Status Updating Systems and Networks

Transcription

1 1 Status Updating Systems and Networks Roy Yates ECE/, Rutgers Research Review December 12, 2014 joint work with Sanjit Kaul, Marco Gruteser & Jing Zhong IIIT-Delhi Rutgers

2 2 V2V Safety Messaging Source Large Networks (Hundreds of cars) Frequent Updates (1 10Hz/ car) Reliability and Timeliness are required

3 3 V2V Safety Messaging Source DSRC standard MAC protocol Message Scheduling, Forwarding/Piggybacking Power/rate adaptation, coverage Performance Metrics?

4 4 The DSRC Network RSU: Road Side Unit OBU RSU OBU OBU: On Board Unit. OBU OBU OBU On-road DSRC infrastructure RSU Wi-Fi like (802.11p CSMA) 5.9GHz

5 5 Network Car u sends updates to car v Updates pass through network/service system Car v wants latest state information. Metric: Age of the latest update

6 6 Simple Analytic Models Service system = Queue Sender u offers updates without knowledge of the queue state

7 7 More Status Updates How often is too often?

8 8 Google Reader Idiosyncratic Service Discipline/Model

9 9 Performance Metric Status Update Age Latest update i sent at time t i Reaches subscriber at time t i At time t i : Status Age =t i t i At time t > t i : Status Age =t t i Age grows in absence of new updates

10 10 Update Age Δ(t) Update Arrival (sent) Departure (rec d) t 1 t 1 t 2 t 2 ' t

11 11 Geometry of Triangles Δ(t) Update Arrival Departure t 1 t 1 t

12 12 Geometry of Triangles Δ(t) Update Arrival Δ Departure Δ t 1 t 1 t

13 13 Update Age Δ(t) Update Arrival Departure t 1 t 1 t 2 t 2 ' Low Update Rate Age gets large between updates t

14 14 Update Age Δ(t) t 1 t 2 t 3 t 1 t 2 ' t 3 ' High Update Rate Queueing Delay

15 15 Average Update Age Δ(t) Average Age = 1 Z 0 (t) dt Update Rate: High Queueing delays Low Infrequent updates }High Average Age

16 16 FCFS Average Update Age Δ(t) ½[(X+T) 2 T 2 ]=½X 2 +XT X= Interarrival Time T= System Time X T = lim!1 = 1 2 E X 2 +E[XT]

17 17 FCFS Average Update Age Δ(t) = 1 2 E X 2 +E[XT] X= Interarrival Time T= System Time X T Weak ergodicity requirements is tricky! X and T negatively correlated

18 18 M/M/1 FCFS Average Age Arrival Rate λ, Service Rate µ Load ρ = λ/µ apple = 1 µ 1

19 19 M/M/1 FCFS Average Age Load ρ=λ/μ ρ * = 0.53

20 20 D/M/1 FCFS Service Rate µ, Load ρ=λ/µ = 1 apple 1 µ e 1/ = W Optimal Load ρ * = 0.515

21 21 M/M/1 FCFS Average Age Load ρ=λ/μ

22 22 Update Age: Lower Bound Sender sees queue state Schedules just-in-time updates " = 1 E S 2 E[S] 2 +(E[S]) 2 # Service Time S

23 23 Age Lower Bounds (Just-in-time updates) Exponential Service E[S] = 1/µ =2 1 µ Deterministic Service S = 1/µ 1 =1.5 µ

24 24 Average Age

25 25 Average Age

26 26 LCFS w/o pre-emption Pre-emption of waiting packet (1 packet waiting room) Source λ μ Monitor

27 27 Competing Updates How often is too often?

28 28 Multiple Sources

29 29 Multiple Sources Models for Source 2: Competing status updater Other traffic

30 30 Δ(t) Average Update Age " E X 2 = +E[XT] 2 # X = Interarrival Time T = System Time X T X,T = interarrival and system time for source 1 T depends on interfering traffic

31 31 Multiple Sources

32 32 Multiple Sources FCFS Status Age Region Δ 2 Δ 1

33 33 Multiple Sources FCFS Trunking Efficiency Δ 2 Optimal Partitioning Optimal Sharing Δ 1

34 34 FCFS Competing Updaters Δ 2 Nash Equilibrium Δ 1

35 35 Source 1 μ Monitor Source 2 Queueing delays increases status age Reduce/Eliminate the queues?

36 LCFS Pre-emption & Discarding (No Queueing) 36 Source 1 λ 1 μ Monitor Source 2 λ 2

37 37 V2V Safety Messaging Network Multiple Sources Fast local server interface Slow Server

38 38 Multiple Sources FCFS/LCFS Age Δ 2 λ=2 λ=1 λ=0.6 FCFS LCFS Δ 1

39 39 Timely Compression A Status Updating Problem Encoder FIFO buffer Rate R bit pipe Decoder a 1 a 2 a a 1 a 2 a 3 Encoder input symbol = status update Block coding è Bursty bit arrivals at FIFO buffer Bit pipe queueing delay Decoding delay

40 40 Timely Compression A Status Updating Problem Encoder FIFO buffer Rate R bit pipe Decoder a 1 a 2 a 3 a 4 a 5 a 6 a a 1 a 2 a 3 a 4 t

41 41 Time Compression Huffman Coding Example Status Age Low rate pipe: Use large blocks High rate pipe: use small blocks Channel Rate R

42 42 Summary New status age performance metric Status Age Minimization Principles Match the load to the network/system Redesign the system Give priority to timely updates Discard stale updates Many applications