Algorithm for finding all routes in Data Vortex switch

Transcription

1 Algorithm for finding all routes in Data Vortex switch Neha Sharma, Devi Chadha, Vinod Chandra* Department of Electrical Engineering, Indian Institute of Technology, Delhi, New Delhi, INDIA ABSTRACT It is realized, that in optical networks, the enormous bandwidth offered by optical fibers cannot be fully utilized because the electronic switching is the biggest bottleneck. All-Optical switch fabrics play a central role in the effort to migrate the switching functions to the optical layer. Various architectures have been suggested for all-optical packet switching but the issues such as buffering for contention resolution, bit level processing for header decoding, and, TDM header and payload synchronization remain the key challenges in photonic packet switching. The Data Vortex switch architecture has been proposed as a scalable, low-latency interconnection fabric for optical switches that can overcome the above stated challenges 1. It has the advantages that no internal buffering is required, WDM header encoding eliminates bit level processing, and complexity involved with header and payload synchronization is eliminated. In this paper, we generate the distance matrix corresponding to data vortex switch architecture and propose an algorithm to obtain all possible routes between every source-destination node pair in the data vortex switch. This can have applications for various areas, like survivability and quality of service implementations. The algorithm can be used to study fault tolerance in the data vortex switch by analyzing the effect of various links and node failures. Since different applications/end users need different levels of fault tolerance and differ in how much they are willing to pay for the service they get, it is imperative that WDM networks incorporate fault tolerance into QoS requirements with various parameters such as tolerance to single or multiple component failures, protection bandwidth, recovery time, etc. Keywords: All-optical switch fabrics, packet switching, data vortex switch 1. INTRODUCTION The continuously growing demand on high bandwidth communication requires new wide area networks, which are able to provide the necessary transmission capacity. In this context optical networks are considered to meet this requirement. For the last few years, it has been realized, that in optical networks, the enormous bandwidth offered by optical fibers cannot be fully utilized because the electronic switching is the biggest bottleneck. All-Optical switch fabrics play a central role in the effort to migrate the switching functions to the optical layer. In these networks transmission and switching are both implemented in optical technology without the bottleneck of intermediate optical-to-electrical conversions. Various architectures have been suggested for all-optical packet switching but the issues such as buffering for contention resolution, bit level processing for header decoding, and, TDM header and payload synchronization, remain the key challenges in photonic packet switching. The Data Vortex switch architecture has been proposed as a scalable, low -latency interconnection fabric for optical switches that can overcome the above stated challenges 1. It has the advantages that no internal buffering is required, WDM header encoding eliminates bit level processing, and complexity involved with header and payload synchronization is eliminated. As optical WDM networks carry a huge volume of traffic, including voice, data and various multimedia services, it is required that routing and swit ching in such networks should be robust, and scalable. In the present scenario this should also contribute to quality of service. In this paper, we generate the distance matrix for the data vortex switch architecture and propose an algorithm to obtain all possible connections between every node pair in the data vortex switch. This can have applications for various areas, like survivability and quality of service implementations. The algorithm can be used to study fault tolerance 2 in the data vortex switch by analyzing the effect of various links and node failures. Since different applications/end users need different levels of fault tolerance and differ in how much they are willing to pay for the service they get, it is imperative that WDM networks incorporate fault tolerance into QoS requirements 3 with various parameters such as tolerance to single or multiple component failures, protection bandwidth, recovery time, etc. The data vortex switch is a suitable candidate which can be used to provide fault tolerance and quality of service requirements in bufferless photonic packet switching.

2 2. DATA VORTEX TOPOLOGY The Data Vortex switch architecture 4 has been proposed as a scalable, low -latency interconnection fabric for optical switches. It has the advantages that no internal buffering is required, WDM header encoding eliminates bit level processing, and complexity involved with header and payload synchronization is eliminated. Figure 1 to 6 shows the schematic of the data vortex switch architecture. The nodes of the switch are distributed along the angle dimensions and height dimensions on the same cylinder level and consists of a number of concentric cylinders. The size of the data vortex can be described by three parameters, C, A, H, corresponding to the cylinder, angle, and height dimensions, respectively, where C=log2H. It supports (A*H) input and output ports. Data packets ingress from input nodes at the outermost cylinder and exit from output nodes at the innermost cylinder. The connection links within the cylinders cross in a binary tree fashion to fix the next MSB of the header address before the packet is forwarded to an inner cylinder level. The connections between cylinders simply forward packets maintaining the packet height. The A parameter represents the angle dimensions along which nodes are placed on the same cylinder. Figure 1 shows the placement of nodes for A=3, 5, 7. For A=3 angular separation between the nodes is 120 0, for A=5 it is 72 0, and so on. To satisfy the routing conditions of the topology, A is taken as odd. The nodes are represented by angle index a, where 0<a<A. Figure 1: The Angle Dimension The H parameter represents the height dimensions on the cylinder. H should have the value equal to 2 to the pow er m where m is an integer. The height index of the node is given by h, where 0<h<H. Figure 2 shows the placement of nodes for H=4, & H=8. h=o h=1 h=2 h=3 h=0 h=1 h=2 h=3 h=4 h=5 h=6 h=7 H =4 H =8 Figure 2: The Height dimension; A=5

3 The parameter C represents the total number of concentric cylindrical levels in the switch. C dep ends on H where C=log2H+1. The cylinder index of the node is given by c where 0<c<C. Figure 3 shows the arrangement of nodes for C=3, A=5, H=4 c=2 c=1 c=1 c=0 c=0 A = 5, H = 4 C = log 2 H+1 =3 Figure 3: Cylindrical levels Any node on the switch can be represented as (a, c, h). Each node has two input and two output connections, one input from the outer neighboring cylinder and one input from the same cylinder level, similarly one output to the neighboring inner cylinder and one output to the same cylinder level. Figure 4 shows the interconnection among nodes on neighboring cylinders, represented by dashed lines. A node at angle a is connected to another node at angle a+1 and the connections lie on the same height index. a=3 c=0 c=1 c=2 a=2 a=4 a=1 a=0 Figure 4: Interconnections with neighboring cylinders The connections of nodes on the same cylinder level are shown in figure 5, which are found as follows-a node at angle a is connected to another node at angle a+1. Divide the total number of nodes along the height H into 2 c subgroups, where c is the cylinder index. Then in first subgroup connect the top half nodes at angle a to bottom half nodes at angle a+1. Repeat this step until all nodes of first subgroup are connected from angle a to next angle

4 a+1 (represented as nxa variable in distance matrix generation), and height h to next height h (h =nxh variable in distance matrix generation and is different for each node). The other subgroups copy the pattern of the first subgroup and these connections are repeated from angle to angle. a=4 h=0 h=1 a=0 a=1 c=0 a=2 h=2 h=3 (1, 0, 3) Figure 5: interconnections on same cylinder levels Figure 6 shows the interconnection of nodes on the same cylinder level and neighboring cylinders. Data packets enter the switch from input nodes at the outermost cylinder and exit from output nodes at the innermost cylinder. Thus it has (A*H) input and output ports. The total number of nodes in the switch is N=n=A*H*C. Thus for A=5, H=4, and C=3: total number of nodes N=60, number of input nodes (on the outer most cylinder) is 20, number of output nodes (on the innermost cylinder) is 20. a = 3 a = 2 h = 0 a = 4 (4, 0, 0) c = 2 a = 1 c = 1 h = 1 c = 0 a = 0 h = 2 (1, 1, 2) h = 3 (0, 0, 2) Figure 6: Interconnections on same cylinder and neighboring cylinders.

5 3. DISTANCE MATRIX GENERATION FOR DATA VORTEX Distance matrix is also known as weight matrix or cost matrix. A weighted graph of N nodes can be represented by an N N matrix D= [dij], such that- dij is the distance (or weight or cost of edge) between nodes i and j In the case of distance matrix for data vortex- dij=a=5, if connection exists between i and j on the same cylinder d ij =ß=4, if connection exists between i and j on the neighboring cylinder d ij =0, if i=j d ij =8, if no connection exists between i and j The distance matrix d [N] [N] for the given interconnection pattern of data vortex is generated as follows, with reference to figure a = 4 a = 3 12 h = 0 0 a = 0 20 c = 2 c = 1 a = 2 8 h = 1 h = c = 0 a =5 a = β= d [0][6] =a = 5 d [0] [24] = β = 4 d [0][0] = 0 d [0] [1] = INF = 999 h = Figure 7: Interconnection pattern storage in Distance matrix d [N] [N] Each node (a, c, h) is converted to its equivalent decimal value nd=h*a+ (A*H)*c+h Then according to the given interconnection pattern, the node on the same cylinder level, given by snd that is connected to nd is found as follows:-

6 snd=h*nxa+ (A*H)*c+nxh where, nxa= (a+1) %A, nxh- depends on the interconnection pattern as explained in section 2 The node on the inner cylinder level, given by ind that is connected to nd is found ind =H*nxa+ (A*H)*(c+1) +h To satisfy the routing constraints, the distance between connected nodes on the same cylinder are taken α and distances between connected nodes on different cylinders are taken as β such that α 1=β. Example: - Let the node to be considered is (a=0, c=0, h=2), and A=5, H=4, C=3. Then, nxa=1, nxh=1 nd=h*0+ (A*H)*0+2=2 snd=h*1+ (A*H)*0+1=5 ind=h*1+ (A*H)*(0+1) +2=26 Similarly, values are found for all n nodes Then the data is stored in distance matrix d [i] [j], where, 0<i<N, 0<j<N, as follows For any i =nd, j =nd, or snd, or ind d [nd] [nd] =0 d [nd] [snd] =5 d [nd] [ind] =4 if (d[i] [j]! =0 && d[i] [j]! =5 && d[i] [j]! =4) d [i] [j] =INF where INF is some large integer value. A program in C language has been developed which automatically evaluates the interconnections among the nodes and stores in the distance matrix. Simply by varying the input parameters A and H the distance matrix can be generated for any topology. 4. GENERALIZED ALGORITHM A general algorithm 5, 6 is proposed to find all possible connections between every source-destination node pair in the data vortex switch, using the distance matrix generated in section 3. This can have applications for various areas, like survivability and quality of service implementations. The algorithm can be used to study fault tolerance in the data vortex switch by analyzing the effect of various links and node failure and the flowchart is given below.

7 4.1 Flowchart Input Number of nodes-n Number of angles-a Number of heights-h Generate the distance matrix d[n] [n] for the given topology For every source-destination node pair (i, j) Initialize ListAP-stores all paths between (i, j) ListCP-stores current paths from which deviations are found listncp-stores deviations from the current paths, which form the next current paths Find shortest path r, store in ListAP & ListCP Take each path, one by one, of ListCP as current path: For every node m in current path not equal to j, Find shortest path to j (exclude links from m that are in the current path) Append old path from i to m, to newpath found from m to j If newpath from i to j already exists in ListAP, neglect, else store in ListAP & ListNCP No Is ListNCP null Reinitialize ListCP Copy ListNCP to ListCP Yes ListAP stores all possible paths from i to j Stop

8 4.2 Conversion of flowchart to programmable form The generalized algorithm shown in the flowchart can be converted to the programmable form for the case of data vortex switch as shown in the steps below. Step 1. Input number of nodes N, number of angles A, number of heights H, in the given Data Vortex switch Step 2. Evaluate number of cylindrical levels lv=log 2 H+1 in the switch Step 3. For the given switch topology find the Distance matrix d [N] [N] Step 4. Find the shortest routes between every source-destination node pair (i, j) in the network using Floyd s algorithm [2] Step 5. For source i=1 to (A*H), do Step 6. For destination j= ((lv-1)*(a*h) +1) to N, do Step 7. Initialize a list of all shortest paths, ListAP ij,, and a list of all current paths ListCP. Step 8. For (i, j) take the shortest route r, found in step 4 Step 9. Store this path in ListCP = {r} & ListAP ij = {r} Step 10. For each route r c in ListCP, do Step 11. Let current path = r c Step 12. To store deviations from current path r c, initialize a list, ListNCP Step 13 For every node m in the current path, not equal to j, do Step 14. Find shortest route from m, using algorithm by [2], by disconnecting - that link of m which has occurred in current path, and nodes that occur in root path (to avoid loops) Step 15. Call path (i-m) root path and path (m-j) spur path Step 16. Append path (i-m) and path (m -j), if new path from i to j already exists in ListAP ij, neglect, else add to ListNCP & ListAP ij Step 17. End loop 13 Step 18. End loop 10 Step 19. If (ListNCP! = null) reinitialize ListCP and store contents of ListNCP in ListCP, goto step 10, else goto Step 20 Step 20 ListAPij stores all possible routes from i to j Step 21. End loop 6 Step 22. End loop 5 Step 23. End.

9 4. CONCLUSIONS As shown in section 3, the architecture of the data vortex can be easily stored in the form of distance matrix. A program in C language has been developed which automatically evaluates the interconnections among the nodes, and stores in the distance matrix. Simply, by varying the input parameters A and H, the distance matrix can be generated for any topology. The generalized algorithm proposed in this paper, in section 4, utilizes the above generated distance matrix, and obtains all possible connections between every source-destination node pair in the data vortex switch. This can have applications for various areas, like survivability and quality of service implementations. The algorithm can be used to study fault tolerance in the data vortex switch by analyzing the effect of various links and node failures. Since different applications/end users need different levels of fault tolerance and differ in how much they are willing to pay for the service they get, hence it is imperative that WDM networks incorporate fault tolerance into QoS requirements with various parameters such as tolerance to single or multiple component failures, protection bandwidth, recovery time, etc. REFERENCES 1. Multiple Level minimum Logic Network: C.Reed, U.S. Patent , Nov. 30, (1999) 2. Fault Tolerance in GEMNET Topology using Replication of Identified Nodes: N. Sharma, D. Chadha, V. Chandra, Proc. Conference on Distributed Processing and Networking, I.I.T. Kharagpur (W.B.)-India, June, Differentiated Quality of Service for Survivable WDM Optical Networks: C.V. Saradhi, et. al., IEEE Optical Communications, S8(May2004) 4. Optical Packet Routing and Virtual Buffering in Eight-Node Data Vortex Switching Fabric: W. Lu, et. al., IEEE Photonics Technology Letters, Vol. 16, No. 8, 1981(2004) 5. Finding the K-Shortest Loopless Paths in a Network: J.Y. Yen, Management Science, Vol. 17, No. 11,712(1971) 6. Generalized Algorithm for Finding All Connections in an Optical WDM Network: N. Sharma, D. Chadha, V. Chandra, To be presented in WITSP 04( The 3 rd Workshop on the Internet, Telecommunications, and Signal Processing), Adelaide, December, 2004 *vchandra@ee.iitd.ernet.in;