Analyzing Multi-Channel Medium Access Control
Schemes With ALOHA Reservation
Yunghsiang S. Han† ,
Jing Deng‡ and Zygmunt J. Haas♯
†
Graduate Institute of Communication Engineering
National Taipei University, Taiwan, ROC
‡
Dept. of Computer Science
University of New Orleans, USA
♯
School of Electrical & Computer Engineering
Cornell Univ., USA
Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Outline
• Introduction
• The MAC-m scheme
• Calculating the throughput of the MAC-m scheme
• Numerical and simulation results
• Conclusions
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Introduction
• Medium Access Control (MAC) schemes are used to control the
access of active nodes to the shared channel.
• Multi-channel: one control sub-channel and m data
sub-channels.
• The control sub-channel is used for reservation of access to the
data sub-channels over which the data packets are transmitted,
and such reservation can be done through the use of the
RTS/CTS (Ready-To-Send/Clear-To-Send) dialogue.
• Single-channel MAC scheme: MAC-0
• Modified split-channel MAC scheme (m = 1): contention
resolutions take place on the control sub-channel in parallel
with the transmission of data packets on the data sub-channel
(MAC-1).
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
MAC-0, MAC-1S, and MAC-2
MAC−0
w1
Contention Resolution
w2
Contention Resolution
1
1
Æ1
RTS
CTS
DATA
2
2
RTS
CTS
MAC−1S
Æ2
DATA
w2
Contention Resolution
MAC−1
Æ2
2
2
RTS
CTS
DATA
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2
2
RTS
CTS
Æ2
DATA
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Network Assumptions
• The network is fully-connected, i.e., all nodes are in the
transmission range of each other.
• The packet processing delays and the radio propagation delays
are negligible.
• The traffic generated by active nodes (including
retransmissions) is Poisson with rate G.
• The contention resolution on the control sub-channel is solved
by a pure ALOHA technique.
• We normalize all variables with respect to the control packet
transmission time.
• The control package length is fiex at 48 bits in simulations.
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
The MAC-m Scheme
• There is a virtual, distributed queue.
• Every node with data packets to send can compete on the
control sub-channel by sending RTS packet to its intended
receiver, which should reply with a CTS packet.
• When the CTS packet is received at the sender of the RTS
packet, the sender/receiver pair becomes a winner of the
competition.
• The following are the rules that a winner of the competition
follows:
1. If there is an available (idle) data sub-channel after the
requests in the distributed queue are assigned data
sub-channels, the winner of the competition transmits on
the available data sub-channel immediately after the CTS
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
packet is received.
2. If all data sub-channels are busy and the distributed queue
is not full, the winner of the competition adds itself to the
distributed queue and waits for an available data
sub-channel.
3. If all data sub-channels are busy and the distributed queue
is full, the winner of the competition drops its right to
transmit and goes back to the competition.
• After transmission on the data sub-channel, the sender needs
to go back to the control sub-channel to compete for the right
of transmission for the next packet.
• Whenever a data sub-channel becomes available due to the end
of its current data transmission, it serves one of the customers
in the distributed queue. If the queue is empty, the data
sub-channel becomes idle.
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Contention Resolution of the MAC-m
• A contention resolution period (W ) begins on the control
sub-channel after a successful RTS/CTS dialogue.
• The contention period lasts until there is a successful
RTS/CTS dialogue.
Contention Period, W
CTS
RTS
CTS
• The average duration of the contention period is
1
W =
−1 .
Ge−2G
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Arrival Statistics
• We approximate the arrivals of successful RTS/CTS dialogues
on the control sub-channel as a Poisson process, with arrival
rate of λ.
• The average arrival rate of successful RTS/CTS dialogues can
be determined as
Ge−2G
1
=
.
λ=
−2G
W +2
1 + Ge
• In the steady state, the throughput of the whole system is at
most the capacity of the control sub-channel.
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m (m = 1)
• The throughput by (M/D/1/1 + q model) is
Sm
ρ
1
=
·
.
r + 1 p(d) + ρ
0
• r is the ratio of the data rate of the control sub-channel to the
data rate of the data sub-channel.
• ρ = λkr is the utilization factor, where k is the ratio of data
packet size to the control packet size.
(d)
• p0 is the steady state probability of the empty virtual queue
at the departure instant of customer from the system.
• Let πn , n = 0, 1, . . . , q, q + 1, be the steady state probabilities
that there are n customers in the system at any instant of time.
• The average arrival rate of customers actually entering the
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
system is λe = λ(1 − πq+1 ).
• Therefore, the effective utilization factor is
ρe = ρ(1 − πq+1 ) .
• The system will be stable when the effective utilization factor
is less than 1.
• Hence, to determine the maximum achievable throughput, we
need to maximize throughput under the constraint that ρe < 1.
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m (m > 1)
• The throughput (M/M/m/m + q model) is
Sm
1
=
r+m
m+q
X
min{n, m} · πn
n=1
!
.
• The effective utilization factor is
ρe = ρ(1 − πq+m ) .
• The system will be stable when the effective utilization factor
is less than 1.
• Hence, to determine the maximum achievable throughput, we
need to maximize throughput under the constraint that ρe < 1.
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m with m = 1 = q in the
fixed-total-bandwidth scenario
1
0.9
0.8
Throughput of MAC−m, Sm
0.7
0.6
0.5
0.4
0.3
Ld=4096, Tobagi
L =4096, pdf
d
Ld=4096, M/D/1/2
Ld=1024, Tobagi
L =1024, pdf
d
Ld=1024, M/D/1/2
0.2
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Ratio of control/data sub−channel data rates, r
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0.8
0.9
1
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m with m = 1, Ld = 1024 in the
fixed-total-bandwidth scenario
0.8
MAC−0
q=10
q=3
q=2
q=1
q=0
0.7
Throughput, S
0.6
0.5
0.4
0.3
0.2
0.1
0
0.2
0.4
0.6
0.8
1
1.2
Ratio of control/data sub−channel data rates, r
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1.4
1.6
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Optimal throughput of MAC-m with m = 1 in the
fixed-total-bandwidth scenario
1
Optimum Throughput of MAC−m, S
m
0.9
0.8
0.7
0.6
0.5
0.4
Ld=4096
Ld=2048
Ld=1024
0
1
2
3
4
5
6
7
Size of virtual distributed queue, q
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Optimum throughput of MAC-m (Ld = 1024) in the
fixed-total-bandwidth scenario
0.75
Optimum Throughput, Sm
0.7
0.65
0.6
0.55
0.5
0.45
m=10
m=5
m=3
m=2
0
2
4
6
8
10
12
14
Size of virtual distributed queue, q
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18
20
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m (q = m) with different m and Ld in the
fixed-total-bandwidth scenario
1
0.95
0.9
Optimum Throughput, S
0.85
0.8
0.75
0.7
0.65
MAC−M, L =4096
d
MAC−M, Ld=2048
MAC−M, Ld=1024
MAC−0, Ld=4096
MAC−0, Ld=2048
MAC−0, L =1024
0.6
0.55
d
0.5
0
10
20
30
40
50
60
70
Number of data sub−channels, m
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80
90
100
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m with q = m in the fixed-channel-bandwidth
scenario (r = 1)
1
0.9
0.8
Optimum Throughput, S
m
0.7
0.6
0.5
0.4
0.3
0.2
Ld=4096
Ld=2048
Ld=1024
0.1
0
2
5
10
15
20
Number of data sub−channels, m
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25
30
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m schemes (m = 3, q = 3) for variable data
packet length (Simulation and Analytical results) in the
fixed-total-bandwidth scenario
1
0.9
0.8
Throughput of MAC−m, S
m
0.7
0.6
0.5
0.4
0.3
L =4096, analysis
d
L =2048, analysis
d
L =1024, analysis
d
L =4096, simulation
d
L =2048, simulation
d
L =1024, simulation
0.2
0.1
d
0
0
0.5
1
Ratio of control/data sub−channel data rates, r
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1.5
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Throughput of MAC-m with different m and Ld (Simulation and
Analytical results) in the fixed-channel-bandwidth scenario
1
0.9
0.8
Throughput, S
m
0.7
0.6
0.5
0.4
0.3
L =4096, fixed length, simulations
d
L =2048, fixed length, simulations
d
L =1024, fixed length, simulations
d
Ld=4096, variable length, analysis
Ld=2048, variable length, analysis
Ld=1024, variable length, analysis
0.2
0.1
0
2
4
6
8
10
12
14
16
Number of Data Sub−channels, m
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Analyzing Multi-Channel Channel MAC Schemes
Deng, Han, and Haas
Conclusions
• Based on the pure ALOHA contention resolution technique on
the control sub-channel, we have developed a queueing model
to study the performance of the MAC-m schemes with
fixed-total-bandwidth scenario and fixed-channel-bandwidth
scenario.
• In fixed-total-bandwidth scenario, our analysis shows that
multiple channel MAC schemes are always out-performed by
the corresponding single shared channel schemes, given that
the propagation delays are negligible.
• In the fixed-channel-bandwidth scenario, each sub-channel
always has the same data rate. Our study shows that there is
an optimum number of sub-channels in these MAC schemes.
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