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A Fast Delay-Constrained Multicast Routing Algorithm
Baoxian Zhang; Krunz, M.M.; Changjia Chen
Communications, 2001. ICC 2001. IEEE International Conference on , Volume: 9 , 2001
Page(s): 2676 -2680
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Outline
Motivation,model and problem SDCR heuristic for unicast DCMA heuristic for multicast Simulation results Conclusion
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Motivation
Objective
– Construct a delay-constrained multicast tree with lower complexity
– DCMA heuristic : Earlier research
– BSMA heuristic :– KPP heuristic :– CKMB heuristic :
)log||( 3 VVkO
)||( 3VO )||( 2VmO
|)|log( VmmO
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Model and Problem
Given – A network graph : G(V,E)– Each link has
• Delay value D(e)• Link cost C(e)
– Source node s– Destination set – Delay constraint
Ee
sVS
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Model and Problem
Finda tree T rooted at s and span all nodes satisfying – – is minimum
)( GT
),()(
vsPeeD
TeeC )(
Sv
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Routing information
Source routing strategy– Source maintain full information– OSPF is used
Two vectors – Delay vector– Cost vector– Each has |V|-1 entries for sVv j
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Routing information (cont.)
Entry for in delay vector– Destination ID– End to end delay of least delay path– Predecessor of on
Entry for in cost vector – Destination ID– End to end delay of least cost path – Predecessor of on
jv
),( jld vsP
jv ),( jld vsP
jv
),( jlc vsP
),( jlc vsPjv
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Outline
Motivation,model and problem SDCR heuristic for unicast DCMA heuristic for multicast Simulation results Conclusion
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Source-based Delay Constrained Routing (SDCR)
Objective– Find a delay-constrained least cost path
between source and a destination Idea
– Start from d – Backward to s along until
•
– Then continues along until reach s
),( dsPld
)),(()),(( dvPDvsPD ldlc
),( vsPlc
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Example of SDCR Heuristic
s
D
F
E
Destination : F
Each link has {cost,delay} pair
Delay constraint : 6
(1,3) (1,4)
(5,1) (3,1)
(3,1)
s
D
E
F s
D
F
ERelay node
(a) (b)
(a) SDCR
(b) LD path
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SDCR Heuristic (cont.)
Complexity is O(|V|) Lemma
– SDCR returns a loop-free path Idea
– can not contain any node on ,besides relay node u
),( usPlc ),( duPld
s u v d
LD path
LC path
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Outline
Motivation,model and problem SDCR heuristic for unicast DCMA heuristic for multicast Simulation results Conclusion
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Delay Constrained Multicast Algorithm (DCMA)
Based on SDCR algorithm Earlier research
– Union of all delay-constrained unicast paths– Loop will happen
Loop phenomenon
s v
d2
d1
w
relay node of d1
u
relay node of d2LD path
LC path
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Loop free DCMA Heuristic
Idea – First phase
• Proceed along path• Until a node v
– Marked or satisfy
– Second phase • Connect each v to s along• Until
– Reach s or a node on existing tree
),( dsPld
)),(()),(( dvPDvsPD ldlc
),( vsPlc
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First Phase of DCMA Heuristic
while S is not empty active_node d remove d while ON[active_node]=0 if ON[active_node] ld_lhop active_node ld_lhop else Q[d]=active_node break
)),_(())_,(( dnodeactivePDnodeactivesPD ldlc
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Second Phase of DCMA Heuristic
for i=1 to |S| if Q[i] NULL active_node = Q[i] while ON[active_node]=0 ON[active_node] lc_lhop active_node lc_lhop
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Example of DCMA Heuristic
s
d1
d2v
uS = {d1,d2}Q[d1]=Q[d2]=u LD path LC path
relay node=Q[d1]
s
u
v
d1
d2
Final tree
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DCMA Heuristic (cont.)
Lemma– The tree constructed by DCMA is always
loop-free Possible case for loop
– Source s,destination {x,y,z}
s
u
q
z
vx
y
s
u
q
z
v w
x
y
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Outline
Motivation,model and problem SDCR heuristic for unicast DCMA heuristic for multicast Simulation results Conclusion
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Simulation
Parameters – Link capacity with 155 Mbps– Cost
• Total reserved bandwidth
– Traffic• Uniform distributed 10M and 120Mbps
Performance evaluation• Cost of LD, DCMA, CDKS heuristics with
respect to CKMB
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Simulation Results
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Outline
Motivation,model and problem SDCR heuristic for unicast DCMA heuristic for multicast Simulation results Conclusion
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Conclusion
Complexity– SDCR : O(|V|)– DCMA : O(mlogm+|V|)
DCMA heuristic– achieve good performance and complexity