Multicast Traffic Scheduling in Single-Hop WDM Networks with Tuning Latencies

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

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

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

5. QoS Parameters • CBR and ABR traffic types are considered. • Multicast virtual circuits (MVC’s) • A 2-tuple notation <c, d> 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, <c, d> just means that slots within a L-slot period should be assigned to it.

6. QoS Parameters (contd.) • Minimum cell rate (MCR) and peak cell rate (PCR) • For a CBR MVC, MCR=PCR • 6-tuple notation to identify a MVC • <cm, dm, cp, dp, s, M> • MCR, PCR, the source ID, and the set of destination Ids • For a CBR MVC, < cp, dp > = <-1, -1>

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

8. : MVC1, <3, 8, -1, -1, s1, {m1, m2}> : MVC2, <3, 4, -1, -1, s2, {m3, m4}> W = 3, d = 1 : MVC3, <1, 4, 1, 4, s3, {m5, m6}>

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 rs = < cm, dm, cp, dp, s, M>, find a new feasible slot-allocation matrixDnew with a new global cycle length Lnew such that rs is arranged into Dnew 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 matrixA • A = [aij]WL , aij{0, 1} • Some nonzero entries may not be allocated simultaneously due to the tuning latency constraint.

12. B : 1 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 (b) D and A for a request MVC3 = <1, 16, -1, -1, s1, {m3, m4}> (c) Assignable matrix B for A in (b)

13. 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. • Find the maximum clique in the graph

15. The Optimal MAS (OMAS) Solution • The Optimal MAS (OMAS) Strategy • 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, F2  F, where F2 = {ac | ab, bc  F} • The maximum clique problem is polynomial-time solvable in comparability graphs.

16. Optimal MAS (OMAS) Solution (contd.) • Auxiliary Graph Transformation • For each nonzero entry aij in the first  columns, move the column contains aijto the leftmost and then set all entries that cannot be assigned concurrently with aijto zero. The auxiliary graph of the new matrix Pij 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 Pij 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. • Longest Segment First (LSF) • A segment : a set of continuous available time slots on the same wavelength • Assign the slots on the segment basis • O(|A|2log|A|) • Freest Wavelength First (FWF) • Freest wavelength : the wavelength that contains the most available time slots • Assign the slots on the wavelength basis • O(W|A|log|A|)

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

20. 0.0386 LSF FWF 0.0376 OMAS 0.0366 0.0356 Blocking Probability 0.0346 0.0336 0.0326 1 2 3 4 5 6 7 8 9 10 d Tuning Latency Performance Evaluation

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