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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. Outline. Network Model QoS Parameters Multicast QoS Traffic Scheduling Algorithm

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multicast traffic scheduling in single hop wdm networks with tuning latencies

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

outline
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
network model
Network Model
  • A broadcast-and-select star-coupler topology is considered.
network model contd
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).
qos parameters
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.
qos parameters contd
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>
qos parameters contd1
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}
slide8

: 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}>

the multicast qos traffic scheduling problem
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.
the multicast qos traffic scheduling algorithm available slot scan
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.
slide12

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)

the multicast qos traffic scheduling algorithm the maximum assignable slots 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.
    • Find the maximum clique in the graph
the optimal mas omas solution
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.
optimal mas omas solution contd
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
near optimal solutions to the mas problem
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|)
slide19

Freest Wavelength First (FWF)

Longest Segment First (LSF)

performance evaluation

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
conclusions
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.
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