1. Chapter 11 Wavelength Conversion

2. To establish a lightpath, we require that the same wavelength be allocated on all the links in the path. This requirement is known as the wavelength- continuity constraint (e.g., see [BaMu96]). This constraint distinguishes the wavelength- routed network from a circuit-switched network which blocks calls only when there is no capacity along any of the links in the path. assigned to the call.

5. Wavelength conversion wavelength conversion: – It is easy to eliminate the wavelength-continuity constraint, if we were able to convert the data arriving on one wavelength along a link into another wavelength at an intermediate node and forward it along the next link. a single lightpath in such a wavelength-convertible network can use a different wavelength along each of the links in its path. Thus, wavelength conversion may improve the efficiency in the network by resolving the wavelength conflicts of the lightpaths.

6. Wavelength converter

7. Characteristics of WC transparency to bit rates and signal formats, fast setup time of output wavelength, conversion to both shorter and longer wavelengths, moderate input power levels, possibility for same input and output wavelengths (i.e., no conversion), insensitivity to input signal polarization, low-chirp output signal with high extinction ratio7 and large signal-to-noise ratio, and simple implementation.

8. Wavelength Conversion Technologies Wavelength conversion techniques can be broadly classified into two types: –opto-electronic wavelength conversion: the optical signal must first be converted into an electronic signal; and –all-optical wavelength conversion: the signal remains in the optical domain. coherent effects cross modulation.

9. Wavelength Conversion in Switches Where do we place them in the network? switches (crossconnects) A possible architecture of such a wavelength- convertible switching node is the dedicated wavelength-convertible switch (from [LeLi93]). (wavelength interchanging crossconnect (WIXC)),. Each wavelength along each output link in a switch has a dedicated wavelength converter i.e., an M x M switch in an N-wavelength system requires M x N converters.

10. The incoming optical signal from a link at the switch is first wavelength demultiplexed into separate wavelengths. Each wavelength is switched to the desired output port by the nonblocking optical switch. The output signal may have its wavelength changed by its wavelength converter. Finally, various wavelengths combine to form an aggregate signal coupled to an outbound fiber.

11. Wavelength Conversion in Switches

12. Switch sharing converter the dedicated wavelength-convertible switch is not very cost efficient since all of its converters may not be required all the time [InMu96]. An effective method to cut costs is to share the converters. Two architectures: –share­per-node structure –share-per-link structure

13. share­per-node structure All the converters at the switching node are collected in a converter bank. A converter bank is a collection of a few wavelength converters. This bank can be accessed by any wavelength on any incoming fiber by appropriately configuring the larger optical switch. In this architecture, only the wavelengths which require conversion are directed to the converter bank. The converted wavelengths are then switched to the appropriate outbound fiber link by the second optical switch.

14. Share-per-Node WC

15. Share-per-link structure Each outgoing fiber link is provided with a dedicated converter bank which can be accessed only by those lightpaths traveling on that particular outbound link. The optical switch can be configured appropriately to direct wavelengths to-ward a particular link, either with conversion or without conversion.

16. Share-per-link structure

17. 11.3 network design Network designs must evolve to incorporate wavelength conversion effectively. Network designers must choose not only among the various conversion techniques but also among the several switch archi­tectures described. An important challenge in the design is to overcome the limitations in using wavelength conversion technology. These limitations fall into the following three categories: –Limited availability of wavelength converters at the nodes. –Sharing of converters. –Limited ‑ range wavelength conversion.

18. Limited availability of wavelength converters at the nodes. As long as wavelength converters remain expensive [Yoo96], it may not be economically viable to equip all the nodes in a WDM network with them. Some effects of sparse conversion (i.e., having only a few converting switches in the network) have been examined [SuAS96]. An interesting question which has not been answered is where (optimally?) to place these few converters in the network.

19. Sharing of converters. Even among the switches capable of wavelength conversion, it may not be cost effective to equip all the output ports of a switch with this capability. Designs of switch architectures have been proposed which allow sharing of converters among the various signals at a switch. It has been shown in [LeLi93] that the performance of such a network saturates when the number of converters at a switch increases beyond a certain threshold. An interesting problem is to quantify the dependence of this threshold on the routing algorithm used and the blocking probability desired.

20. Limited ‑ range wavelength conversion. Four ‑ wave ‑ mixing ‑ based all­optical wavelength converters provide only a limited ‑ range conversion capability. If the range is limited to k, then an input wavelength λ i can only be converted to wavelengths λ max(i-k,1) through λ max(i+k,N) –where N is the number of wavelengths in the system (indexed 1 through N). Analysis shows that networks employing such devices, however, compare favorably with those utilizing converters with full ‑ range capability, under certain conditions.

21. Network Control Control algorithms are required in a network to manage its resources effectively. An important task of the control mechanism is to provide routes to the lightpath requests while maximizing a desired system parameter, e.g., throughput. Such routing schemes can be classified into static and dynamic categories depending on whether the lightpath requests are known a priori or not.

22. Dynamic Routing In a wavelength ‑ routed optical network, lightpath requests arrive at random between source ‑ destination pairs and each lightpath has a random holding time after which it is torn down. These lightpaths need to be set up dynamically between source ‑ destination pairs by determining a route through the network connecting the source to the destination and assigning a free wavelength along this path. Two lightpaths which have at least a link in common cannot use the same wavelength. Moreover, the same wavelength has to be assigned to a path on all of its links. This is the wavelength ‑ continuity constraint described in Section 11.1. This routing and wavelength assignment (RWA) problem

23. Dynamic Routing However, if all switches in the network have full wavelength conversion, the network becomes equivalent to a circuit­switched telephone network [RaSi95]. Routing algorithms have been proposed for use in wavelength ‑ convertible networks. In [LeLi93], the routing algorithm approximates the cost function of routing as the sum of individual costs due to using channels and wavelength converters. For this purpose, an auxiliary graph is created [BaSB91] and the shortest­path algorithm is applied on the graph to determine the route. In [ChFZ96], an algorithm with provably optimal running time has been provided for such a technique.

24. Dynamic Routing Algorithms have also been studied which use a fixed path or deterministic routing [RaSi95]. In such a scheme, there is a fixed path between every source ‑ destination pair in the network. Several RWA heuristics have been designed based on which wavelength to assign to a lightpath along the fixed path [BaSB91, MoAz96a, MoAz96b] and which, if any, lightpaths to block selectively. However, design of efficient routing algorithms which incorporate the limitations in Section 11.3.1 still remains an open problem.

25. Static Routing Static RWA problem assumes that all the lightpaths that areto be set up in the network are known initially. The objective is to maximize the total throughput in the network, i.e., the total number of light-paths which can be established simultaneously in the network. An upper bound on the carried traffic per available wavelength has been obtained (for a network with and without wavelength conversion) by relaxing the corresponding integer linear program (ILP) [RaSi95]. Several heuristic­based approaches have been proposed for solving the static RWA problem in a network without wavelength conversion [ChBa96]. Again, efficient algorithms which incorporate the limitations in Section 11.3.1 for a wavelength ‑ convertible network are still unavailable.

26. Network Management Issues arise in network management regarding the use of wavelength conversion to promote interoperability across sub-networks managed by independent operators. Wavelength conversion supports the distribution of network control and management functionalities into smaller sub-networks by allowing flexible wavelength assignments within each sub-network [Yoo96].

28. Related Issue RWA on wavelength convertible WDM Converter placement problem Converter allocation problem

31. RWA on wavelength convertible WDM Graph model Layered graph WS (wavelength selected) WC (wavelength convertible) Node Vertical edge Horizontal edge M(N+K) nodes

32. Example Book in p. 115

36. Converter placement problem Given k number of converters, how can the mean blocking probability in a network be computed? Is it possible to achieve performance close to the best achievement with only a few converters? What is the effect of network topology on the number of converter required? Given k number of converters, how can the best k nodes be chosen to place them, to achieve optimal performance?

46. Converter allocation problem Allocating Wavelength Converters in All-Optical Networks WC’s can be distinguished into two types: –a full-range wavelength converter (FWC) can convert an incoming wavelength to any outgoing wavelength and –a limited range wavelength converter can convert an incoming wavelength to a subset of the outgoing wavelengths.

47. Types When the number of FWC’s in a node is equal to the total number of outgoing wavelength channels of this node (which is equal to the number of outgoing fibers times the number of wavelength channels per fiber), FWC’s are always available when they are needed. We call this scenario a complete wavelength conversion. It may be more cost-effective to use a fewer number of FWC’s; this scenario is called partial wavelength conversion. Given a limited number of FWC’s, it is necessary to allocate these FWC’s to the node.

50. With the above idea, we divide the problem into thefollowing two subproblems. –1) Record the utilization matrix via computer simulations. –2) Based on the utilization matrix, optimize the allocations of the FWC’s.

51. Recording Utilization Matrix We record the utilization matrix via simulation experiments. One important issue is that, when there is wavelength conflict, we need to determine where we should perform wavelength conversion. Different methods can lead to different utilization matrices. In our study, we design and adopt one possible method to resolve wavelength conflict that gives good results. However, our simulation-based optimization methodology is also applicable to any other conflict resolution method. For any given call duration statistics, we can generate the duration for each transmission.

52. Recording Algorithm

54. Conflict Resolution Algorithm The main idea is to transform the problem of resolving wavelength conflict into an equivalent shortest path problem in a directed graph, where the length of a path in the directed graph is determined by: –1) the total number of FWC’s used and –2) the maximum number of FWC’s being used on every node of the source-to-destination path. By determining the shortest path in this directed graph, we can fulfill both of our objectives.. Along the source-to-destination path in the network, the intermediate nodes (excluding the source and destination nodes) are indexed from 1 to L. Let W(L) denotes the number of FWC’s being used on the the intermediate node. Auxiliary graph construction Minimum-Cost Path Selected

55. Auxiliary graph construction

59. Conflict Resolution Algorithm

61. Allocating FWC’s In this subsection, we optimize the allocations of a given number of FWC’s based on the utilization matrix. After allocating a certain number of FWC’s to a node, we can get from the percentage of time that this node has sufficient FWC’s to serve the transmission. For convenience, we call this quantity the total utilization.

62. Three different objectives Maximize the sum of total utilizations of all the nodes, so that the overall utilization of FWC’s can be improved. As a result, the overall blocking probability can be smaller and, hence, the mean quality of service is better. Maximize the product of the total utilizations of all the nodes. In this manner, the overall utilization of FWC’s can be improved (i.e., better mean quality of service) and the allocation of FWC’s to the nodes can be more fair. Maximize the minimum value of total utilization of the nodes, so that the allocation of FWC’s to the nodes can be more fair.

63. Maximize the sum of total utilizations of all the nodes

65. Maximize the product of the total utilizations of all the nodes

66. Maximize the minimum value of total utilization of the nodes