Multicast traffic scheduling in single hop wdm networks with tuning latencies
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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 Tuning Latencies

  • 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 Tuning Latencies

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


Network model contd
Network Model (contd.) Tuning Latencies

  • 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 Tuning Latencies

  • 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.) Tuning Latencies

  • 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.) Tuning Latencies

  • 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}


: Tuning LatenciesMVC1, <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 Tuning Latencies

  • 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 -- Tuning LatenciesAvailable 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.


B Tuning Latencies :

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 -- Tuning LatenciesThe 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 Tuning Latencies

  • 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.) Tuning Latencies

  • 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 Tuning Latencies

  • 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|)


Freest Wavelength First (FWF) Tuning Latencies

Longest Segment First (LSF)


Performance evaluation

0.0386 Tuning Latencies

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 Tuning Latencies

  • 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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