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
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
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
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