the traffic () j i ts which means the outgoing traffic number should equals to the destinations of the traffic.4) Variable constraints ,, Repeat Steps 3 for all members of the domain 1 D and get the maximum of 1 __ N D i .Then make the node 1 , Di v to be the candidate center node in the domain 1 D .Step 5 Repeat Steps 3 and 4 for all of the domains 12 { , ,..., } m D D D and get the candidate center node list 12 { , ,..., } m c c c , corresponding minimal cost multicast tree list be the first center node of the multi-core shared multicast tress and the tree , ' Di rT is the first tree of the multicast light forest F.Moreover, we could get the node list of the MP2MP session

Figure 4 .
Figure 4. Average number of center nodes with different delay constraints changesIn the second simulation, we verify the networks resources cost based on occupied number.We assume the MP2MP routing delay constraint is 5ms.We compared and analyzed 1000 times with the same group size between different heuristic algorithms.From Figure.5 it can be observed that the occupied wavelength number increases with the increase of group size for all four heuristic algorithms which means MP2MP routing will cost much more networks resources when the group size is large.In addition, we could observe that the MCSMT saves more wavelength resources than the other three algorithms.This is assigned with MCSMT is first-fit, the wavelength occupied number is determined by the center node number.In the third simulation, we compare the MP2MP based success ratio between the four heuristic algorithms under the same networks resources provision.We assume each link contains 16 wavelengths.The delay constraint rang is 5ms.There are three type MP2MP request randomly generated which group sizes are 5, 10 and 15.To examine the proposed heuristic algorithm for multi-core shared trees we simulated each light-forest size 50,000 times in turn.We set 25% of the arriving calls to be MP2MP.As can be seen from Figure.6, the average success rate of MP2MP increases with increasing traffic load among all four heuristics.This is because the limitation of wavelength number in each link.In addition, the performance of MCMSMT is much better than the other three heuristic algorithms which with because the center node assigned and wavelength occupied are all much little than the other algorithms.In order to verify the ability of path computing and elastic resources providing performance of the SPC architecture, We selected four typical PCE architectures through comparison, distributed individual domain PCE architecture (DPA), improved hierarchical PCE architecture model (HPA), DRE and SPC.The simulation assumes that requests arrive according to a Poisson distribution.The arrival rate is equal

Figure 5 .Figure 7 .Figure 8 .
Figure 5. average number of wavelength with different group size