On Efficiency and Validity of Previous
Homeplug MAC Performance Analysis
Cristina Cano and David Malone
Hamilton Institute, NUI Maynooth.
Supported by Science Foundation Ireland grants 08/SRC/I1403 and 07/SK/I1216a.
MAC Modeling
The Homeplug/1901 MAC similar to 802.11’s DCF.
802.11’s MAC extensively studied using Bianchi’s model1
and extensions.
This has been extended to cover the Homeplug/19012.
Deferral counter requires extra states in Markov Chain.
1
2
Bianchi. Performance analysis of the IEEE 802.11 distributed coordination function. Selected Areas in Communications, IEEE Journal on 18.3 (2000): 535-547.
Chung et al., Performance analysis of HomePlug 1.0 MAC with CSMA/CA, IEEE Journal on Selected Areas in
Communications, vol. 24, no. 7, pp. 1411-1420, 2006.
Solving the model is computationally expensive
1 iteration loop that contains 2 more loops
Computationally expensive operations
Aimed to simplify model to make it quicker to solve.
Same assumptions as considered by Chung et al.
Infinite queue size and retry limit.
Exponential distributed interarrival of packets.
Ideal channel conditions.
Contention among homogeneous access categories.
Simplification
We take a renewal reward approach34 .
We compute the waiting times at each backoff stage
Define the probability to fail at backoff stage i,
(i)
(i)
(i)
pf = p · pbo + pdefer ..
Then compute average time in backoff to successfully
transmit.
We can precompute deferral probability and expected
backoff times.
Can also make exponential approx. to simplify further.
stations
10
50
3
4
Original Analysis
584.5 s
420.0 s
Simplified
3.7 s
4.2 s
Exponential
1.7 s
3.5 s
10000s Simulation
165.5 s
866.2 s
Kumar et al., New insights from a fixed point analysis of single cell IEEE 802.11 WLANs, INFOCOM 2005.
Bianchi and Tinnirello, Remarks on IEEE 802.11 DCF performance analysis, IEEE Communication Letters, 2005.
Validation Problems
Saturated Conditions
Same results as Chung. et al.
6
9
x 10
8
0.25
Exact Calculation
Exp. Approx.
Simulations
7
MAC Acccess Delay [s]
Throughput [bits/s]
CA1/0
6
5
4
CA3/2
3
0.2
0.15
CA3/2
0.1
2
1
0
0
CA1/0
0.05
Exact Calculation
Exp. Approx.
Simulations
10
20
30
Number of stations (n)
40
50
0
0
10
20
30
Number of stations (n)
40
50
Unsaturated Conditions
The results were not fitting but prior to saturation only
Explanation
Obtaining Two Solutions
Depending on the starting parameters:
6
9
x 10
8
7
Throughput [bits/s]
n=10
6
5
n=30
4
3
n=50
2
1
0
0
Analysis 1
Analysis 2
10
20
30
40
50
λ [packets/s]
60
70
80
Due to coupling of queue dynamics and channel access.
Something similar in WiFi5 .
5
Duffy, Mean field Markov models of wireless local area networks, Markov
Processes and Related Fields, vol. 16, no. 2, pp. 295-328, 2010.
Temporal Evaluation
Evolution of throughput/Queue size (max, av, min):
6
x 10
1000
6
800
5
Queue Size [packets]
Instantaneous Throughput [bits/s]
900
5.5
4.5
4
3.5
3
maximum→
700
600
←average
500
400
←minimum
300
200
2.5
100
2
0
5
10
15
Time [h]
20
25
30
0
15.45
15.5
15.55
Time [h]
15.6
15.65
Validation
Simulations (with pre-loaded queues) fit saturated solution:
6
9
x 10
8
7
Throughput [bits/s]
n=10
6
5
n=30
4
3
n=50
2
Analysis 1
Analysis 2
Simulations
1
0
0
10
20
30
40
50
λ [packets/s]
60
70
80
Summary
For large queues: long transitory phase before saturation.
Shows up as extra fixed point in model.
Can lead to misinterpretation of analysis and simulations.
Model improvements for PLC at
http://arxiv.org/abs/1401.6803.
Actually present in Wi-Fi and other protocols too.
Thinking about practical implications.