Formal Modeling and Analysis of Stream Processing Systems

Transcription

1 Formal Modeling and Analysis of Stream Processing Systems Linh T.X. Phan March 2009 Computer and Information Science University of Pennsylvania 1

2 High performance Highly optimized requirements systems 2

3 Overview Stream Processing Methods discussed here are applicable to general real-time embedded systems 3

4 Inside the box 4

5 A complete system Target Platform 5

6 1. Streaming application tasks 6

7 2. Heterogeneous computing and memory resources Image Coprocessor DSP RISC FPGA CAN Interface 7

8 3. Heterogeneous RTOS scheduling and synchronization protocols TDMA FCFS EDF Proportional Share Dynamic Fixed Priority Static 8

9 4. Heterogeneous communication resources Topology (ring, mesh, star) Switching strategies (packet, circuit) Routing strategies (static, dynamic, reconfigurable) Arbitration policies (dynamic, TDM, CDMA) 9

10 The Design Problem Application Target Platform Build a system from subsystems that satisfy the application s Image Coprocessor DSP requirements and resource constraints TDMA FCFS RISC FPGA EDF Proportional Share CAN Interface Dynamic Fixed Priority Static 10

11 The Design Process 11

12 The Performance Analysis Problem Compute/verify the performance properties of the system model 12

13 e.g. Architecture of a Picture-in-Picture App. Maximum fill-level (backlog) of the buffers? Maximum end-to-end delay of the stream? Characteristics of the output stream? Characteristics of the remaining resource?

14 Key Challenges: Complex Event Streams Infinite sequence of items (events) Highly bursty Events of multiple types interleaving Varied memory and execution demands Historically dependent or dynamically controlled 14

15 Key Challenges: Complex Tasks & Architectures Complex processing semantics fill-level of the buffers execution of an internal automaton synchronization between different streams Heterogeneous computing and communication resources Various scheduling policies EDF, Fixed-Priority, TDMA, etc. complex state-dependent scheduling schemes 15

16 Complex Trade-offs Computational Demand Throughput Memory Size 16

17 Two Categories of Performance Analysis Analysis bound An input trace Simulation An output trace e.g. A set of input traces Hybrid of Simulation & Formal Analysis An abstract input model Formal Analysis Analysis bound 17

18 Simulation vs Formal Analysis analysis bound Our focus! actual worst case Real System Formal Analysis Simulation actual best case running time 18

19 Formal Analysis Overview 19

20 Formal Analysis Overview How event streams arrive and its characteristics 20

21 Formal Analysis Overview How much and when the resource are available 21

22 Formal Analysis Overview How events are scheduled and processed 22

23 Formal Models and Analysis Methods 1 Standard Event Models (SEM) periodic, periodic with jitter/burst and variations Simple, easy to analyze Unrealistic assumptions Too restrictive Overly pessimistic results 23

24 2 Real-Time Calculus (RTC) streams & resources: count-based abstraction analysis: (min,+) algebra Capture burstiness of streams & resource availability Highly efficient Cannot model state-dependencies 24

25 3 Timed Automata model streams at very detailed level capture exact arrival time of each event Models state-dependencies Highly accurate Too detailed large models Large systems inefficient 25

26 4 Event Count Automata (ECA) syntax: similar to Timed Automata semantics: count-based abstraction capture #events in an interval of time Models state-dependencies Highly accurate Large systems inefficient 26

27 5 Hybrid Models and Methods RTC + SEM RTC + ECA Multi-Mode RTC Good accuracy-efficiency trade-off 27

28 The rest of the talk Formal Analysis using Real-Time Calculus (RTC) 28

29 RTC Background Originated from Network Calculus in computer networks domain extended for real-time embedded systems Worst-case deterministic formal analysis variant of classical queuing theory Abstract models: count-based abstraction Analysis: min-plus / max-plus algebra 29

30 Recall 30

31 RTC Performance Model 31

32 # events An Arrival Pattern R(t) = number of events that arrive in [0,t) 10 R(t) 5 0 t #events that arrive in [t, t+δ) is: R(t+Δ) - R(t) 32

33 sliding window size Count-based Abstraction Δ Lower bound Upper bound A set of arrival patterns Δ=1 t concrete time instant 33

34 Load Model: Arrival Functions α = (α l,α u ) Δ α l (Δ) α u (Δ) A set of arrival patterns Δ=1 t An arrival pattern R(t) satisfies α iff α l (Δ) R(t+Δ) - R(t) α u (Δ) 34

35 A Service Pattern # events 10 C(t) = number of events that can be processed in [0,t) C(t) 5 0 t #events that can be processed in [t, t+δ) is: C(t+Δ) - C(t) 35

36 Service Model: Service Functions β = (β l, β u ) Δ β l (Δ) β u (Δ) A set of service patterns Δ=2 t A service pattern C(t) satisfies β iff β l (Δ) C(t+Δ) - C(t) β u (Δ) 36

37 Units of Arrival and Service Functions [R(t), α(δ)] and [C(t), β(δ)] can also be specified in terms of the number of resource units processor cycles, transmiting bit, etc. Should always convert to the same unit before performing analysis 37