Traffic Modeling for Aggregated Periodic IoT Data

comnet.informatik.uni-wuerzburg.de
Institute of Computer Science
Chair of Communication Networks
Prof. Dr. Tobias Hossfeld
Traffic Modeling for
Aggregated Periodic IoT Data
Tobias Hoßfeld, Florian Metzger, Poul E. Heegaard

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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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?

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]

Tobias Hoßfeld
Measurement, Simulation, Analysis
number of nodes
106
waitingtime
Linear
relationship?

Tobias Hoßfeld
number of nodes
waitingtime
106
Is there an
upper bound?

Tobias Hoßfeld
number of nodes
waitingtime
106

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

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

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.

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
…

Tobias Hoßfeld
Superposition of Periodic Traffic
12
for large
number n
…
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?

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

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

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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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

Tobias Hoßfeld
Distribution of Interarrival Times
 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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Tobias Hoßfeld
Some Performance Metrics
 Compare Poisson
process with
aggregated periodic
process (APP)
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Tobias Hoßfeld
Quantification of Bias due to Poisson Assumption
 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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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

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

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:

Tobias Hoßfeld
Number of Customers in the System
 Overdimensioning due to Poisson process assumption!
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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!

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!

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

Tobias Hoßfeld
Traffic Pattern: Autocorrelation
 Autocorrelation and traffic pattern „destroyed“
 May be crucial for some characteristics like signaling load
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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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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

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:
 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
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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

Traffic Modeling for Aggregated Periodic IoT Data

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