OPTICAL NETWORKS Virtual Topology Design A. Gençata İTÜ, Dept. Computer Engineering 2005
Virtual Topology A lightpath provides single-hop communication between any two nodes, which could be far apart in the physical topology. However, having limited number of wavelengths, it may not be possible to set up lightpaths between all user pairs. Multi-hopping between lightpaths may be necessary. The virtual topology consists of a set of lightpaths. packets of information are carried by the virtual topology as far as possible in the optical domain using optical circuit switching packet forwarding from lightpath to lightpath is performed via electronic packet switching, whenever required. Lightpaths in the virtual topology is set up using RWA techniques. The virtual topology is also referred to as Lambda Grid, or just Grid. 2
Problem An optimization problem to optimally select a virtual topology subject to transceiver (transmitter and receiver) wavelength constraints with one of two possible objective functions: 1. for a given traffic matrix, minimize the network-wide average packet delay. 2. maximize the scale factor by which the traffic matrix can be scaled up (to provide the maximum capacity upgrade for future traffic demands). Since the objective functions are nonlinear and since simpler versions of the problem have been shown to be NP-hard, we shall explore heuristic approaches. 3
NSFNET Backbone 4
General Problem Statement Problem: Embedding a desired virtual topology on a given physical topology (fiber network). We are given: A physical topology G p = (V,E p ) consisting of a weighted undirected graph, where V is the set of network nodes, E p is the set of links connecting the nodes. Undirected means that each link in the physical topology is bidirectional. A node i is equipped with a D p (i) D p (i) WRS, where Dp(i) is the number of physical fiber links emanating out of (as well as terminating at) node i. 5
General Problem Statement Number of wavelengths carried by each fiber, M. An N N traffic matrix, where N is the number of network nodes, The (i, j)-th element is the average rate of packet traffic flow from node i to node j. The traffic flows may be asymmetric. The number of wavelength-tunable lasers (transmitters) and wavelength-tunable filters (receivers) at each node. 6
General Problem Statement The goal is to determine: A virtual topology G v = (V,E v ) as another graph where: the out-degree of a node is the number of transmitters at that node the in-degree of a node is the number of receivers at that node. The nodes of the virtual topology correspond to the nodes in the physical topology. Each link in the virtual topology corresponds to a lightpath between the corresponding nodes in the physical topology. Each lightpath may be routed over one of several possible paths on the physical topology. 7
General Problem Statement A wavelength assignment for lightpaths. If two lightpaths share a common physical link, they must necessarily employ different wavelengths. The sizes and configurations of the WRSs at the intermediate nodes. Once the virtual topology is determined and the wavelength assignments have been performed, the switch sizes and configurations follow directly. 8
Packet Communication Communication between any two nodes takes place by following a path (a sequence of lightpaths) from the source node to the destination node on the virtual topology. Each intermediate node in the path must perform: 1. an opto-electronic conversion, 2. electronic routing (or packet switching in the electronic domain), and 3. electro-optic forwarding onto the next lightpath. 9
Illustrative Example How WDM can be used to upgrade an existing fiber-based network. Using the NSFNET as an example, a hypercube can be embedded as a virtual topology over this physical topology. We assume an undirected virtual topology. bidirectional lightpaths In general, the virtual topology may be a directed graph. The physical topology is enhanced by adding two fictitious nodes, AB and XY. 10
Illustrative Example The switching architecture of nodes consists of: An optical component. a wavelength-routing switch (WRS) can switch some lightpaths, can locally terminate some other lightpaths by directing them to node s electronic component. An electronic component. an electronic packet router (may be an IP router: IP-over-WDM) serves as a store-and forward electronic overlay on top of the optical virtual topology. 11
Example The virtual topology chosen is a 16-node hypercube. 12
Example: A Possible Embedding 13
Example This solution requires 7 wavelengths. Each link in the virtual topology is a lightpath with electronic terminations at its two ends only. Example: The CA1-NE lightpath could be set up as an optical channel on one of several possible wavelengths on one of several possible physical paths: CA1-UT-CO-NE, or CA1-WA-IL-NE, or others. According to the solution, the first path is chosen on wavelength 2 for CA1-NE lightpath. This means that the WRSs at the UT and CO nodes must be properly configured to establish this CA1-NE lightpath. The switch at UT must have wavelength 2 on its fiber to CA1 connected to wavelength 2 on its fiber to CO. Since connections are bidirectional, the CA1-NE connection implies two lightpaths, one from CA1 to NE and one from NE to CA1. 14
UT Node 15
UT Node The switch UT has to support four incoming fibers plus four outgoing fibers, one each to nodes AB, CA1, CO, and MI, as dictated by the physical topology. In general, each switch interfaces with four lasers (inputs) and four filters (outputs), each laser-filter pair is dedicated to accommodate each of the four virtual links on the virtual topology. The labels 1l 2b 3d 5l on the output fiber to CO: The UT-CO fiber uses four wavelengths 1, 2, 3, and 5. Wavelengths 2 and 3 are clear channels through the UT switch and directed to the physical neighbors CA1 and MI, respectively. Wavelengths 1 and 5 connect to two local lasers. 16
UT Node The box labeled Router is an electronic switch which takes information from: terminated lightpaths (1c 4b 5c) a local source and routes them via electronic packet switching to: the local destination the local lasers (lightpath originators) The router can be any electronic switch. e.g., an IP router. The non-router portions of the node architecture are the optical parts that may be incorporated to upgrade the electronic switch to incorporate a WRS. 17
Formulation of the Optimization Problem Notation: s and d used as subscript or superscript to denote source and destination of a packet, respectively. i and j denote originating and terminating nodes, respectively, in a lightpath. m and n denote endpoints of a physical link. 18
Formulation: Given Given: Number of nodes in the network: N. Maximum number of wavelengths per fiber: M Physical topology P mn P mn = P nm = 1 if there is a direct physical fiber link between nodes m and n P mn = P nm = 0 otherwise The problem can be generalized to accommodate multi-fiber networks, where P mn can take integer values. 19
Formulation: Given Distance matrix whose elements are fiber distance d mn from node m to node n. For simplicity in expressing packet delays, dmn is expressed as a propagation delay (in time units). d mn = d nm d mn = 0 if P mn = 0. Number of transmitters at node i = T i (T i 1). Number of receivers at node i = R i (R i 1). Capacity of each channel: C normally expressed in bits per second, but converted to units of packets per second by knowing the mean packet length. 20
Formulation: Given Traffic matrix λ sd the average rate of traffic flow from node s to node d λ ss = 0 Additional assumptions: Packet inter-arrival durations at node s and packet lengths are exponentially distributed. So standard M/M/1 queuing results can be applied to each network link (or hop ) by employing the independence assumption on inter-arrivals and packet lengths due to traffic multiplexing at intermediate hops. By knowing the mean packet length (in bits per packet), the λ sd can be expressed in units of packets per second. 21
Formulation: Variables Variables: Virtual topology V ij : 1 if there is a lightpath from i to j in the virtual topology 0 otherwise. The formulation is general since lightpaths are not necessarily assumed to be bidirectional. V ij = 1 V ji = 1. Further generalization of the problem can be performed by allowing multiple lightpaths between node pairs, i.e., Vij > 1. 22
Formulation: Variables Traffic routing variable λ sd ij denotes the traffic flowing from s to d and employing V ij as an intermediate virtual link. traffic from s to d may be bifurcated with different fractions taking different sets of lightpaths. Physical-topology route variable p ij mn is: 1 if the fiber link P mn is used in the lightpath V ij ; 0 otherwise. Wavelength color variable c ij k is: 1 if a lightpath from i to j is assigned the color k 0 otherwise. 23
Formulation: Constraints Constraints: On virtual-topology connection matrix V ij : These equations ensure that: The number of lightpaths emanating out of and terminating at a node are at most equal to that node s out-degree and in-degree, respectively. 24
Formulation: Constraints On physical route variables p ij mn: First two equations constrain the problem so that p ij mn exist only if there is a fiber (m,n) and a lightpath (i,j). The remaining equations are the multi-commodity equations that account for the routing of a lightpath from its origin to its termination. 25
Formulation: Constraints On virtual-topology traffic variables λ sd ij : Equations for the routing of packet traffic on the virtual topology. They take into account that the combined traffic flowing through a channel cannot exceed the channel capacity. 26
Formulation: Constraints On coloring of lightpaths c ij k : First equation requires that a lightpath be of one color only. Second equation ensures that the colors used in different lightpaths are mutually exclusive over a physical link. 27
Formulation: Objective 1 Delay Minimization: The innermost brackets: the first component corresponds to the propagation delays on the links mn which form the lightpath ij the second component corresponds to delay due to queuing and packet transmission on lightpath ij. If we assume shortest-path routing of the lightpaths over the physical topology, then the p ij mn values become deterministic. If, in addition, we neglect queuing delays, the optimization problem reduces to minimizing the first component. 28
Formulation: Objective 2 Maximizing Load (Minimizing Maximum Flow): Also nonlinear Minimizes the maximum amount of traffic that flows through any lightpath. Corresponds to obtaining a virtual topology which can maximize the offered load to the network if the traffic matrix is allowed to be scaled up. 29
Algorithms for VT Design The problem of optimal virtual-topology design can be partitioned into the following four subproblems, which are not necessarily independent: Determine a good virtual topology. which transmitter should be directly connected to which receiver? Route the lightpaths over the physical topology. Assign wavelengths optimally to the various lightpaths. Route packet traffic on the virtual topology. 30
Solutions Several heuristic approaches have been employed to solve these problems. Labourdette and Acampora, Logically rearrangeable multihop lightwave networks, IEEE Transactions on Comm., Aug. 1991. I. Chlamtac, A. Ganz, and G. Karmi, Lightnets: Topologies for high speed optical networks, IEEE/OSA Journal of Lightwave Technology, May/June 1993. B. Mukherjee, S. Ramamurthy, D. Banerjee, and A. Mukherjee, Some principles for designing a wide-area optical network, Proceedings, IEEE INFOCOM 94, June 1994. R. Ramaswami and K. Sivarajan, Design of logical topologies for wavelength-routed all-optical networks, Proceedings, IEEE INFOCOM 95, April 1995. Z. Zhang and A. Acampora, A heuristic wavelength assignment algorithm for multihop WDM networks with wavelength routing and wavelength reuse, IEEE/ACM Transactions on Networking, vol. 3, pp. 281 288, June 1995. 31
Solutions Embedding of a packet-switched virtual topology on a physical fiber plant in a switched network was first introduced in the second reference, and this network architecture was referred to as a lightnet. The work in ref. 4 proposes a virtual-topology design where the average hop distance is minimized, which automatically increases the network traffic supported. This work uses the physical topology as a subset of the virtual topology. 32
Solution Approach To obtain a thorough understanding of the problem, we concentrate on Sub-problems 1 and 4 above. the number of available wavelengths is not a constraint. In the expanded problem, both the number of wavelengths and their exact assignments are critical. An iterative approach consisting of simulated annealing to search for a good virtual topology (Sub-problem 1) The flow-deviation algorithm for optimal (possibly bifurcated ) routing of packet traffic on the virtual topology (Sub-problem 4). 33
Solution Approach We will consider lightpaths to be bidirectional in our solution here most (Internet) network protocols rely on bidirectional paths and links. We consider Optimization Criterion (2) (maximizing offered load) for our illustrative solution. mainly because we are interested in upgrading an existing fiber-based network to a WDM solution. 34
Simulated Annealing Simulated annealing (along with genetic algorithms) has been found to provide good solutions for complex optimization problems. In the simulated annealing process, the algorithm starts with an initial random configuration for the virtual topology. Node-exchange operations are used to arrive at neighboring configurations. In a node-exchange operation, adjacent nodes in the virtual topology are examined for swapping. Example: if node i is connected to nodes j, a, and b, while node j is connected to nodes p, q, and i in the virtual topology, after the node-exchange operation between nodes i and j, node i will be connected to nodes p, q, and j, while node j will be connected to nodes a, b, and i. 35
Simulated Annealing Neighboring configurations which give better results (lower average packet delay) than the current solution are accepted automatically. Solutions which are worse than the current one are accepted with a certain probability. This probability is determined by a system control parameter. The probability with which these failed configurations are chosen decreases as the algorithm progresses in time so as to simulate the cooling process of annealing. The probability of acceptance is based on a negative exponential factor inversely proportional to the difference between the current solution and the best solution obtained so far. 36
Simulated Annealing The initial stages of the annealing process examine random configurations in the search space to obtain different initial starting configurations without getting stuck at a local minimum as in a greedy approach. However, as time progresses, the probability of accepting bad solutions goes down, the algorithm settles down into a minimum, after several iterations. The state become frozen when there is no improvement in the objective function of the solution after a large number of iterations. 37
Flow Deviation By properly adjusting link flows, the flow-deviation algorithm provides an optimal algorithm for minimizing the network-wide average packet delay. Traffic from a given source to a destination may be bifurcated. different fractions of it may be routed along different paths to minimize the packet delay. Idea: If the flows are not balanced, then excessively loading of a particular channel may lead to large delays on that channel and thus have a negative influence on the network-wide average packet delay. 38
Flow Deviation The algorithm is based on the notion of shortest-path flows. First calculates the linear rate of increase in the delay with an infinitesimal increase in the flow on any particular channel. These lengths or cost rates are used to pose a shortest-path flow problem (can be solved using one of several well-known algorithms such as Dijkstra s algorithm, Bellman-Ford algorithm, etc.) The resulting paths represent the cheapest paths on which some of the flow may be deviated. An iterative algorithm determines how much of the original flow needs to be deviated. The algorithm continues until a certain performance tolerance level is reached. 39
Experimental Results The traffic matrix employed is an actual measurement of the traffic on the NSFNET backbone for a 15-minute period. 11:45 pm to midnight on January 12, 1992, EST. The raw traffic matrix shows traffic flow in bytes per 15- minute intervals between network nodes. Nodal distances used are the actual geographical distances. Initially, each node can set up at most four bidirectional lightpath channels. Later more experiments were conducted to study the effect of having higher nodal degree. The number of wavelengths per fiber was assumed to be large enough. all possible virtual topologies could be embedded. 40
Traffic Matrix 41
For each experiment, Experimental Results the maximum scale-up achieved the corresponding individual delay components, the maximum and minimum link loading the average hop distance is tabulated. 42
Experimental Results The aggregate capacity for the carried traffic is fixed by the number of links in the network. reducing the average hop distance can lead to higher values of load that the network can carry. The queuing delay was calculated using a standard M/M/1 queuing system. mean packet length calculated from the measured traffic: 133.54 bytes per packet. link speed is 45 Mbps. Infinite buffers at all nodes. The cooling parameter for the simulated annealing is updated after every 100 acceptances using a geometric parameter of value 0.9. A state is considered frozen when there is no improvement over 100 consecutive trials. 43
Physical Topology as Virtual Topology (No WDM) Goal: to obtain a fair estimate of what optical hardware can provide in terms of extra capabilities. Start off with just the existing hardware, comprising: fiber and point-to-point connections a single bidirectional lightpath channel per fiber link no WDM The maximum scale-up achieved: 49 The load of the link with the maximum traffic: 98% The load of the link with the minimum traffic: 32%. These values serve as a basis for comparison as to what can be gained in terms of throughput by adding extra WDM optical hardware: tunable transceivers wavelength routing switches. 44
Multiple Point-to-Point Links (No WRS) Goal: to determine how much throughput we could obtain from the network: without adding any photonic switching capability at a node by adding extra transceivers (up to four) at each node The initial network had 21 bidirectional links in the physical topology. Using extra transceivers at the nodes, extra links are set up on the paths NE-CO, NE-IL, WA-CA2, CA1-UT, MI- NJ, and NY-MD. These lightpaths are chosen manually. Different combinations were considered. The channels providing the maximum scale-up was chosen. 45
Arbitrary Virtual Topology (Full WDM) Full WDM with WRSs at all nodes. It is possible to set up lightpaths between any two nodes. All lightpaths are routed over the shortest path on the physical topology. Starting off with a random initial topology, simulated annealing is used to get the best virtual topology. shown in the table. Provides a maximum scale-up of 106. The increased scale-up demonstrates the benefits of the WDM-based virtual-topology approach. 46
Effect of Nodal Degree and Wavelength Requirements If we consider full WDM, and increase the nodal degree to five and six, we find that the maximum scale-up increases nearly proportionally with increasing nodal degree. In the experiments, the observed maximum scale-ups: for P = 5: 135 For P = 6: 163 As the nodal degree is increased, the average hop distance of the virtual topology is reduced. This provides the extra improvement in the scale-up. Minimizing hop distance can be an important optimization problem. 47
Open Problems A significant amount of room exists for developing improved approaches and algorithms. An interesting avenue of research is to study how routing and wavelength assignment of lightpaths can be combined with the choice of virtual topology and its corresponding packet routing in order to arrive at an optimum solution. Dynamic establishment and reconfiguration of lightpaths is an important issue which needs to be thoroughly studied. 48