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
comnet.informatik.uni-wuerzburg.de
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.
Tobias Hoßfeld
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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 𝐸𝐸 𝑋𝑋 = 𝜆𝜆𝜆𝜆[𝑊𝑊]
Tobias Hoßfeld
Measurement, Simulation, Analysis
waiting time
Linear relationship?
106 number of nodes Tobias Hoßfeld
Measurement, Simulation, Analysis
waiting time
Is there an upper bound?
106 number of nodes Tobias Hoßfeld
waiting time
Measurement, Simulation, Analysis
106 number of nodes Tobias Hoßfeld
Agenda
Superposition of Periodic IoT Traffic Palm-Khintchine Theorem: Modeling as Poisson Process Evaluation of Bias: Poisson Process vs. Aggregated Periodic Traffic
Use Case: Load Balancer at IoT Cloud Waiting times: Poisson Process vs. Aggregated Periodic Traffic Impact of Network Transmissions Tobias Hoßfeld
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Periodic Traffic Patterns
Very different number of nodes 3GPP. RAN Improvements for Machine-type Communications. TR37.868. Oct. rates 2011. and
Some results from literature [2] [7]
Draft new Report ITU-R M.[IMT-2020.TECH PERF REQ] – Minimum requirements related to technical performance for IMT2020 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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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.”
for large number n …
… Poisson process !
[1] 3GPP. GERAN improvements for MachineType Communications (MTC). TR 43.868. Feb. 2014. Tobias Hoßfeld
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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.”
for large number n …
… Poisson process !
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Superposition of Periodic Traffic
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?
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Scenario: Async. Homogeneous Periodic Traffic
System consists of 𝑛𝑛 sensor nodes Asynchronous sources: Nodes start randomly at 𝑡𝑡𝑖𝑖 Homogeneous: Each node sends periodically with the same sampling period 𝑇𝑇 𝐴𝐴𝑖𝑖 is the time between data from node 𝑖𝑖 and node 𝑖𝑖 + 1
Sampling period 𝑻𝑻 = ∑𝒏𝒏𝒊𝒊=𝟏𝟏 𝑨𝑨𝒊𝒊
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Expected Arrivals
Expected time between arrivals is 𝐸𝐸[𝐴𝐴𝑖𝑖 ] = 𝑇𝑇/(𝑛𝑛 + 1) Idea for proof: distance between two random points 𝑥𝑥1 , 𝑥𝑥2 𝑇𝑇
𝑇𝑇
𝐸𝐸 𝐴𝐴𝑖𝑖 = ∫0 ∫0 𝑡𝑡1 − 𝑡𝑡2 ⋅ 𝑢𝑢 𝑡𝑡1 ⋅ 𝑢𝑢 𝑡𝑡2 𝑑𝑑𝑡𝑡1 𝑑𝑑𝑡𝑡2
=
1 𝑇𝑇 ∫ 𝑇𝑇 2 𝑡𝑡1 =0
𝑡𝑡
Uniform distribution U(0,T) 𝑥𝑥 • CDF 𝑈𝑈 𝑥𝑥 = • PDF 𝑢𝑢 𝑥𝑥 = 𝑇𝑇
(∫𝑡𝑡 1=0(𝑡𝑡1 − 𝑡𝑡2 ) 𝑑𝑑𝑡𝑡2 + ∫𝑡𝑡 2
2 =𝑡𝑡1
Tobias Hoßfeld
𝑇𝑇 𝑑𝑑 𝑑𝑑𝑑𝑑
𝑈𝑈 𝑥𝑥 =
1 𝑇𝑇
𝑡𝑡2 − 𝑡𝑡1 𝑑𝑑𝑡𝑡2 ) 𝑑𝑑𝑡𝑡1 = T/3
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Expected Arrivals: Different Approach
We consider the ascending sequence of time instants Average distance between two consecutive points with 𝑡𝑡0 = 0 and 𝑡𝑡𝑛𝑛+1 = 𝑇𝑇
𝑡𝑡2 − 𝑡𝑡1 + 𝑡𝑡3 − 𝑡𝑡2 + ⋯ + 𝑡𝑡𝑛𝑛 − 𝑡𝑡𝑛𝑛−1 + 𝑇𝑇 + 𝑡𝑡1 − 𝑡𝑡𝑛𝑛 𝐸𝐸 𝐴𝐴 = n+1 𝑡𝑡1 − 0 + 𝑡𝑡2 − 𝑡𝑡1 + 𝑡𝑡3 − 𝑡𝑡2 + ⋯ + 𝑡𝑡𝑛𝑛 − 𝑡𝑡𝑛𝑛−1 + 𝑇𝑇 − 𝑡𝑡𝑛𝑛 = n+1 𝑛𝑛+1 𝑡𝑡𝑛𝑛+1 − 𝑡𝑡0 𝑇𝑇 = = � 𝑡𝑡𝑖𝑖 − 𝑡𝑡𝑖𝑖−1 = 𝑛𝑛 + 1 𝑛𝑛 + 1 𝑖𝑖=1
=
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Expected Arrivals
Expected time between arrivals is 𝐸𝐸[𝐴𝐴𝑖𝑖 ] = 𝑇𝑇/(𝑛𝑛 + 1)
Intervals 𝐴𝐴𝑖𝑖 are not independent in the periodic case: ∑𝑖𝑖 𝐴𝐴𝑖𝑖 = 𝑇𝑇
Periodic system: rate 𝑛𝑛/𝑇𝑇
Poisson process: rate 𝜆𝜆 = (𝑛𝑛 + 1)/𝑇𝑇 Poisson process with rate 𝜆𝜆∗ = 𝑛𝑛/𝑇𝑇
Exponential distribution 𝐸𝐸𝐸𝐸𝐸𝐸(𝜆𝜆) • CDF 𝐴𝐴 𝑥𝑥 = 1 − 𝑒𝑒 −𝜆𝜆𝜆𝜆 𝑑𝑑 • PDF a 𝑥𝑥 = 𝐴𝐴 𝑥𝑥 = 𝜆𝜆𝑒𝑒 −𝜆𝜆𝜆𝜆 𝑑𝑑𝑑𝑑 • Mean 𝐸𝐸 𝐴𝐴 = 1/𝜆𝜆
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Distribution of Interarrival Times
Periodic system: rate 𝑛𝑛/𝑇𝑇 Beta distribution for interarrival times Idea: 𝑋𝑋 is minimum of arrivals 𝑡𝑡𝑖𝑖 (first order statistic of uniform dist.)
Poisson process with rate 𝜆𝜆∗ = 𝑛𝑛/𝑇𝑇 Exponential distribution for interarrival times
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Some Performance Metrics
Compare Poisson process with aggregated periodic process (APP)
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Quantification of Bias due to Poisson Assumption
Periodic system: rate 𝑛𝑛/𝑇𝑇 Poisson process with rate 𝜆𝜆∗ = 𝑛𝑛/𝑇𝑇
Identical rate and expected interarrival times Shift of expected interarrival times 𝑆𝑆̅ = 𝑇𝑇/2𝑛𝑛 < 𝜖𝜖 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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IoT Load Balancer
Constant processing time of messages Aggregated periodic traffic: nD/D/1 Poisson process: M/D/1
Use Case: Load Balancer at IoT Cloud Waiting times: Poisson Process vs. Aggregated Periodic Traffic Impact of Network Transmissions
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M/D/1 and nD/D/1 System
Well known results
Arrival rate 𝜆𝜆 = , service rate 𝜇𝜇, offered load 𝜌𝜌 = 𝜆𝜆/𝜇𝜇
M/D/1
𝑛𝑛 𝑇𝑇
nD/D/1
[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). Tobias Hoßfeld
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M/D/1
Fry‘s equation V. B. Iversen and L. Staalhagen. “Waiting time distribution in M/D/1 queueing systems.” In: Electronics Letters 35.25 (1999).
Poisson distribution 𝝆𝝆 = 𝝀𝝀 ⋅ 𝑺𝑺
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Number of Customers in the System
Overdimensioning due to Poisson process assumption!
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Some more known results …
M/D/1
𝐸𝐸[𝑊𝑊𝑀𝑀/𝑀𝑀/1 ] =
𝐸𝐸[𝑆𝑆]⋅𝜌𝜌 1−𝜌𝜌
= 2 ⋅ 𝐸𝐸[𝑊𝑊𝑀𝑀/𝐷𝐷/1 ]
nD/D/1 Erlang-B formula: blocking prob. for M/G/n/n 𝑎𝑎𝑛𝑛 𝐵𝐵 𝑛𝑛, 𝑎𝑎 = 𝑛𝑛! 𝑖𝑖 𝑎𝑎 ∑𝑛𝑛𝑖𝑖=0 𝑖𝑖! Tobias Hoßfeld
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Bias due to Poisson Assumption
If number of nodes is large enough, small differences between performance measures
For higher load, larger bias!
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Impact of Network Transmission
Constant processing time S=1 at the load balancer Additional delay when packets arrive at load balancer: 𝐷𝐷 + 𝑀𝑀 No relevant influence if number of nodes is large enough, n>100
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Traffic Pattern: Autocorrelation
Autocorrelation and traffic pattern „destroyed“ May be crucial for some characteristics like signaling load
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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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Current Work: IoT Testbed Setup
Fake Data
Attack on aggregator
Attack on cloud
time Aggregator
Real-time analytics
Monitoring Cloud service
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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
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Institute of Computer Science Chair of Communication Networks Prof. Dr. Tobias Hossfeld
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
comnet.informatik.uni-wuerzburg.de
[email protected]
