A Game Approach for Multi-Channel A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Allocation in Multi-Hop Wireless Networks Networks Lin Gao, Xinbing Wang Dept. of Electronic Engineering Shanghai Jiao Tong University Shanghai, China
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A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks Lin Gao, Xinbing Wang Dept. of Electronic Engineering Shanghai Jiao Tong University.
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A Game Approach for Multi-Channel A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless NetworksAllocation in Multi-Hop Wireless Networks
Lin Gao, Xinbing Wang
Dept. of Electronic EngineeringShanghai Jiao Tong University
Shanghai, China
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 2
System Model and Game TheorySystem Model and Game Theory
Existence of MMCPNEExistence of MMCPNE
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 3
MotivationMotivation
The appearance of Multi-hop mobile ad hoc networks (MANETs) The appearance of Multi-hop mobile ad hoc networks (MANETs) A good channel allocation scheme in multi-hop MANET can improve A good channel allocation scheme in multi-hop MANET can improve
the system performance dramatically.the system performance dramatically. Distributed algorithm shows potential ability in channel allocation Distributed algorithm shows potential ability in channel allocation
problem due to the lacking of global central node in multi-hop problem due to the lacking of global central node in multi-hop MANETs.MANETs.
MANETs
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 4
Objectives --Objectives -- How to Solve the Problem? How to Solve the Problem?
In this paper, We model the channel allocation problem as a static In this paper, We model the channel allocation problem as a static cooperative game, in which some players collaborate to achieve high cooperative game, in which some players collaborate to achieve high date rate.date rate.
[1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio channel assignment. [1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio channel assignment. Journal of Graph Theory, 29:263-283, 1998.Journal of Graph Theory, 29:263-283, 1998.
[2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile telecommunication [2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile telecommunication systems: a comprehensive survey. IEEE Personal Communications, 3(3):10-31, Jun 1996.systems: a comprehensive survey. IEEE Personal Communications, 3(3):10-31, Jun 1996.
[3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of the IEEE [3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of the IEEE Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, Sept. 1999.Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, Sept. 1999.
[4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel assignment for WLANs. [4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel assignment for WLANs. Mobile Computing and Communications Review (MC2R), 9(3), 2005.Mobile Computing and Communications Review (MC2R), 9(3), 2005.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 5
OutlineOutline
IntroductionIntroduction
System Model and Game FormulationSystem Model and Game Formulation System Model: Multi-hop MANETSystem Model: Multi-hop MANET Game Theory: Nash EquilibriumGame Theory: Nash Equilibrium
Existence of MMCPNEExistence of MMCPNE
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 6
System Model -- ISystem Model -- I
We assume that there exist several communication sessions in our We assume that there exist several communication sessions in our model and we further assume each user participates in only one model and we further assume each user participates in only one session.session.
An example of 3 communication sessions and 7 An example of 3 communication sessions and 7 users.users.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 7
System Model -- IISystem Model -- II
We assume each user owns a device equipped with several radio We assume each user owns a device equipped with several radio transceivers, denoted by Ttransceivers, denoted by TSS and R and RSS respectively, which used to respectively, which used to
transmit the data packets respectively. transmit the data packets respectively. We assume that there is a mechanism that enables the multiple radios We assume that there is a mechanism that enables the multiple radios
in any Tin any TSS (or R (or RSS) to communicate simultaneously by using orthogonal ) to communicate simultaneously by using orthogonal
channels.channels.
RRSSTTSS
An example of 3 radios in TAn example of 3 radios in TSS (and R (and RSS).).
RRSS RRSS
TTSS TTSS
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 8
System Model -- IIISystem Model -- III
We assume that the total available bandwidth on channel We assume that the total available bandwidth on channel cc is shared is shared equally among the radios deployed on this channel. equally among the radios deployed on this channel.
Utility function:Utility function:
,
,
:
:
:
iu c i
c
c
ii
u cu c
cc C
where
k the total number of radios of u using channel c
k the total number of radios of all users using channel c
R the total available bandwidth of channel c
kR R
k
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 9
Game Formulation -- IGame Formulation -- I We formulate the channel allocation problem with a single stage We formulate the channel allocation problem with a single stage
game, which corresponds to a fixed channel allocation among the game, which corresponds to a fixed channel allocation among the players. Each player's strategy consists in defining the number of players. Each player's strategy consists in defining the number of radios on each of the channels.radios on each of the channels.
The strategy of the previous system model.The strategy of the previous system model.
s1 s2 s1
c1 c2 c3 c4
s1
s2
s3
s3r21
r21
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 10
Game Formulation -- IIGame Formulation -- II Nash Equilibrium (NE): NE expresses the resistance to the deviation Nash Equilibrium (NE): NE expresses the resistance to the deviation
of a single player in non-cooperative game. In other words, in a NE of a single player in non-cooperative game. In other words, in a NE none of the players can unilaterally change its strategy to increase its none of the players can unilaterally change its strategy to increase its utility.utility.
s1 s1 s1
c1 c2 c3 c4 c5 c6
s2 s2
s4
s3
s1 s2 s2
s3 s3
s4s4 s4
s3
An example of the Nash Equilibrium.An example of the Nash Equilibrium.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 11
Game Formulation – IIIGame Formulation – III Non-cooperative game is not suitable for the multi-hop networks for Non-cooperative game is not suitable for the multi-hop networks for
the following two reasons:the following two reasons:
(1) In one hand, the achieved date rate of any player in multi-hop link (1) In one hand, the achieved date rate of any player in multi-hop link is not only determined by the utility itself, but also by the utilities of is not only determined by the utility itself, but also by the utilities of other players in the same link. other players in the same link.
(2) In the other hand, it is possible that the players in the same multi-(2) In the other hand, it is possible that the players in the same multi-hop link cooperatively choose their strategies for the purpose of high hop link cooperatively choose their strategies for the purpose of high achieved date rate.achieved date rate.
u2
u2
u1 u1 u1
c1 c2 c3 c4 c5 c6 channels
u2
An example of the Nash Equilibrium with poor performance An example of the Nash Equilibrium with poor performance where u1 and u2 belong to the same multi-hop link.where u1 and u2 belong to the same multi-hop link.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 12
Game Formulation – IVGame Formulation – IV we define a novel coalition-proof Nash equilibrium in cooperative we define a novel coalition-proof Nash equilibrium in cooperative
game, named as min-max coalition-proof Nash equilibrium game, named as min-max coalition-proof Nash equilibrium (MMCPNE), in which players make their decisions so as to improve (MMCPNE), in which players make their decisions so as to improve the minimal payoff of players in the coalition.the minimal payoff of players in the coalition.
u2
u2
u1 u1 u1
c1 c2 c3 c4 c5 c6 channels
u2
An example of the MMCPNE.An example of the MMCPNE.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 13
Game Theory – VGame Theory – V By jointly searching the strategy in the strategies set of | By jointly searching the strategy in the strategies set of | lli i | players. | players.
The computation of achieving MMCPNE increases exponentially with The computation of achieving MMCPNE increases exponentially with the size of link.the size of link.
To reduce the large computation in finding MMCPNE, we introduce To reduce the large computation in finding MMCPNE, we introduce three approximate solutions, denoted by minimal coalition-proof Nash three approximate solutions, denoted by minimal coalition-proof Nash equilibrium (MCPNE), average coalition-proof Nash equilibrium equilibrium (MCPNE), average coalition-proof Nash equilibrium (ACPNE) and i coalition-proof Nash equilibrium (ICPNE). The (ACPNE) and i coalition-proof Nash equilibrium (ICPNE). The definitions of MCPNE, ACPNE and ICPNE are shown in Section IV.definitions of MCPNE, ACPNE and ICPNE are shown in Section IV.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 14
Definition of MMCPNEDefinition of MMCPNE We define a novel coalition-proof Nash equilibrium in cooperative We define a novel coalition-proof Nash equilibrium in cooperative
game, named as min-max coalition-proof Nash equilibrium game, named as min-max coalition-proof Nash equilibrium (MMCPNE), in which players make their decisions so as to improve (MMCPNE), in which players make their decisions so as to improve the minimal payoff of players in the coalition.the minimal payoff of players in the coalition.
: (Min-Max Coalition-Proof Nash Equilibrium
- MMCPNE) :
- ,
, :
min
Definition 4
i
mm
i
u
The strategy matrix defines a novel
coalition proof Nash Equilibrium if for every coalition
co we have
X
'
'
, min ,
.
i i i i i ii i i
i
i mm mm i mmu co co u co co
co u co
co
R R
for every strategy set
X X X X
X
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 15
Definition of MCPNEDefinition of MCPNE In MCPNE, players in a coalition select their strategies to maximize In MCPNE, players in a coalition select their strategies to maximize
the minimal utilities of players in the coalition.the minimal utilities of players in the coalition.
: (Minimal Coalition-Proof Nash Equilibrium
- MCPNE) :
- ,
, :
min
Definition 5
i i
m
i
uu co
The strategy matrix defines a special
coalition proof Nash Equilibrium if for every player
u we have
R
X
'
'
, min ,
.
i i i i i ii i
i
i m m i mu u u u uu co
u
R
for every strategy
x x
x
X X
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 16
Definition of ACPNEDefinition of ACPNE In ACPNE, players in a coalition select their strategies to maximize In ACPNE, players in a coalition select their strategies to maximize
the average utility while do not decrease the minimal utility of players the average utility while do not decrease the minimal utility of players in the coalition.in the coalition.
: (Average Coalition-Proof Nash Equilibrium
- ACPNE) : -
- , , :
min
Definition 6
i i
a
i
u co
The strategy matrix defines a special coalit
ion proof Nash Equilibrium if for every player u we have
R
X
'
'
'
'
, min ,
min , min ,
, ,
.
i i i i i ii i
i i i i i ii i i i
i i i i i i
i i i i
i
i a a i au u u u u uu co
i a a i au u u u u uu co u co
i a a i au u u u u u
u co u co
u
R
or
R R
R R
for every strategy
x x
x x
x x
x
X X
X X
X X
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 17
Definition of ICPNEDefinition of ICPNE In ICPNE, however, players in a coalition select their strategies to In ICPNE, however, players in a coalition select their strategies to
maximize their own utilities while do not decrease the minimal utility maximize their own utilities while do not decrease the minimal utility of players in the same coalition.of players in the same coalition.
: (I Coalition-Proof Nash Equilibrium - ICPNE) :
-
, , :
min
Definition 7
i ii i
i
i
i iu uu co
The strategy matrix defines a special coalition proof
Nash Equilibrium if for every player u we have
R
x
X
'
'
'
'
, min ,
min , min ,
, ,
.
i i i ii i
i i i i i ii i i i
i i i i i i
i
i i iu u u uu co
i i i i iu u u u u u
u co u co
i i i i iu u u u u u
u
R
or
R R
R R
for every strategy
x
x x
x x
x
X X
X X
X X
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 18
Intuition among these NE definitionsIntuition among these NE definitions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 19
OutlineOutline IntroductionIntroduction
System Model and Game FormulationSystem Model and Game Formulation
Existence of MMCPNEExistence of MMCPNE Theorem 1Theorem 1 Proposition 1, Lemma 2 ~ 5 Proposition 1, Lemma 2 ~ 5 Theorem 2Theorem 2
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 20
Theorem 1Theorem 1
,
,
,
:
:
(1) 1
(2) 1 ,
:
Theorem 1
i iu c u
b c
b c b c
A channel allocation is a NE iff the following
conditions hold
k and k k
for any b c C
where
k k the difference of radios number between
X
.channel b and c
The existence of Nash Equilibrium [5]:The existence of Nash Equilibrium [5]:
[5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-radio [5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-radio Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference on Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference on Computer Communications (INFOCOM '07), March 13-17 2007.Computer Communications (INFOCOM '07), March 13-17 2007.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 21
Proposition 1Proposition 1 We divide the MMCPNE states into two sets according to theorem 1. We divide the MMCPNE states into two sets according to theorem 1.
We denote the MMCPNE states which satisfy the theorem 1 by We denote the MMCPNE states which satisfy the theorem 1 by MMCPNE-1 and denote the remainder MMCPNE states by MMCPNE-MMCPNE-1 and denote the remainder MMCPNE states by MMCPNE-2. We find that the multi-hop links in MMCPNE-1 states always occupy 2. We find that the multi-hop links in MMCPNE-1 states always occupy more bandwidth compared with those in MMCPNE-2 states.more bandwidth compared with those in MMCPNE-2 states.
The basic criterion of finding MMCPNEThe basic criterion of finding MMCPNE:
,
, . ., 1 .
Proposition 1 Assume that there exists a MMCPNE channel
allocation with high bandwidth occupied then is a Nash
equilibrium i e the conditions of theorem hold
X X
All Channel Allocations
Lemma 2 Lemma 3
Lemma 4&5
NE
MMCPNE-1 Unknow Region
The value of Proposition The value of Proposition 1 is that it provides a 1 is that it provides a method to choose the method to choose the MMCPNE with the high MMCPNE with the high bandwidth occupied, i.e., bandwidth occupied, i.e., MMCPNE-1.MMCPNE-1.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 22
Lemma 2&3Lemma 2&3
1 2
1 2
1 2
1 2
, ,
: { , }
.
1 0, , .
Lemma 2
i i
i u u
u c u c
Assume that there exists a link l u u and R R in a NE
channel allocation If there exist two channels c C and c C such
that k and k i then is not MMCPNE
w
X
X
( ) : max (min ) .
here
C C the channel with the imum imum number of radios
Moving from NE to MMCPNE: link members relocate their radios to Moving from NE to MMCPNE: link members relocate their radios to improve the payoff of others when two members share any channels.improve the payoff of others when two members share any channels.
u2u2 u2 u2
u1 u1
u1
u1
c1 c2 c3 c4 c5 c6 channels
NE
An example of a NE channel An example of a NE channel allocation corresponding to allocation corresponding to
Lemma 2.Lemma 2.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 23
Lemma 4&5Lemma 4&5
2 1
1 1 2 1 1
1 2
1 2
, , ,
1 1: { , }
.
1 0
Lemma 4 i u u
u c u c u c
Assume that there exists a link l u u and R R in
a NE channel allocation If there exist two channels c C and c C such that
k and k whereas k
X
2 2 2, 0 1, .
( ) : ( )
u cand k then is not MMCPNE
where
the number of radios of any channel in C C
X
Moving from NE to MMCPNE: link members Moving from NE to MMCPNE: link members helping each other is that helping each other is that they mutually exchange some radios with each other.they mutually exchange some radios with each other.
u2
u2
u1 u1 u1
c1 c2 c3 c4 c5 c6 channels
NE
u2 An example of a NE channel An example of a NE channel allocation corresponding to allocation corresponding to
Lemma 4.Lemma 4.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 24
Theorem 2Theorem 2 The necessary conditions that enables a NE to be MMCPNE:The necessary conditions that enables a NE to be MMCPNE:
1 2
2 1
1 2
1 2 : { , }
. , :
1 1(1)
(2) 1:
Theorem 2 i u u
u u
u u
Assume that there exists a link l u u and R R in
a NE channel allocation If is MMCPNE the follow conditions hold
R R and
case if R R then ther
X X
1 2 1 2
1 2
1
, , , ,
1 2
1 2 ,
1 0,
2 : { , }
{ , } i
u b u b u c u c
u u
u b u
e does not exist two channels b C and
c C such that k k whereas k k
case if R R then there does not exist four channels b b C
and c c C such that k k
2 1 2, , , 1, 1, .
i j jb u c u ci whereas k k j
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 25
Conjecture 1Conjecture 1
1 2
1 2 1: { , }
.
2 , .
Conjecture i
u u
Assume that there exists a link l u u and
R R in a NE channel allocation If the conditions in
theorem hold then is MMCPNE
X
X
The sufficient conditions that enables a NE to be MMCPNE:The sufficient conditions that enables a NE to be MMCPNE:
All Channel Allocations
Lemma 2 Lemma 3
Lemma 4&5
NE
MMCPNE-1 Unknow Region
The unknown region The unknown region converges to NULL set converges to NULL set according to Conjecture 1.according to Conjecture 1.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 26
OutlineOutline
IntroductionIntroduction
System Model and Game FormulationSystem Model and Game Formulation
Existence of MMCPNEExistence of MMCPNE
Convergence Algorithm and SimulationConvergence Algorithm and Simulation Convergence algorithmConvergence algorithm Simulation Results Simulation Results
ConclusionsConclusions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 27
Convergence Algorithm -- IConvergence Algorithm -- I MMCP AlgorithmMMCP Algorithm
(1) In the first stage, the coalitions move their radios to achieve high (1) In the first stage, the coalitions move their radios to achieve high utility. Thus we call this stage as inter-link competition stage. utility. Thus we call this stage as inter-link competition stage.
(2) In the second state, players in the same link mutually adjust their (2) In the second state, players in the same link mutually adjust their radios to achieve higher date rate. We call this stage as intra-link radios to achieve higher date rate. We call this stage as intra-link improvement stage.improvement stage.
link to the code
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 28
Convergence Algorithm -- IIConvergence Algorithm -- II DCP AlgorithmDCP Algorithm
By transforming the mutual operation of multiple players into multiple By transforming the mutual operation of multiple players into multiple independent operations of the players, DCP algorithm efficiently independent operations of the players, DCP algorithm efficiently reduces the computational complexity, specifically, from exponentially reduces the computational complexity, specifically, from exponentially increasing with the number of players to linear increasing with it.increasing with the number of players to linear increasing with it.
link to the code
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 29
Simulation Results -- ISimulation Results -- I Performance criterion:Performance criterion:
: the coalition utility of any coalition is
defined as the ratio of the total bandwidth it occupied to
the average bandwidth per user.
: the coalition usage fact
Coalition Utility
Coalition Usage Factor or of any
coalition is defined as the ratio of the achieved date rate
to the total bandwidth it occupied.
: the coalition efficiency of any coalition
is defined as the ability of an
Coalition Efficiency
y coalition to achieve a given
payoff (or achieved date rate).
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 30
Simulation Results -- IISimulation Results -- II Average Coalition Utility vs. TimeAverage Coalition Utility vs. Time
Channel Number: 8Channel Number: 8
User number: 5User number: 5
Link number: 4Link number: 4
Radio number: 4Radio number: 4
Coalition: {u1,u2}Coalition: {u1,u2}
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 31
Simulation Results – IIISimulation Results – III Average Coalition Efficiency vs. TimeAverage Coalition Efficiency vs. Time
Channel Number: 8Channel Number: 8
User number: 5User number: 5
Link number: 4Link number: 4
Radio number: 4Radio number: 4
Coalition: {u1,u2}Coalition: {u1,u2}
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 32
Simulation Results – IVSimulation Results – IV Average Coalition Usage Factor vs. TimeAverage Coalition Usage Factor vs. Time
Channel Number: 8Channel Number: 8
User number: 5User number: 5
Link number: 4Link number: 4
Radio number: 4Radio number: 4
Coalition: {u1,u2}Coalition: {u1,u2}
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 33
Simulation Results – VSimulation Results – V Average Coalition Usage Factor vs. Users NumberAverage Coalition Usage Factor vs. Users Number
Channel Number: 8Channel Number: 8
Radio number: 4Radio number: 4
Coalition: {u1,u2}Coalition: {u1,u2}
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 34
OutlineOutline
IntroductionIntroduction
System Model and Game TheorySystem Model and Game Theory
Existence of MMCPNEExistence of MMCPNE
Convergence Algorithm and SimulationConvergence Algorithm and Simulation
ConclusionsConclusions ConclusionsConclusions
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 35
ConclusionsConclusions In this paper, we have studied the problem of competitive channel allocation In this paper, we have studied the problem of competitive channel allocation
among devices which use multiple radios in the multi-hop system. among devices which use multiple radios in the multi-hop system. We propose a novel coalition-proof Nash equilibrium, denoted by MMCPNE, to We propose a novel coalition-proof Nash equilibrium, denoted by MMCPNE, to
ensure the multi-hop links to achieve high date rate without worsening the date ensure the multi-hop links to achieve high date rate without worsening the date rates of single-hop links. rates of single-hop links.
We investigate the existence of MMCPNE and propose the necessary We investigate the existence of MMCPNE and propose the necessary conditions for the existence of MMCPNE. conditions for the existence of MMCPNE.
Finally, we provide several algorithms to achieve the exact and approximate Finally, we provide several algorithms to achieve the exact and approximate MMCPNE states. We study their convergence properties theoretically. MMCPNE states. We study their convergence properties theoretically. Simulation results show that MMCPNE outperforms CPNE and NE schemes in Simulation results show that MMCPNE outperforms CPNE and NE schemes in terms of achieved data rates of links due to cooperation gain.terms of achieved data rates of links due to cooperation gain.
Thank you !Thank you !
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 37
ReferenceReference [1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio [1] J. van den Heuvel, R. A. Leese, and M. A. Shepherd. Graph labeling and radio
channel assignment. Journal of Graph Theory, 29:263-283, 1998.channel assignment. Journal of Graph Theory, 29:263-283, 1998. [2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile [2] I. Katzela and M. Naghshineh. Channel assignment schemes for cellular mobile
telecommunication systems: a comprehensive survey. IEEE Personal Communications, telecommunication systems: a comprehensive survey. IEEE Personal Communications, 3(3):10-31, Jun 1996.3(3):10-31, Jun 1996.
[3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of [3] Hac A and Z. Chen. Hybrid channel allocation in wireless networks. In Proceedings of the IEEE Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, the IEEE Conference on Vehicular Technology Conference (VTC'99), 50(4):2329-2333, Sept. 1999.Sept. 1999.
[4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel [4] A. Mishra, S. Banerjee, and W. Arbaugh. Weighted coloring based channel assignment for WLANs. Mobile Computing and Communications Review (MC2R), 9(3), assignment for WLANs. Mobile Computing and Communications Review (MC2R), 9(3), 2005.2005.
[5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-[5] M. Felegyhazi, M. Cagalj, S. S. Bidokhti, and J. P. Hubaux. Non-cooperative Multi-radio Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference radio Channel Allocation in Wireless Networks. In Proceedings of the IEEE Conference on Computer Communications (INFOCOM '07), March 13-17 2007.on Computer Communications (INFOCOM '07), March 13-17 2007.
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 38
MMCP-AlgorithmMMCP-Algorithm
back
A Game Approach for Multi-Channel Allocation in Multi-Hop Wireless Networks 39