WINLAB

1

WINLAB Research Review

Spring 2015

Roy Yates WINLAB Rutgers University

(Collaborators Sanjit Kaul and Marco Gruteser)

Connected Vehicles as a Status

Updating Network

WINLAB

2

Large Networks (Hundreds of cars)

Frequent Updates (1 ndash 10Hz car)

Reliability and Timeliness are required

The Safety Messaging Challenge

Source

WINLAB

2

Large Networks (Hundreds of cars)

Frequent Updates (1 ndash 10Hz car)

Reliability and Timeliness are required

The Safety Messaging Challenge

Source

WINLAB

3

Wi-Fi like radios (80211p CSMA DSRC)

On-road DSRC infrastructure

The DSRC Network

RSU Road Side Unit

OBU

OBU On Board Unit

OBU

OBU

OBU

OBU

RSU

RSU

10MHz Channels 59GHz

WINLAB

4

Periodic Safety Messaging

At 8035o 12040o

Cruising at 70mph

At 8135o 12040o

Accelerating to 80mph

Each car Broadcasts Periodically

Position Speed Turn signal Brake Yaw rate Headinghellip

Time Critical Messaging

State Information

WINLAB

5

Performance Metric

Cars u and v want each others latest state information

WINLAB

6

State Age Metric

WINLAB

7

Average Age

Periodic Updates

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

4

Periodic Safety Messaging

At 8035o 12040o

Cruising at 70mph

At 8135o 12040o

Accelerating to 80mph

Each car Broadcasts Periodically

Position Speed Turn signal Brake Yaw rate Headinghellip

Time Critical Messaging

State Information

WINLAB

5

Performance Metric

Cars u and v want each others latest state information

WINLAB

6

State Age Metric

WINLAB

7

Average Age

Periodic Updates

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

5

Performance Metric

Cars u and v want each others latest state information

WINLAB

6

State Age Metric

WINLAB

7

Average Age

Periodic Updates

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

6

State Age Metric

WINLAB

7

Average Age

Periodic Updates

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

7

Average Age

Periodic Updates

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

8

N Vehicle Networks

Network Goal Minimize System Age(over all wireless network configurations)

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

9

Piggybacking(multi-hop broadcasting)

Header | State OWN | State 1 | State 2 hellip

A packet will contain one header and one or more states

IEEE 16092 =gt Total = 262 bytes PayloadState =53 bytes

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

10

Assume Round Robin Scheduling

bull Eliminates penalties suffered due to

randomized access

ndash Optimal scheduling for safety applications

bull Concentrate on mechanisms that lead to

accumulation of agedelay in multi-hop

networks

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

11

A Graph Connectivity Model

Reliable Communication has sharp threshold behavior

System Employs Strong Coding

Connected nodes decode all packet transmissions of each other

Disconnected nodes are unable to decode any transmissions from each other

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

12

An Example Graph

12

6

3

7 8

4

Example Sequence 1 3 2 4 7 8 6 5

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

13

Connected Nodes

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

4 gets update from 3

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

14

Connected Nodes

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

18

13

3

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

15

Disconnected Nodes

12

6

3

78

4

4 gets state(3) 5 gets state(3) via 4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

16

Disconnected Nodes

Round Robin Delays Scheduling Delays TX (last hop) Delays

12

6

3

78

4

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

17

Scheduling Delays Can be Large(Longer than the round robin cycle)

12

6

3

78

4

543 2 d52=25 slots

7

|1|2|1|2|3|1|2|1|2|1|2|1|2|1|2|3|1|2|L=18 slots

TX Node 1 3 2 4 8 6 5

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

18

Why Multi-Hop

Larger packets but faster links

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

19

Network Optimization Methods

Node SchedulingTransmit power code rate (code rate =gt net topology)Piggybacking By whom For whom

Substantial age reductions are possible

12

6

3

7 8

4

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

20

Improvements in System Age

improvement (Blue) = (67 55 42 30 20)

4-lane 100 carslane 10 MHz Bandwidth

Blue lines are for chosen schedule

Red for randomly chosen permutations

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

21

bull Service Time Ybull Simple model for network access delay

Y

Optimal Update Rates

NetInterface

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

22

Update AgeD(t) Update

Sent

Received

tt1 t2t1rsquo t2

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

23

Update AgeD(t)

bull Low Update Rate

Age gets large between updates

UpdateArrival

Departure

tt1 t2t1rsquo t2

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

24

Update AgeD(t)

bull High Update Rate Queueing Delay

t1 t2 t1rsquo t2t3 t3

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

25

Average Update Age

D(t)

bull Update Ratebull High Queueing delaysbull Low Infrequent updates

High Average Age

Average Age

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

26

Average Age(Queueing at Network Interface)

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

27

Average Age(Queueing at Network Interface)

Just-in-Timelower bound

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

28

Rate Controlled Updates

bull After service time Y update Delay Z=z (Y )

bull Calc of Variations minz(y) D

st update rate = l

D(t) Update Sent

Update Recrsquod

t

Y Z

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

29

Thm Lazy Updating is Optimalβ-Minimum Updating

For update rate λ le 1E [Y] ∆ is minimized by

Zi =z(Yi )=(βminusYi )+

such that β satisfies E[max(βY )] 1113092 = 1λ 1113092

This policy achieves status age ∆lowast = λE1113092[max(β2Y 2 )]1113092+E[Y ]

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

30

Rate Controlled UpdatingExponential Service

30

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

31

Rate Controlled UpdatingExponential Service

31

Just-in-timeupdating

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

32

Rate Controlled UpdatingExponential Service

32

Lazy Updatingbeats just-in-time

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

33

Lazy Updates Whatrsquos the deal

bull Insight

ndash As prior service time -gt 0 next update becomes

worthless

ndash Lazy Updating avoids wasting service resources on

worthless updates

33

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications

WINLAB

34

Summary

bull Vehicular safety messaging

ndash status age performance metric

ndash Scheduling power rate optimization

bull Status Age Optimization

ndash New class of optimization problems

ndash New systems design problems

bull Many applications