Network Performance under Mobility in Ad Hoc Networks

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Network Performance under Mobility in Ad Hoc
Networks
Richard Boucherie, Roland de Haan and Jan-Kees
van Ommeren
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Motivation (i)

• Analytical model for MOBILE ad hoc network
  performance

• ApproachConsider networks of bouncing nodes

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Motivation (ii)

• Bouncing node-network (practice)

?
?
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Motivation (iii)

• Bouncing node-network

S
D
M
M
M

• Network connectivity changes over time

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Objectives

• Performance measures for ad hoc networks
• Total transfer time of a packet
• Buffer levels at stations

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Modelling (i)

• Simple model 1 bouncing node

?
S
D

• Unreliable server queueing model

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Modelling (i)

• Chain model 2 bouncing nodes

Dependence between queues
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Modelling (i)

• Sink model 1 bouncing node

?
?
S1
D
S2

• System states
• S1 connected to D
• S2 connected to D
• No connection

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Modelling (ii)

• Extended sink model 1 bouncing node

S
?
?
?
S
D
S
?
S

• System states
• Some S connected to D
• No connection

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Polling model (i)

• Single-server polling model
• General characteristics
• M infinite-buffer queues
• Poisson arrival of jobs
• General service times
• General switch-over times
• Service in cyclic order

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Polling model (ii)

• Specific characteristics

• Preemptive service

• Autonomous server (i.e., server behaves
  independent of system state)

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Analysis (i)

• Queue-length distribution
• Relate distribution at various instants
• Via counting relation (cf. Eisenberg, 1970)
• Additional relations (cf. Eisenberg, 1970)
• Explicit computation of q.-l. distribution at
  visit completion instants

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Eisenbergs relation (i)

• Consider tagged queue i

w
w
b
p
b
p
a
a
Qi
Qi
Qi
Qi

• Instants

• Visit beginning instant a
• Visit completion instant b
• Service beginning instant w
• Service completion instant p

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Eisenbergs relation (ii)

• Counting relation (for state n until time t)

a(tn) p(tn) w(tn) b(tn)
gt Relation between p.g.f.s a(z), p(z), w(z),
b(z)
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Additional relations

• Additional relations (in terms of p.g.f.s)
• Between service events

• Between visit events

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Our model (i)

• New instants related to idle periods

w
a
b
w
b
b
w
p
p
p
a
a
b
b
Qi
Qi
Qi
a(tn) p(tn) p(tn) b(tn) b(tn)
w(tn) b(tn) a(tn)
or
a(tn) p(tn) b(tn) w(tn) a(tn)
p(tn) b(tn) b(tn)
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Our model (ii)

• Similar additional equations
• Service events ( w p, p)
• Idle period events (a b, b)
• Switch-over time relation (a b)
• Explicit computation Leung, 1991
• b(z), p(z)

gt Queue-length distribution at defined instants
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Dependency of Queues

• Coefficient of Correlation
• Total Variation

Measure
Results for an example network 3 symmetric
queues with at every queue arrival rate ?,
service rate µ1 and server departure rate ?.
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Dependency of Queues
Total variation
Correlation
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On-going research

• Product form approximation
• Performance measures
• Other visit time distributions
• Networks / chains of bouncing nodes

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Thanks for your attention