Optimizing Age of Information in Wireless Networks with

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Optimizing Age of Information in Wireless Networks with Throughput Constraints Igor Kadota, Abhishek Sinha

Optimizing Age of Information in Wireless Networks with Throughput Constraints Igor Kadota, Abhishek Sinha and Eytan Modiano IEEE INFOCOM, April 19, 2018 1

Outline • Age of Information and Motivation • Network Model • Scheduling Policies and

Outline • Age of Information and Motivation • Network Model • Scheduling Policies and Performance Guarantees • Stationary Randomized Policy • Max-Weight Policy • Whittle’s Index Policy • Numerical Results 2

Age of Information (Ao. I) Example: Interdelivery Time Delivery of Packets to BS Packet

Age of Information (Ao. I) Example: Interdelivery Time Delivery of Packets to BS Packet Generation at i Single Source i BS Single Destination Time L[1] L[2] Packet Delay How fresh is the information at the destination? 3

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at i Single Source i Interdelivery Time L[1] L[2] Packet Delay Ao. I BS Single Destination L[1] Time 4

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at i Single Source i Interdelivery Time L[1] L[2] Packet Delay Ao. I BS Single Destination L[1] Time 5

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at

Age of Information (Ao. I) Example: Delivery of Packets to BS Packet Generation at i Single Source i Interdelivery Time L[1] L[2] Packet Delay Ao. I BS Single Destination L[1] L[2] Time 6

Age of Information (Ao. I) Ao. I: time elapsed since the most recently delivered

Age of Information (Ao. I) Ao. I: time elapsed since the most recently delivered packet was generated. Interdelivery Time L[1] Relation between Ao. I, delay and interdelivery time? L[2] Packet Delay Ao. I L[1] L[2] Time 7

Ao. I, Delay and Interdelivery time Source • Average Ao. I 0. 01 0.

Ao. I, Delay and Interdelivery time Source • Average Ao. I 0. 01 0. 53 0. 99 1. 01 2. 13 100. 00 1. 89 1. 01 Destination [1] S. Kaul, R. Yates, and M. Gruteser, “Real-time status: How often should one update? ”, 2012. 8

Ao. I, Delay and Interdelivery time Source • 0. 01 0. 53 0. 99

Ao. I, Delay and Interdelivery time Source • 0. 01 0. 53 0. 99 1. 01 2. 13 100. 00 1. 89 1. 01 Average Ao. I 101. 00 3. 48 100. 02 Destination [1] S. Kaul, R. Yates, and M. Gruteser, “Real-time status: How often should one update? ”, 2012. 9

Network - Example Wireless Parking Sensor Wireless Rearview Camera Wireless Tire-Pressure Monitoring System 10

Network - Example Wireless Parking Sensor Wireless Rearview Camera Wireless Tire-Pressure Monitoring System 10

Network - Description Sensors / Nodes 1 … M BS Central Monitor 11

Network - Description Sensors / Nodes 1 … M BS Central Monitor 11

 Sensors / Nodes … 1 M BS 12

Sensors / Nodes … 1 M BS 12

Network - Age of Information Delivery of packets from sensor i to the BS

Network - Age of Information Delivery of packets from sensor i to the BS • Slots 3 2 1 Slots 13

Network - Objective Function • 14

Network - Objective Function • 14

Scheduling Policies • (Age of Information) (Minimum Throughput) (Channel Interference) 16

Scheduling Policies • (Age of Information) (Minimum Throughput) (Channel Interference) 16

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy Renewal Theory 2 -optimal ~ 2 -optimal Max-Weight Policy Lyapunov Optimization 4 -optimal close to optimal Whittle’s Index Policy RMAB Framework 8 -optimal close to optimal Simulation Result 17

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy Renewal Theory 2 -optimal ~ 2 -optimal Max-Weight Policy Lyapunov Optimization 4 -optimal close to optimal Whittle’s Index Policy RMAB Framework 8 -optimal close to optimal Simulation Result 18

Stationary Randomized Policies • 4 3 2 1 19

Stationary Randomized Policies • 4 3 2 1 19

Stationary Randomized Policies • 4 3 2 1 20

Stationary Randomized Policies • 4 3 2 1 20

Stationary Randomized Policies • (Age of Information) (Minimum Throughput) (Probability) 21

Stationary Randomized Policies • (Age of Information) (Minimum Throughput) (Probability) 21

Stationary Randomized Policies • 22

Stationary Randomized Policies • 22

Stationary Randomized Policies • 23

Stationary Randomized Policies • 23

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy Renewal Theory 2 -optimal ~ 2 -optimal Max-Weight Policy Lyapunov Optimization 4 -optimal close to optimal Whittle’s Index Policy RMAB Framework 8 -optimal close to optimal Simulation Result 24

Max-Weight Policy • Minimum Throughput Requirements: • Throughput debt: • Lyapunov Function: , where

Max-Weight Policy • Minimum Throughput Requirements: • Throughput debt: • Lyapunov Function: , where V is a constant 25

Max-Weight Policy • 26

Max-Weight Policy • 26

Max-Weight Policy • 27

Max-Weight Policy • 27

Max-Weight Policy vs Whittle’s Index Policy • 28

Max-Weight Policy vs Whittle’s Index Policy • 28

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy

Scheduling Policies Summary of Results: Scheduling Policy Technique Optimality Ratio Optimal Stationary Randomized Policy Renewal Theory 2 -optimal ~ 2 -optimal Max-Weight Policy Lyapunov Optimization 4 -optimal close to optimal Whittle’s Index Policy RMAB Framework 8 -optimal close to optimal Simulation Result 29

Numerical Results • 30

Numerical Results • 30

 2 x 31

2 x 31

 2 x 32

2 x 32

Final Remarks • In this presentation: • Age of Information and Network Model •

Final Remarks • In this presentation: • Age of Information and Network Model • Three low-complexity scheduling policies • Performance guarantees • Numerical Results: Max-Weight has superior performance 1 … M BS • In the paper: • Derive Universal Lower Bound on Age of Information • Discuss Indexability and Whittle’s Index Policy • Additional simulation results • Recent result not in the paper: Drift-Plus Penalty Policy is 2 -optimal 33

END 34

END 34

Lower Bound 35

Lower Bound 35

Stationary Randomized Policies 37

Stationary Randomized Policies 37

Optimal Stationary Randomized policy • 40

Optimal Stationary Randomized policy • 40

Drift-Plus-Penalty Policy 41

Drift-Plus-Penalty Policy 41

Drift-Plus-Penalty Policy • 42

Drift-Plus-Penalty Policy • 42

Drift-Plus-Penalty Policy • 43

Drift-Plus-Penalty Policy • 43

Whittle’s Index Policy 44

Whittle’s Index Policy 44

Whittle’s Index Policy • [21] P. Whittle, “Restless bandits: Activity allocation in a changing

Whittle’s Index Policy • [21] P. Whittle, “Restless bandits: Activity allocation in a changing world”, 1988. 45

Whittle’s Index Policy • 46

Whittle’s Index Policy • 46

Whittle’s Index Policy 47

Whittle’s Index Policy 47

Whittle’s Index Policy 48

Whittle’s Index Policy 48

Whittle’s Index Policy • 49

Whittle’s Index Policy • 49

Numerical Results 50

Numerical Results 50

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CHANGE FIGURES to flip indexes and delete Whittle w/o constraint 52

CHANGE FIGURES to flip indexes and delete Whittle w/o constraint 52

Index of Topics • Presentation: • • Definition of Ao. I Network Model Summary

Index of Topics • Presentation: • • Definition of Ao. I Network Model Summary of Results Max-Weight Policy Ao. I in M/M/1 Objective Function Randomized Policy Numerical Results • Additional Topics: • Lower Bound • Drift-Plus-Penalty Policy • Additional Numerical Results Details on the Randomized Policy Whittle’s Index Policy 53