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

OutlineOutline

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 ModelNetwork Model

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

WDMStar

Coupler

: bidirectional fibre

station 1

station 2

station 3

station N-2

station N-1

station N

. . .

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 ParametersQoS 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.L

d

c

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 (contd.)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}

imd i

md

: MVC1, <3, 8, -1, -1, s1, {m1, m2}>

: MVC2, <3, 4, -1, -1, s2, {m3, m4}>

: MVC3, <1, 4, 1, 4, s3, {m5, m6}>W = 3, = 1

0000

000000

000

1222

31

22231

MVCMVCMVCMVC

MVCMVC

MVCMVCMVCMVCMVC

D

13w

1

2

3

23w

33w

11w

21w

12w

22w

32w

The Multicast QoS Traffic The Multicast QoS Traffic Scheduling ProblemScheduling 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 matrix Dnew 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 The Multicast QoS Traffic Scheduling AlgorithmScheduling Algorithm

normalization

start

affordabilitycheck

requestrejected

failed

passed

available slotscan

failed

passed

slot assignment

requestaccepted

The Multicast QoS Traffic The Multicast QoS Traffic Scheduling Algorithm -- Scheduling Algorithm -- Available Slot ScanAvailable Slot Scan

Available slot matrix A A = [aij]WL , aij{0, 1}

Some nonzero entries may not be allocated simultaneously due to the tuning latency constraint.

otherwise1

on slot at or for violatedis

constraintlatency or tuningbusy is ,

, ofreceiver or the ofer transmitt theif0

iij jms

Mm

ms

a

0 0 0 0 0 0 0

0 0 0 0 0 0 0

MVC1

MVC2

: MVC1, <1, 8, -1, -1, s1, {m1, m2}>

L=8, W=2, =2

D :

: MVC2, <1, 8, -1, -1, s2, {m2, m3}>

0 0 0 0 0 0 0

0 0 0 0 0 0 0

MVC2

MVC10 0 0 0 0 0 0

0 0 0 0 0 0 0

MVC1

MVC2

D:

1 1 0 0 0 0 0 0

0 0 0 0 0 0 1 1

A : 1 1 0 0 0 0 0 0

0 0 0 0 0 0 1 1

1 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

1 1 0 0 0 0 0 0

0 0 0 0 0 0 0 0

B :

(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 The Multicast QoS Traffic Scheduling Algorithm -- Scheduling Algorithm -- The The Maximum Assignable Slots (MAS) MAS) ProblemProblem

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

27v

22v21v

a26

a13 a19 a1A

a21 a22

a12

a27

A:

W=2, L=10 and =2

13v

12v

26v

19v

1Av

The Optimal MAS (OMAS) The Optimal MAS (OMAS) SolutionSolution

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 Optimal MAS (OMAS) Solution (contd.)(contd.)

Auxiliary Graph Transformation For each nonzero entry aij in the first columns, move

the column contains aij to the leftmost and then set all entries that cannot be assigned concurrently with aij to 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

P22:

a26

a13 a19 a1A

a21a22

a12

a27

P21:

a26

a13 a19 a1A

a21 a22

a12

a27

P12:

a26

a13 a19 a1A

a21a22

a12

a27

a26

a13 a19 a1A

a21 a22

a12

a27

Q:

a26

a13 a19 a1A

a21 a22

a12

a27

A:

W=2, L=10 and =2

1213v 12

A1v

1212v

1226v 12

27v

1219v

2226v 22

27v

2222v

2219v 22

21v

2126v 21

27v

2121v 21

22v

26v 27v

13v

19v A1v

G12: G22:

G21: G:

Near- Optimal Solutions to The Near- Optimal Solutions to The MAS ProblemMAS 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|)

a26

a13 a19 a1A

a21 a22

a12

a27

A:

W=2, L=10 and =2

a27a26

a13 a19 a1A

a21 a22

a12

Step 1:

a27a26

a13 a19 a1A

a21 a22

a12

Step 2:

Step 3:

a26

a13 a19 a1A

a21 a22

a12

a27

a27a26

a13 a19 a1A

a21 a22

a12

Step 1:

a27a26

a13 a19 a1A

a21 a22

a12

Step 2:

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

Performance EvaluationPerformance Evaluation

0.0326

0.0336

0.0346

0.0356

0.0366

0.0376

0.0386

1 2 3 4 5 6 7 8 9 10

Tuning Latency

Blo

ckin

g P

rob

abil

ity

LSF

FWF

OMAS

ConclusionsConclusions

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.