The prevalence of IoT is driven by industrial requirements and scales, but also by community curiosity and tinkering in participatory crowdsensing endeavours. This tutorial first explores the practical requirements and options of modern IoT appliances and projects, including all aspects of the diverse stack, from PHY to application. With that as base, traffic models can now be derived and evaluated for these IoT topologies that might provide a better fit than traditional approaches.
The slides discuss the second part dedicated to traffic modeling for Aggregated Periodic IoT Data.
2. Tobias Hoßfeld
Disclaimer
More details of the tutorial can be found in the related paper.
Tobias Hoßfeld, Florian Metzger, Poul E. Heegaard, Traffic
Modeling for Aggregated Periodic IoT Data, 21st Conference on
Innovations in Clouds, Internet and Networks (ICIN 2018),
Feb 19-22, 2018, Paris, France
The tutorial was presented at MMB 2018, the 19th International GI/ITG
Conference on “Measurement, Modelling and Evaluation of Computing
Systems”, Feb 26, 2018, Erlangen, Germany.
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3. Tobias Hoßfeld
Use Case: IoT Cloud
Many sensors send data to an IoT cloud
IoT cloud load balancer is used
What about the scalability of the IoT Cloud Load Balancer?
How to dimension for certain QoS requirements?
4. Tobias Hoßfeld
Use Case: IoT Cloud
Many sensors send data to an IoT cloud
IoT cloud load balancer is used
How to answer those questions? Scalability, Dimensioning?
Measurement Simulation Analysis
𝐸 𝑋 = 𝜆𝐸[𝑊]
8. Tobias Hoßfeld
Agenda
Superposition of Periodic IoT Traffic
Palm-Khintchine Theorem: Modeling as Poisson Process
Evaluation of Bias: Poisson Process vs. Aggregated Periodic Traffic
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Use Case: Load Balancer at IoT Cloud
Waiting times: Poisson Process vs. Aggregated Periodic Traffic
Impact of Network Transmissions
9. Tobias Hoßfeld
Periodic Traffic Patterns
Some results from literature
[2] 3GPP. RAN Improvements for Machine-type Communications. TR37.868. Oct. 2011.
[7] Draft new Report ITU-R M.[IMT-2020.TECH PERF REQ] – Minimum requirements related to technical performance for IMT-
2020 radio interface(s). International Telecommunication Union Radiocommunication Sector, Feb. 2017.
[19] Massive IoT in the City. Ericsson White paper, Nov. 2016.
[28] R. Ratasuk et al. “Recent advancements in M2M communications in 4G networks and evolution towards 5G.” In: 18th
International Conference on Intelligence in Next Generation Networks. Feb. 2015.
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Very different number of nodes
and rates
10. Tobias Hoßfeld
Superposition of Traffic
In [1] the 3GPP notes that “[...] for a large amount of users the
overall arrival process can be modelled as a Poisson arrival process
regardless of the individual arrival process.”
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for large
number n
…
… Poisson process !
[1] 3GPP. GERAN improvements for Machine-
Type Communications (MTC). TR 43.868. Feb.
2014.
11. Tobias Hoßfeld
Superposition of Traffic
In [1] the 3GPP notes that “[...] for a large amount of users the
overall arrival process can be modelled as a Poisson arrival process
regardless of the individual arrival process.”
11
for large
number n
…
… Poisson process !
12. Tobias Hoßfeld
Superposition of Periodic Traffic
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for large
number n
…
… Poisson process !
When is n large enough so that the Poisson process
is a proper assumption?
How much bias is introduced by this assumption?
Which traffic characteristics are affected?
13. Tobias Hoßfeld
Scenario: Async. Homogeneous Periodic Traffic
System consists of 𝑛 sensor nodes
Asynchronous sources: Nodes start randomly at 𝑡𝑖
Homogeneous: Each node sends periodically with the same
sampling period 𝑇
𝐴𝑖 is the time between data from node 𝑖 and node 𝑖 + 1
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Sampling period 𝑻 = 𝒊=𝟏
𝒏
𝑨𝒊
14. Tobias Hoßfeld
Expected Arrivals
Expected time between arrivals is 𝐸[𝐴𝑖] = 𝑇/(𝑛 + 1)
Idea for proof: distance between two random points 𝑥1, 𝑥2
𝐸 𝐴𝑖 = 0
𝑇
0
𝑇
𝑡1 − 𝑡2 ⋅ 𝑢 𝑡1 ⋅ 𝑢 𝑡2 𝑑𝑡1 𝑑𝑡2
=
1
𝑇2 𝑡1=0
𝑇
( 𝑡2=0
𝑡1
(𝑡1 − 𝑡2) 𝑑𝑡2 + 𝑡2=𝑡1
𝑇
𝑡2 − 𝑡1 𝑑𝑡2 ) 𝑑𝑡1 = T/3
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Uniform distribution U(0,T)
• CDF 𝑈 𝑥 =
𝑥
𝑇
• PDF 𝑢 𝑥 =
𝑑
𝑑𝑥
𝑈 𝑥 =
1
𝑇
15. Tobias Hoßfeld
Expected Arrivals: Different Approach
We consider the ascending sequence of time instants
Average distance between two consecutive points
with 𝑡0 = 0 and 𝑡 𝑛+1 = 𝑇
𝐸 𝐴 =
𝑡2 − 𝑡1 + 𝑡3 − 𝑡2 + ⋯ + 𝑡 𝑛 − 𝑡 𝑛−1 + 𝑇 + 𝑡1 − 𝑡 𝑛
n + 1
=
𝑡1 − 0 + 𝑡2 − 𝑡1 + 𝑡3 − 𝑡2 + ⋯ + 𝑡 𝑛 − 𝑡 𝑛−1 + 𝑇 − 𝑡 𝑛
n + 1
=
𝑖=1
𝑛+1
𝑡𝑖 − 𝑡𝑖−1 =
𝑡 𝑛+1 − 𝑡0
𝑛 + 1
=
𝑇
𝑛 + 1
=
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16. Tobias Hoßfeld
Expected Arrivals
Expected time between arrivals is 𝐸[𝐴𝑖] = 𝑇/(𝑛 + 1)
Periodic system: rate 𝑛/𝑇
Poisson process: rate 𝜆 = (𝑛 + 1)/𝑇
Poisson process with rate 𝜆∗ = 𝑛/𝑇
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Intervals 𝐴𝑖 are not independent in
the periodic case: 𝑖 𝐴𝑖 = 𝑇
Exponential distribution 𝐸𝑥𝑝(𝜆)
• CDF 𝐴 𝑥 = 1 − 𝑒−𝜆𝑥
• PDF a 𝑥 =
𝑑
𝑑𝑥
𝐴 𝑥 = 𝜆𝑒−𝜆𝑥
• Mean 𝐸 𝐴 = 1/𝜆
17. Tobias Hoßfeld
Distribution of Interarrival Times
Periodic system: rate 𝑛/𝑇
Beta distribution for interarrival times
Idea: 𝑋 is minimum of arrivals 𝑡𝑖
(first order statistic of uniform dist.)
Poisson process with rate 𝜆∗
= 𝑛/𝑇
Exponential distribution for interarrival times
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19. Tobias Hoßfeld
Quantification of Bias due to Poisson Assumption
Periodic system: rate 𝑛/𝑇
Poisson process with rate 𝜆∗ = 𝑛/𝑇
Identical rate and expected interarrival times
Shift of expected interarrival times 𝑆 = 𝑇/2𝑛 < 𝜖
Difference between Coefficient of Variation of IAT should be zero
Number of arrivals in T should be close to n for Poisson process
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20. Tobias Hoßfeld
IoT Load Balancer
Constant processing time of messages
Aggregated periodic traffic: nD/D/1
Poisson process: M/D/1
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Use Case: Load Balancer at IoT Cloud
Waiting times: Poisson Process vs. Aggregated Periodic Traffic
Impact of Network Transmissions
21. Tobias Hoßfeld
M/D/1 and nD/D/1 System
Well known results
Arrival rate 𝜆 =
𝑛
𝑇
, service rate 𝜇, offered load 𝜌 = 𝜆/𝜇
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[10] T. C. Fry et al. Probability and its engineering uses. Van Nostrand New York, 1928.
[13] V. B. Iversen and L. Staalhagen. “Waiting time distribution in M/D/1 queueing systems.” In:
Electronics Letters 35.25 (1999).
[30] J. W. Roberts and J. T. Virtamo. “The superposition of periodic cell arrival streams in an ATM
multiplexer.” In: IEEE Transactions on Communications 39.2 (1991).
M/D/1 nD/D/1
22. Tobias Hoßfeld
M/D/1
Fry‘s equation
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Poisson distribution
𝝆 = 𝝀 ⋅ 𝑺
V. B. Iversen and L. Staalhagen. “Waiting time
distribution in M/D/1 queueing systems.” In:
Electronics Letters 35.25 (1999).
23. Tobias Hoßfeld
Number of Customers in the System
Overdimensioning due to Poisson process assumption!
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24. Tobias Hoßfeld
Some more known results …
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M/D/1
nD/D/1
𝐸[𝑊 𝑀/𝑀/1] =
𝐸[𝑆]⋅𝜌
1−𝜌
= 2 ⋅ 𝐸[𝑊 𝑀/𝐷/1]
Erlang-B formula:
blocking prob. for M/G/n/n
𝐵 𝑛, 𝑎 =
𝑎 𝑛
𝑛!
𝑖=0
𝑛 𝑎 𝑖
𝑖!
25. Tobias Hoßfeld
Bias due to Poisson Assumption
If number of nodes is large enough, small differences between
performance measures
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For higher load, larger bias!
26. Tobias Hoßfeld
Impact of Network Transmission
Constant processing time S=1 at the load balancer
Additional delay when packets arrive at load balancer: 𝐷 + 𝑀
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No relevant influence if
number of nodes is
large enough, n>100
27. Tobias Hoßfeld
Traffic Pattern: Autocorrelation
Autocorrelation and traffic pattern „destroyed“
May be crucial for some characteristics like signaling load
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28. Tobias Hoßfeld
Conclusions
Analytical methods appropriate for investigating scalability
Poisson approximation only valid for large number of nodes …
… but not for all characteristics like autocorrelation
Bias strongly depends on considered characteristic
Future work integrates those results
Adaptive sending frequency: energy vs. quality of information
Scalable systems
e.g. hierarchical
architecture
Heterogeneous
nodes
Impact of security
mechanisms
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29. Tobias Hoßfeld
Current Work: IoT Testbed Setup
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Aggregator Monitoring
Cloud service
Real-time
analytics
time
FakeData
Attack on
cloud
Attack on
aggregator
30. Tobias Hoßfeld
Literature (Suggestions and references therein)
M/D/1 system
T. C. Fry et al. Probability and its engineering uses. Van Nostrand New York, 1928.
V. B. Iversen and L. Staalhagen. “Waiting time distribution in M/D/1 queueing systems.” In:
Electronics Letters 35.25 (1999).
nD/D/1 system
A. Eckberg. “The single server queue with periodic arrival process and deterministic
service times.” In: IEEE Transactions on communications 27.3 (1979).
M. Menth and S. Muehleck. “Packet waiting time for multiplexed periodic on/off streams
in the presence of overbooking.” In: International Journal of Communication Networks
and Distributed Systems 4.2 (2010).
J. Roberts, U. Mocci, and J. Virtamo. “Broadband Network Teletraffic: Final Report of
Action COST 242.” In: (1996).
J. W. Roberts and J. T. Virtamo. “The superposition of periodic cell arrival streams in an
ATM multiplexer.” In: IEEE Transactions on Communications 39.2 (1991).
Modeling of IoT traffic
Tobias Hoßfeld, Florian Metzger, Poul E. Heegaard, Traffic Modeling for Aggregated
Periodic IoT Data, 21st Conference on Innovations in Clouds, Internet and Networks (ICIN
2018), Paris, France
30
31. comnet.informatik.uni-wuerzburg.de
Institute of Computer Science
Chair of Communication Networks
Prof. Dr. Tobias Hossfeld
Tobias Hoßfeld, Florian Metzger, Poul E. Heegaard
tobias.hossfeld@uni-wuerzburg.de
Traffic Modeling for Aggregated Periodic IoT Data
21st Conference on Innovations in Clouds, Internet and
Networks (ICIN 2018), Paris, France
Notes de l'éditeur
Scalability: “means that the application maintains its performance goals/SLAs even when its workload increases (up to a certain workload bound)”
Elasticity in Cloud Computing: What It Is, and What It Is Not Nikolas Roman Herbst, Samuel Kounev, Ralf Reussner
Scalability: “means that the application maintains its performance goals/SLAs even when its workload increases (up to a certain workload bound)”
Elasticity in Cloud Computing: What It Is, and What It Is Not Nikolas Roman Herbst, Samuel Kounev, Ralf Reussner