Age of Information in Random Access Channels 2020 IEEE ISIT, Los Angeles, California, USA Xingran Chen Konstantinos Gatsis Hamed Hassani Shirin Saeedi Bidokhti University of Pennsylvania
Background & Motivation • Communication networks have witnessed rapid growth in the past few decades cyber-physical systems, the Internet of Things, smart cities, healthcare systems • Reliable and high speed Time-sensitive remote sensing, estimation, control • Transmission policies keeping freshest information — Age of Information markovity of the underlying physical processes [Kadota-Sinha-Biyikoglu-Singh-Modiano-18], [Kadota-Sinha-Modiano-19], [Hsu-Modiano-Duan-19], [Kadota-Modiano-20], [Kaul-Yates-17], [Talak-Karanman-Modiano-18], [Kosta-Pappas-Ephremides-Angelakis-19], [Jiang-Krishnamachari-Zheng-Zhou-Niu-18] [Jiang-Krishnamachari-Zhou-Niu-18], [Yates-Kaul-20] • We design for the first time decentralized age-based transmission policies • Provide analytical results on the age of information
Background & Motivation • Communication networks have witnessed rapid growth in the past few decades cyber-physical systems, the Internet of Things, smart cities, healthcare systems • Reliable and high speed Time-sensitive remote sensing, estimation, control • Transmission policies keeping freshest information — Age of Information markovity of the underlying physical processes [Kadota-Sinha-Biyikoglu-Singh-Modiano-18], [Kadota-Sinha-Modiano-19], [Hsu-Modiano-Duan-19], [Kadota-Modiano-20], [Kaul-Yates-17], [Talak-Karanman-Modiano-18], [Kosta-Pappas-Ephremides-Angelakis-19], [Jiang-Krishnamachari-Zheng-Zhou-Niu-18] [Jiang-Krishnamachari-Zhou-Niu-18], [Yates-Kaul-20] • We design for the first time decentralized age-based transmission policies • Provide analytical results on the age of information
Background & Motivation • Communication networks have witnessed rapid growth in the past few decades cyber-physical systems, the Internet of Things, smart cities, healthcare systems • Reliable and high speed Time-sensitive remote sensing, estimation, control • Transmission policies keeping freshest information — Age of Information markovity of the underlying physical processes [Kadota-Sinha-Biyikoglu-Singh-Modiano-18], [Kadota-Sinha-Modiano-19], [Hsu-Modiano-Duan-19], [Kadota-Modiano-20], [Kaul-Yates-17], [Talak-Karanman-Modiano-18], [Kosta-Pappas-Ephremides-Angelakis-19], [Jiang-Krishnamachari-Zheng-Zhou-Niu-18] [Jiang-Krishnamachari-Zhou-Niu-18], [Yates-Kaul-20] • We design for the first time decentralized age-based transmission policies • Provide analytical results on the age of information
Background & Motivation • Communication networks have witnessed rapid growth in the past few decades cyber-physical systems, the Internet of Things, smart cities, healthcare systems • Reliable and high speed Time-sensitive remote sensing, estimation, control • Transmission policies keeping freshest information — Age of Information markovity of the underlying physical processes [Kadota-Sinha-Biyikoglu-Singh-Modiano-18], [Kadota-Sinha-Modiano-19], [Hsu-Modiano-Duan-19], [Kadota-Modiano-20], [Kaul-Yates-17], [Talak-Karanman-Modiano-18], [Kosta-Pappas-Ephremides-Angelakis-19], [Jiang-Krishnamachari-Zheng-Zhou-Niu-18] [Jiang-Krishnamachari-Zhou-Niu-18], [Yates-Kaul-20] • We design for the first time decentralized age-based transmission policies • Provide analytical results on the age of information
Background & Motivation • Communication networks have witnessed rapid growth in the past few decades cyber-physical systems, the Internet of Things, smart cities, healthcare systems • Reliable and high speed Time-sensitive remote sensing, estimation, control • Transmission policies keeping freshest information — Age of Information markovity of the underlying physical processes [Kadota-Sinha-Biyikoglu-Singh-Modiano-18], [Kadota-Sinha-Modiano-19], [Hsu-Modiano-Duan-19], [Kadota-Modiano-20], [Kaul-Yates-17], [Talak-Karanman-Modiano-18], [Kosta-Pappas-Ephremides-Angelakis-19], [Jiang-Krishnamachari-Zheng-Zhou-Niu-18] [Jiang-Krishnamachari-Zhou-Niu-18], [Yates-Kaul-20] • We design for the first time decentralized age-based transmission policies • Provide analytical results on the age of information
Age of Information (AoI) • A new metric to quantify the freshness of information (2011) [Kaul-Yates-Gruteser 11] • : timestamp of the most recently received update; . u ( t ) h ( t ) = t − u ( t ) • : the receiving time of k th status update t ′ k • status update k th : the generation time of t k T T ∫ 1 • Time average age: lim h ( t ) T →∞ 0
Age of Information (AoI) • A new metric to quantify the freshness of information (2011) [Kaul-Yates-Gruteser 11] • : timestamp of the most recently received update; . u ( t ) h ( t ) = t − u ( t ) • : the receiving time of k th status update t ′ k • status update k th : the generation time of t k T T ∫ 1 • Time average age: lim h ( t ) T →∞ 0
Age of Information (AoI) • A new metric to quantify the freshness of information (2011) [Kaul-Yates-Gruteser 11] • : timestamp of the most recently received update; . u ( t ) h ( t ) = t − u ( t ) • : the receiving time of k th status update t ′ k • status update k th : the generation time of t k T T ∫ 1 • Time average age: lim h ( t ) T →∞ 0
Age of Information (AoI) • A new metric to quantify the freshness of information (2011) [Kaul-Yates-Gruteser 11] • : timestamp of the most recently received update; . u ( t ) h ( t ) = t − u ( t ) • : the receiving time of k th status update t ′ k • status update k th : the generation time of t k T T ∫ 1 • Time average age: lim h ( t ) T →∞ 0
Age of Information (AoI) • A new metric to quantify the freshness of information (2011) [Kaul-Yates-Gruteser 11] • : timestamp of the most recently received update; . u ( t ) h ( t ) = t − u ( t ) • : the receiving time of k th status update t ′ k • status update k th : the generation time of t k T T ∫ 1 • Time average age: lim h ( t ) T →∞ 0
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
System Model sensor i • statistically identical source nodes M arrival rate θ • Slotted time • Stochastic arrival/generation process θ • Collision channel, collision feedback • One unit transmission delay • Find transmission policy that minimizes Normalized Expected Weighted Sum π M K 1 ∑ ∑ AoI (NEWSAoI) h π lim i ( k ) KM 2 K →∞ i =1 k =1
Evolution of Age w i ( k + 1) = { no new packet arrives w i ( k ) + 1 Source AoI a new packet arrives 0 h i ( k + 1) = { a packet is delivered w i ( k ) + 1 Destination AoI no packet is delivered h i ( k ) + 1
Lower Bound Theorem: For any transmission policy, NEWSAoI is lowered bounded by NEWSAoI ≥ 1 1) small arrival rates M θ 1 + 1 2) NEWSAoI ≥ large arrival rates 2 C RA 2 M where denote the sum-capacity of the underlying random access channel C RA • RA with feedback C RA ≤ 0.568 ( M → ∞ ) [Tasybakov-Likhanov] Probl. Peredachi Inf , vol. 23 • RA with CSMA C RA ≤ 1 C RA ≤ 1 • RA without feedback ( M → ∞ ) e
Lower Bound Theorem: For any transmission policy, NEWSAoI is lowered bounded by NEWSAoI ≥ 1 1) small arrival rates M θ 1 + 1 2) NEWSAoI ≥ large arrival rates 2 C RA 2 M where denote the sum-capacity of the underlying random access channel C RA • RA with feedback C RA ≤ 0.568 ( M → ∞ ) [Tasybakov-Likhanov] Probl. Peredachi Inf , vol. 23 • RA with CSMA C RA ≤ 1 C RA ≤ 1 • RA without feedback ( M → ∞ ) e
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