Optical Networks – Some Open Problems (Part 3) Dr. Arunita Jaekel

1. Optical Networks – Some Open Problems (Part 3)Dr. ArunitaJaekel

2. WDM Networks design • Optimization problems in WDM network design: • How to best define the logical topology of a multi-hop network. • How to set up a lightpath, or a set of lightpaths, to make optimum use of the network resources. • Given a logic topology, what is the optimum strategy to handle all the requests for data communication in the network. • How to handle faults in the network. • Use MIP (may become computationally intractable) or heuristics to solve the problem

3. WDM Network design • The constraints in designing a logical topology for a wavelength-routed network: • The physical topology of the network. • The optical hardware available at each end node which determines how many lightpaths may originate from or end at that end node. • The characteristics of the fibers (if RWA is also performed). • the amount of data that may be carried by a single lightpath, • The traffic requirements between each pair of end nodes.

4. Logical Topology Design • The formulation for the logical topology design problem must optimize network performance by determining: • the set of lightpaths (i.e., the set of logical edges EL in graph GL) to be created, • for each lightpath in EL, • its route through the physical topology, • its channel number on each fiber in its route, • the strategy for routing the traffic T over the logical topology.

5. Logical Topology Design • MIP-Based Solution of the Logical Topology Design and the Routing Problem • Notation used:

6. Logical Topology Design • MILP-Based Solution of the Logical Topology Design • Notation used: (continued)

7. Logical Topology Design • Objective function: minimize Лmax • Subject to:

8. Logical Topology Design • Subject to: (continue)

9. Logical Topology Design • Subject to: (continue)

10. Logical Topology Design Heuristic logical topology design algorithm: Pick the highest entry tsd in the traffic matrix Check if there is sufficient capacity on existing logical edges to route tsd If yes, set tsd =0 and update residual capacities on the corresponding logical edges Otherwise, Check if suffiecient resources exist to create a new logical edge (lightpath) l from s to d If yes create the lightpath and route tsd over l, then set tsd =0 Continue until there are no non-zero entries in the traffic matrix

11. Taffic Grooming Traffic Grooming combine low-speed individual requests for connections onto high-speed lightpaths in an efficient manner. two basic approaches: For a given set of traffic requests, minimize the total network cost, with the condition that all traffic requests are satisfied. For given resource limitations and traffic demands, maximize the network throughput, measured by the total amount of traffic that is successfully carried by the network. Fault-Tolerant Traffic Grooming guarantee that each low-rate data communication will continue when a fault occurs

12. Taffic Grooming Example of Traffic Grooming Inputs Binary Variables • Q: Set of all traffic requests. • sq (dq) : Source (Destination) node of traffic request q. • tq : Data communication rate for traffic request q, using OC-n notation. • P : Set of directed edges (lightpaths) in the logical topology. • o(p) (l(p)) : Originating (Terminating) node of lightpath p. • g: Capacity of lightpath p, using OC-n notation.

13. Taffic Grooming Objective function: • maximize amount of traffic that can be successfully handled • If a request q is blocked, (i.e., yq= 0), then it is not allocated any bandwidth on any lightpath (fp,q ≤ yq , ∀p, p Є P). • Ensure that total demand on a lightpath does not exceed its capacity.

14. Open issues and Problems • Traffic Models • Static traffic The set of lightpaths to be established is known in advance. • Dynamic traffic The arrival time and duration of demands are generated randomly, based on certain distributions. • Incremental traffic • Scheduled traffic model Setup and teardown times of the demands are known in advance.

15. Scheduled Traffic Scheduled Traffic Models Fixed window scheduled traffic model Each scheduled lightpath demands (SLDs) is represented by a tuple ( s ,d ,n ,ts ,te ), where s and d are the source and destination, n represents the number of requested lightpaths for the demand and ts , te are the setup and teardown times of the demand. Sliding scheduled traffic model The demand setup and teardown times (tsand te) are not known beforehand. Instead a larger window of time (α,ω), as well as a demand holding time τ ( 0 < τ ≤ ω - α) is specified for each demand.

16. Scheduled Traffic A set of lightpath demands L = {( sl, dl, nl, al, wl, tl)} for the sliding scheduled traffic model = 1, if and only if demand lp ends after demand lq is scheduled to start, i.e. stl = the actual start time of demand l, within its specified window. = 1, if and only if demands lp and lq overlap in time. M = a large constant.

17. MIP FORMULATION FOR SCHEDULING DEMANDS IN TIME Minimize (1) • (1) Minimizes total demand overlap. • (2a) and (2b) ensure that each demand is always scheduled within its specified window. • Equation (3) forces the binary variable to be 1, if demand lp ends after demand lqstarts. • (4a)-(4c) force = 1, if both and are 1. Subject to: (2a) (2b) (3) (4a) (4b) (4c)

18. Open issues and Problems • Survivable routing • In a logical topology design, the routing for lightpaths must be designed in such a way that a single-link failure does not disconnect the logical topology. Such a routing is termed survivable. • The survivable routing problem is shown to be NP-complete.

19. Open issues and Problems 2 2 3 3 • Survivable routing 2 3 1 1 1 5 5 4 4 5 4 (a) NOT survivable routing Logical topology (b) survivable routing

20. Optical Devices components • Wavelength Converter (WC) • a device that allows the carrier wavelength of an optical signal to be changed. • has an input carrying incoming signals and an output carrying the same number of outgoing signals. • Each outgoing signal encodes the same data as an incoming signal but the carrier wavelength of an outgoing signal is allowed to be different from that of the corresponding incoming signal. Figure 8: A block diagram of a wavelength converter

21. Optical Devices components • Wavelength Converters may be categorized as follows: • full wavelength conversion where the channel cjof an incoming signal can be any channel, 1 ≤j ≤ nch . By changing the switch settings, the channel cj used by the input signal may be changed to any other channel, say ck , 1 ≤k ≤ nch, used by the corresponding outgoing signal. • fixed wavelength conversion where cjcan be any channel, 1 ≤j ≤ nch , but if the incoming signal uses channel cj, the outgoing signal always at channel ck, where k is fixed for a given j and there is no switch setting to change. • limited wavelength conversion where, for a given channel number cj, the corresponding channel number ckis a member of a predefined subset of the set {1,2,…, nch}.

22. Optical Devices components Figure 9a: Full wavelength conversion Figure 9c: Limited wavelength conversion Figure 9b: Fixed wavelength conversion

23. Basic Concepts • Multi-fiber networks • A network where each link between nodes consists of a bundle of fibers is called a multi-fiber Network. • A multi-fiber network is called even, if the number of fibers in each link is the same. • If the number of fibers varies from one link to another, it is called an uneven multi-fiber network.

24. Wavelength Routed Networks • Virtual wavelength translation (VWT) • Lgical wavelength translation at a node accomplished using routers to switch between fibers without using any wavelength translators in optical domain. • In VWT a wavelength that can not continue on the next hop can be switched to another fiber, if the same wavelength is free on one of the other fibers. • Such a network can be considered functionally equivalent to a single fiber network, with partial wavelength conversion. Figure 18: Illustration of virtual wavelength translation