1. Multicast Traffic Scheduling in Single-Hop WDM Networks with Tuning Latencies Ching-Fang Hsu Department of Computer Science and Information Engineering National Cheng Kung University June 2004

2. Outline v Network Model v QoS Parameters v Multicast QoS Traffic Scheduling Algorithm v The Maximum Assignable Slots (MAS) Problem v The Optimal MAS Solution v Near-optimal Solutions to The MAS Problem v Performance Evaluation v Conclusions

3. Network Model v A broadcast-and-select star-coupler topology is considered.

4. Network Model (contd.) v Transmission in the network operates in a time-slotted fashion. v The normalized tuning delay, is expressed in units of cell duration. v All transceivers are tunable over all wavelengths with the same delay. u Each station is equipped with a pair of fixed transceivers (control channel) and a pair of tunable transceivers (data channel ).

5. QoS Parameters v CBR and ABR traffic types are considered. v Multicast virtual circuits (MVCs) A 2-tuple notation to describe cell rate c is the maximum number of slots that can arrive in any d slots. For CBR transmission, d is also the relative deadline, i.e., a cell of a CBR MVC must be sent before slot t+d if it arrives in slot t For an ABR VC, just means that slots within a L-slot period should be assigned to it.

6. QoS Parameters (contd.) v Minimum cell rate (MCR) and peak cell rate (PCR) u For a CBR MVC, MCR=PCR v 6-tuple notation to identify a MVC o MCR, PCR, the source ID, and the set of destination Ids For a CBR MVC, =

7. QoS Parameters (contd.) Each CBR MVC has its own deadline ( d m ), or local cycle length. v Global cycle length -- the period of a traffic scheduling containing CBR traffic L=lcm( ), where { | is the local cycle length of MVC i 's MCR}

8. : MVC 1, : MVC 2, : MVC 3, W = 3, = 1

9. The Multicast QoS Traffic Scheduling Problem Given N stations, W available wavelengths for data transmission, L-slot global cycle and a W L slot- allocation matrix D; each station is equipped with a pair of tunable transceiver and each needs time slots for tuning from i to j, i j. For a setup request r s =, find a new feasible slot- allocation matrix D new with a new global cycle length L new such that r s is arranged into D new and all the QoS requirements of accepted MVC's in D are not affected.

10. The Multicast QoS Traffic Scheduling Algorithm

11. The Multicast QoS Traffic Scheduling Algorithm -- Available Slot Scan Available slot matrix A u A = [a ij ] W L, a ij {0, 1} v Some nonzero entries may not be allocated simultaneously due to the tuning latency constraint.

12. 1 1 0 0 0 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 B : (b) D and A for a request MVC 3 = (c) Assignable matrix B for A in (b)

13. The Multicast QoS Traffic Scheduling Algorithm -- The MAS) Problem The Multicast QoS Traffic Scheduling Algorithm -- The Maximum Assignable Slots ( MAS) Problem How to retrieve the maximum available slots concurrently for assignment from available matrix A? Derive an auxiliary graph with each entry in A with value 1 as a node and a link is created between two nodes whose representative entries can be assigned concurrently. u Find the maximum clique in the graph

15. The Optimal MAS (OMAS) Solution v The Optimal MAS (OMAS) Strategy u Comparability graphs An undirected graph G = (V, E) is a comparability graph if there exists an orientation ( V, F ) of G satisfying F F -1 =, F + F -1 = E, F 2 F, where F 2 = { ac | ab, bc F } o The maximum clique problem is polynomial- time solvable in comparability graphs.

16. Optimal MAS (OMAS) Solution (contd.) v Auxiliary Graph Transformation For each nonzero entry a ij in the first columns, move the column contains a ij to the leftmost and then set all entries that cannot be assigned concurrently with a ij to zero. The auxiliary graph of the new matrix P ij is a comparability graph. Set the entries of the first columns to zero, the auxiliary graph of the new matrix Q is a comparability graph. The OMAS solution is the maximum of the solutions among P ij and Q

18. Near- Optimal Solutions to The MAS Problem The time complexity of OMAS strategy is O( W|A| 2 ) in the worst case. v Longest Segment First (LSF) u A segment : a set of continuous available time slots on the same wavelength u Assign the slots on the segment basis O(|A| 2 log|A|) v Freest Wavelength First (FWF) u Freest wavelength : the wavelength that contains the most available time slots u Assign the slots on the wavelength basis u O(W|A|log|A|)

19. Longest Segment First (LSF) Freest Wavelength First (FWF)

20. Performance Evaluation

21. Conclusions v QoS multicast services in WDM star- coupled networks is investigated. v The slot scanning problem is defined as the MAS problem and its optimal solution is derived. v FWF is a considerable replacement of OMAS for its lower complexity and near-optimal blocking performance.