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A family of resource-bound process algebras for modeling and analysis of embedded systems

A family of resource-bound process algebras for modeling and analysis of embedded systems. Insup Lee 1 , Oleg Sokolsky 1 , Anna Philippou 2 . 1 SDRL (Systems Design Research Lab) RTG (Real-Time Systems Group) Department of Computer and Information Science University of Pennsylvania

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A family of resource-bound process algebras for modeling and analysis of embedded systems

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  1. A family of resource-bound process algebras for modeling and analysis of embedded systems Insup Lee1, Oleg Sokolsky1,Anna Philippou2 • 1SDRL (Systems Design Research Lab) • RTG (Real-Time Systems Group) • Department of Computer and Information Science • University of Pennsylvania • Philadelphia, PA 2Department of Computer Science University of Cyprus Nicosia, CY ETAPS 2002

  2. Outline • Embedded systems • Resource-bound computation • Resource-bound process algebras • ACSR (Algebra of communicating shared resources) • PACSR (Probabilistic ACSR) • P2ACSR (Probabilistic ACSR with power consumption) • ACSR-VP (ACSR with Value-Passing) • Conclusions ETAPS 2002

  3. Embedded Systems • Difficulties • Increasing complexity • Decentralized • Safety critical • End-to-end timing constraints • Resource constrained • Non-functional: power, size, etc. • Development of reliable and robust embedded software ETAPS 2002

  4. Properties of embedded systems • Adherence to safety-critical properties • Meeting timing constraints • Satisfaction of resource constraints • Confinement of resource accesses • Supporting fault tolerance • Domain specific requirements • Mobility • Software configuration ETAPS 2002

  5. Real-time Behaviors • Correctness and reliability of real-time systems depends on • Functional correctness • Temporal correctness • Factors that affect temporal behavior are • Synchronization and communication • Resource limitations and availability/failures • Scheduling algorithms • End-to-end temporal constraints • An integrated framework to bridge the gap between concurrency theory and real-time scheduling ETAPS 2002

  6. Scheduling Problems • Priority Assignment Problem • Schedulability Analysis Problem • Soft timing/performance analysis (Probabilistic Performance Analysis) • End-to-end Design Problem • Parametric Analysis • End-to-end constraints, intermediate timing constraints • Execution Synchronization Problem • Start-time Assignment Problem with Inter-job Temporal Constraints • Fault tolerance: dealing with failures, overloads ETAPS 2002

  7. Scheduling Factors • Static priority vs dynamic priority • Cyclic executive, RM (Rate Monotonic), EDF (Earliest Deadline First) • Priority inversion problem • Independent tasks vs. dependent tasks • Single processor vs. multiple processors • Communication delays ETAPS 2002

  8. Example: Simple Scheduling Problem CPU1 CPU2 CPU3 • ( period, [ e-, e+ ] ), where e- and e+ are the lower and upper bound of execution time, respectively. • Goal is to find the priority of each job so that jobs are schedulable • Considering only worst case leads to scheduling anomaly J2,2 J1,1 J1,2 (12, [1,2]) (4, [1,2]) (4, [1,2]) J3,1 J2,1 (4, [2,3]) (12, [1,3]) ETAPS 2002

  9. J1,1 J2,1 J1,1 J2,1 J1,1 CPU2 4 8 12 J3,1 J3,1 J2,2 J3,1 CPU1 4 8 12 Example (2) CPU2 CPU3 CPU1 J2,2 J1,1 J1,2 (12, [1,2]) (4, [1,2]) J3,1 J2,1 (4, [1,2]) (4, [2,3]) (12, [1,3]) LetJ1,1 J2,1andJ2,2  J3,1 Consider worst case execution time for all jobs, i.e., Execution time E1,1= 2,E2,1= 3, E2,2 = 2,E3,1 = 3 ETAPS 2002

  10. CPU1 CPU2 CPU3 J2,2 J1,1 J1,2 (12, [1,2]) (4, [1,2]) J3,1 J2,1 (4, [1,2]) (4, [2,3]) (12, [1,3]) J1,1 J2,1 J1,1 J1,1 CPU2 4 8 12 J3,1 missed its deadline J3,1 J2,2 CPU1 4 8 12 Example (3) With same priorities, J1,1 J2,1andJ2,2  J3,1 Let execution time E1,1 = 1,E2,1 = 1,E2,2 = 2,E3,1 = 3 So with the priority assignment of J1,1 J2,1andJ2,2  J3,1, jobs cannot be scheduled and scheduling problems are in general NP-hard ETAPS 2002

  11. End-to-end Design Problem • Given a task set with end-to-end constraints on inputs and outputs • Freshness from input X to output Y (F(Y|X)) constraints: bound time from input X to output Y • Correlation between input X1 and X2 (C(Y|X1,X2)) constraints: max time-skew between inputs to output • Separation between output Y (u(Y) and l(Y)) constraints: separation between consecutive values on a single output Y • Derive scheduling for every task • Periods, offsets, deadlines • priorities • Meet the end-to-end requirements • Subject to • Resource limitations, e.g., memory, power, weight, bandwidth ETAPS 2002

  12.  25  14  12  10 [ 5,7 ] [ 3,4 ] Job1 Job2 s1 s1+e1 s2 s2+e2 Example: Start-time Problem Start-time Assignment Problem with Inter-job Temporal Constraints Goal is to statically determine the range of start times for each job so that jobs are schedulable and all inter-job temporal constraints are satisfied. ETAPS 2002

  13. Example: power-aware RT scheduling • Dynamic Voltage Scaling allows tradeoffs between performance and power consumption • Problem is how to minimize power consumption while meeting timing constraints. • Example: three tasks with probabilistic execution time distribution ETAPS 2002

  14. Our approach and objectives • Design formalisms for real-time and embedded systems • Resource-bound real-time process algebras • Executable specifications • Logic for specifying properties • Design analysis techniques • Automated verification techniques • Parameterized end-to-end schedulability analysis • Toolset implementation ETAPS 2002

  15. Resource-bound computation • Computational systems are always constrained in their behaviors • Resources capture physical constraints • Resources should be supported as a first-class notion in modeling and analysis • Resource-bound computation is a general framework of wide applicability ETAPS 2002

  16. Resources • Resources capture constraints on executions • Resources can be • Serially reusable: • processors, memory, communication channels • Consumable • power • Resource capacities • Single-capacity resources • Multiple-capacity resources • Time-sliced, etc. ETAPS 2002

  17. Process Algebras • Process algebras are abstract and compositional methodologies for concurrent-system specification and analysis. • “Design methodology which systematically allows to build complex systems from smaller ones” [Milner] ETAPS 2002

  18. Process Algebras • A process algebra consists of • a set of operators and syntactic rules for constructing processes • a semantic mapping which assigns meaning or interpretation to every process • a notion of equivalence or partial order between processes • a set of algebraic laws that allow syntactic manipulation of processes. • Ancestors • CCS, CSP, ACP,… • focus on communication and concurrency ETAPS 2002

  19. Advantages of Process Algebra • A large system can be broken into simpler subsystems and then proved correct in a modular fashion. • A hiding or restriction operator allows one to abstract away unnecessary details. • Equality for the process algebra is also a congruence relation; and thus, allows the substitution of one component with another equal component in large systems. ETAPS 2002

  20. ACSR • ACSR (Algebra of Communicating Shared Resource) • A real-time process algebra which features discrete time, resources, and priorities • Timeouts, interrupts, and exception handling • Two types of actions: • Instantaneous events • Timed actions ETAPS 2002

  21. Events • Events represent non-time consuming activities • events are instantaneous: crash • point-to-point synchronization ETAPS 2002

  22. Events • Events • have priorities: • have input and output capabilities or ETAPS 2002

  23. Actions • Actions represent activities that • take time • require access to resources • each resource usage has priority of access • each resource can be used at most once • resources of action A: • idling action: • Examples: {(cpu,2}}, {(cpu1,3),(cpu2,4)}, {(semaphore,5)} ETAPS 2002

  24. Syntax for ACSR processes • Process terms • Process names ETAPS 2002

  25. Constant and Nil C is a constant that represents the process algebra expression P P = NIL P does nothing ETAPS 2002

  26. Prefix Operators P performs timed action A and then behaves as Q P = A:Q P performs event (a,n) and then behaves as Q P = (a,n).Q EXAMPLE ETAPS 2002

  27. Choice P can choose nondeterministically to behave like Q or R P = Q+R EXAMPLE ETAPS 2002

  28. Parallel Composition P is composed by Q and R that may synchronize on events and must synchronize on timed actions P = Q || R EXAMPLE ETAPS 2002

  29. Scope Q may execute for at most t time units. If message a is produced, control is delegated to R, else control is delegated to S. At any time T may interrupt. EXAMPLE ETAPS 2002

  30. P behaves just as Q but resources in I are no longer visible to the environment Hiding/Restriction P = [Q]I P behaves just as Q but labels in F are no longer visible to the environment P = Q\F EXAMPLE ETAPS 2002

  31. ACSR semantics • Gives an unambiguous meaning to language expressions. • Semantics is operational, given by a set of semantic rules. • Example of a labeled transition system: Labeled transition system Semantic rules ACSR specification ETAPS 2002

  32. ACSR semantics • Two-level semantics: • A collection of inference rules gives the unprioritized transition relation • A preemption relation on actions and events disables some of the transitions, giving a prioritized transition relation ETAPS 2002

  33. Prefix operators • Choice • Parallel Unprioritized transition relation ETAPS 2002

  34. Resource-constrained execution • Priority-based communication • Resource closure Unprioritized transition relation (II) ETAPS 2002

  35. Examples • Resource conflict • Processes must provide for preemption • Unprioritized transitions: ETAPS 2002

  36. Unprioritized transition relation (III) ETAPS 2002

  37. Example • A Scheduler rc rc kill  Sched Sched Sched ETAPS 2002

  38. To take priorities into account in the semantics we define the relation  is preempted by  : • An action  preempts action  iff • no lower priorities: • some higher priorities: • it contains fewer resources • e.g. • An event preempts an action iff •  with non-zero priority preempts all actions e.g. • An event preempts another event iff • same label, higher priority e.g. Preemption relation ETAPS 2002

  39. Prioritized transition relation • We define when • there is an unprioritized transition • there is no such that • Compositional ETAPS 2002

  40. Example • Unprioritized and prioritized transitions:   ETAPS 2002

  41. Example (cont.) • Resource closure enforces progress  ETAPS 2002

  42. A a a B C c b D E  A a B b c C D Bisimulation • Observational equivalence is based on the idea • that two equivalent systems exhibit the same • behavior at their interfaces with the environment. • This requirement was captured formally through • the notion of bisimulation, a binary relation on • the states of systems. • Two states are bisimilar if for each single • computational step of the one there exists an • appropriate matching (multiple) step of the other, • leading to bisimilar states. ETAPS 2002

  43. Prioritized strong equivalence • An equivalence relation is congruence when it is preserved by all the operators of the language. • This implies that replacement of equivalent components in any complex system leads to equivalent behavior. • Strong bisimulation over is a congruence relation with respect to the ACSR operators. ETAPS 2002

  44. Equational Laws • Equational laws are a set of axioms on the syntactic level of the language that characterize the equivalence relation. • They may be used for manipulating complex systems at the level of their syntactic (ACSR) description. • There is a set of laws that is complete for finite state ACSR processes: ETAPS 2002

  45. Fixed-priority scheduling in ACSR • A set of I tasks with periods pi and execution times ei, sharing the same CPU (resource cpu), where deadline equals period: • each task receives the start signal from the scheduler and begins executing • in each step, the task uses the resource cpu or idles if preempted • Priority of CPU access is based on the process index Taski = (start?,0) . Pi,0 +  : Taski i = {1,…,I} Pi,j = j < ei  (  : Pi,j + {(cpu,i)} : Pi,j+1) + j= ei  Taskii = {1,…,I} j = {0, ei} ETAPS 2002

  46. Scheduling and checking deadlines • Each task is controlled by an actuator process (intuitively, a part of the scheduler) • Starts execution of a task by sending start • Keeps track of deadlines • a task can accept start only after it completes execution in the previous period Actuatori = (starti!, i). Ai,0i = {1,2} Ai,k = k < pi  : Ai,k+1 + k = pi  Actuatorii = {1,2}, k = {0,pi} Jobi = (Taski|Actuatori)\starti ETAPS 2002

  47. Rate-monotonic scheduling • Order the task processes according to their periods • tasks with higher rates have higher indices and thus higher priorities • Compose the task processes and analyze for deadlock • the collection of tasks is schedulable iff there is no deadlock RM = (Job1|…|Jobn)[cpu] ETAPS 2002

  48. Dynamic-priority scheduling • Unlike fixed-priority scheduling, such as RM, the priority of a task changes with time • Earliest Deadline First (EDF) scheduling: priority of a task increases as it nears its deadline: πi = dmax − (pi − t) dmax= max(p1,…,pn) • An EDF task: Taski = (start?,0) . Pi,0,0 +  : Taski, i = {1,…,I} Pi,j,t = j < ei  (  : Pi,j,t+1 + {(cpu, dmax−(pi−t))} : Pi,j+1,t+1) + j= ei  Taskii = {1,…,I} j = {0, ei} t = {0, pi} ETAPS 2002

  49. Probabilistic ACSRfor soft real-time scheduling analysis ETAPS 2002

  50. PACSR (Probabilistic ACSR) • ACSR extension for probabilistic behaviors. • Objective : • formally describe behavioral variations in systems that arise due to failures in physical devices. • Since failing devices are modeled by resources we associate a failure probabilityp(r) with every resource r • at any time unit, r is down with probability p(r) or up with probability 1-p(r) • failures are assumed to be independent ETAPS 2002

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