1. Analysis and simulation of Optical Networks Xin Liu

2. Outline Analytic Approach Probability: Expectation values, Variance Network Global Expectation Model Stochastic Process: Markov chain Packet Delay in OCS networks Simulation Discrete Event Simulation Model OCS and OBS extension on NS

3. Analytic Approach Methods: formal derivation, considered approximation, semi-empirical observation. Intent: To formulate analytic or closed form; To complement, not supplant more accurate, but computationally intensive tools based on numerical simulation.

4. Simulation Methods: To implement discrete event simulation model using generic languages; To extend known simulation platform. Intent: To be close to the real network.

5. Network Global Expectation Model Key idea: Use expectation values to describe required quantities of key network and network element resources. Significance: Provide approximate results for the preliminary evaluation and design of dynamic networks. Assumption: single-tier backbone networks, location-independent traffic demands.

6. Network Global Expectation Model the total network cost the number of network elements of type i the unit cost of network element of type i. Challenge:

7. Network Global Expectation Model Expectation value Example: L is the number of links and N is the number of nodes.

8. Primary Model Variables (Input) Network graph adjacent matrix Network traffic T : the total ingress/egress traffic D : the number of demands : demand matrix

9. Primary Model Variables Specify the difference between one-way and two-way links

10. Output Number of Demands Traffic Demand Bit-Rate Degree of Node

11. Output Number of Hops

12. Divide the network into 4 sectors centered on the selected node square root relation

13. Number of Hops The Moore bound results from the construction of a tree whose root is the parent of vertices and each subsequent vertex is itself the parent of vertices. Logarithmic relation

14. Number of Hops

15. Output Demands on Link Restoration Capacity Inverse dependency upon the degree of the nodes

16. Output Traffic on Link Number of Ports

17. Number of ports

18. Packet Delay in OCS Networks The paper first presents the queue length distribution and the packet delay distribution in a single logical buffer of the edge router, and then extends that discussion to a network of edge routers. To ensure computational tractability, the framework approximates the evolution of each buffer independently.

19. Model Formulation A circuit is a unidirectional lightpath connecting a pair of source-destination edge routers capable of transmitting C b/s uninterruptedly for a period of T seconds. Circuits are allocated to the logical buffers using a policy R based on the queue lengths at all logical buffers.

20. Model Formulation Consider J data streams, each associated with a source-destination pair of edge routers, Qos class, a route and wavelength assignment sequence from the source to the destination, and other external classifications. So there are J logical buffers.

21. Model Formulation Normalized lightpath arrival rates Normalized lightpath transmission rates K Circuit switching decision epoch n

22. Model Formulation The queue length in logical buffer j at epoch n The system state at epoch n A binary vector indicating which of the logical buffers are allocated circuits at state

23. Mathematical Model The process is a Markov chain. But each is not a Markov chain. Let be the probability that algorithm R allocates a circuit to buffer j with length i at epoch n.

24. Simulation Discrete Event Simulation Model. OCS and OBS extension on NS.

25. Discrete Event Simulation Model

26. Event handling Accept Execute RWA for connection requests; Modify the number of arriving requests, the number of successfully established working path; Modify the information of network resource. Create the next event according to assumed distribution and append it into event list. Service Over Release the resource of working channel which is not alive.

27. Basic Modules Phy-Topo : Generate physical topology, such as TORUS, NSFNet. Routing : Implement known routing algorithms, such as Dijkstra ’ s Algorithm, Floyd-based SPF, K-Shortest-With-Loop-Path. Graph Theory Algorithm : provide basic graph theory algorithms, such as MaxFlow, MinCost-Flow. Survival : provides protection and restoration schemes. Resource : Different policies, such as routing, wavelength assignment, control management, survivability schemes, will lead to different efficiency in resource usage. Wave-Assign : Combined with routing Module, it completes the RWA function in WDM networks. V-Topo : This module controls the virtual topology in IP layer. Traffic : It contains Poisson, Gaussian, Self-Similar traffic module. It is used to generate the random sequence of connection requests. Pseudo-Random Number : Generate random number in (0, 1) uniformly. DES : discrete event simulation module. Performance Metrics Statistic : In each DES process, track interested statistics variables. After simulation is over, prints out the values of performance metrics.

28. Basic Modules

29. OBS extension on NS OBS-ns (UMBC) Use centralized structure to assign resource; Add new classes for new types; Ignore the architecture of NS. OBS-extension Keep to the distributed architecture of NS; Add new component in existing composite classes for new features.

30. OBS-extension Task WDM link extension No multi-channel link model in NS; To add a multi-server queue in normal link model. Assembly Module in Ingress Nodes of OBS Networks Signaling, Qos and contention resolution

31. Normal Link Model head_The entry of a link queue_The queue reference of a link link_The reference of a link with delay and bandwidth property ttl_The reference of TTL management drophead_The reference of the head of the drop queue

32. WDM link extension WvAssign : Queue WaveClassifier : Classifier

33. Wavelength Classifier

34. WDM link extension #Create WDM link $ns duplex-link $n3 $n4 1Mb 20ms WvAssign 4 FirstFit 1

35. OBS extension Redirector Redirecting table and redirecting buffer. Similar to route table and cache in traditional router. Assembly Agent Set assembly scheme, parameters and signaling.

36. OBS extension

37. Assembly agent

38. Test

39. Reference Steven K. Korotky, “ Network Global Expectation Model: A Statistical Formalism for Quickly Quantifying Network Needs and Costs ”, Journal of Lightwave Technology Preprint, 2004. Zvi Rosberg, “ Packet Delay in Optical Circuit-Switched Networks ”, 2004. Zvi Rosberg, “ Analysis of OBS Networks with Limited Wavelength Conversion ”, 2004. Jean-Francois Labourdette, “ Fast Approximate Dimensioning and Performance Analysis of Mesh Optical Networks ”, Design of Reliable Communication Networks 2003, 428-438. Damon J. Wischik, “ Mathematical Modeling of Optical Burst-Switched (OBS) Networks ”, 2004.