Distributed Deadlock-Avoidance. IMDEA Software Institute, Spain

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1 Distributed Deadlock-voidance César Sánchez IMDE Software Institute, Spain DRV Workshop, ertinoro 19-May, 216

2 Distributed Deadlock-voidance little story about how static knowledge can help solve unsolvable problems César Sánchez IMDE Software Institute, Spain DRV Workshop, ertinoro 19-May, 216

3 Introduction Goal: Formalization of middleware services pp pp pp Middleware Middleware Event Channels Deadlock voidance OS 1 OS 2 OS 3

4 Deadlocks Deadlock is one of the classical problems in CS One (common) approach is the ostrich approach The other approaches are: detection, prevention and avoidance. centralized distributed detection OK OK prevention OK OK avoidance anker s impractical Efficient dynamic resource allocation can have a big practical impact.

5 Distributed Dinning Philosophers

6 Distributed Dinning Philosophers deadlock state

7 Distributed Dinning Philosophers Detection:

8 Distributed Dinning Philosophers Prevention: 3 2 1

9 Distributed Dinning Philosophers voidance:?

10 Distributed Dinning Philosophers Distributed voidance:???

11 Deadlock voidance Problem Space Centralized Distributed Unsolvable Unsolvable

12 Deadlock voidance Problem Space Centralized Distributed Unsolvable Unsolvable Max utilization

13 Deadlock voidance Problem Space Centralized Distributed Unsolvable Unsolvable Max utilization [Dijkstra 65] [Singhal 95]

14 Deadlock voidance Problem Space Centralized Distributed Unsolvable Unsolvable Max utilization [Dijkstra 65] [Singhal 95] [de lfaro+:5] FMS

15 Deadlock voidance Problem Space Centralized Distributed Unsolvable Unsolvable Max utilization [Dijkstra 65] [Singhal 95] [de lfaro+:5] FMS?

16 Distributed Real-Time and Embedded F C E D

17 Distributed Real-Time and Embedded n 1 F C E D

18 Distributed Real-Time and Embedded n 1 F n 2 C E D

19 Distributed Real-Time and Embedded n 1 n 3 F n 2 C E n 5 D

20 Distributed Real-Time and Embedded n 1 n 4 n 3 F n 2 C E n 5 D

21 Distributed Real-Time and Embedded n 1 n 4 n 3 F n 2 C E n 5 D Sequence of calls: n 1 C n 5 E n 2 n 3 n 1

22 Distributed Real-Time Embedded Systems Distributed Real-Time Embedded Systems: synchronous distributed system Limited Resources Wait-on-connection rbitrary number of processes spawned ll processes terminate Problem: deadlocks are possible if no controller is used

23 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

24 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

25 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

26 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

27 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

28 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

29 Example of Deadlock Two sites, with two resources each: and the call graph: n 1 n 2 m 1 m 2

30 Summary of Contributions Contribution #1 Efficient deadlock voidance can is possible provided call-graphs are know statically

31 Summary of Contributions Contribution #1 Efficient deadlock voidance can is possible provided call-graphs are know statically Contribution #2 Optimal annotations can be efficiently computed. If annotations are not followed anomalies can occurr.

32 Summary of Contributions Contribution #1 Efficient deadlock voidance can is possible provided call-graphs are know statically Contribution #2 Optimal annotations can be efficiently computed. If annotations are not followed anomalies can occurr. Contribution #3 Distributed Deadlock voidance with (individual) liveness guarantees can be efficiently achieved.

33 Model of Computation Remote procedure call (with Wait-On-Connection) synchronous messages ll to all communication Finite resources: T total number of threads F C E D

34 Model of Computation Remote procedure call (with Wait-On-Connection) synchronous messages ll to all communication Finite resources: T total number of threads F C E D We seek a deadlock avoidance solution with no extra communication

35 Distributed Deadlock voidance Solution Two parts: 1. Static: 2. Dynamic:

36 Distributed Deadlock voidance Solution Two parts: 1. Static: 1 n 1 C n 5 E n 2 n 3 n 1 2. Dynamic:

37 Distributed Deadlock voidance Solution Two parts: 1. Static: 1 n 1 C n 5 E n 2 n 3 n 1 2. Dynamic: when En do In n 1 () Out } entry section } method invocation } exit section

38 nnotations nnotations are computed statically n 1 n 2 m 1 m 2

39 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n same node. m whenever α(n) m for two calls in the

40 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n m whenever α(n) m for two calls in the same node. n 1 n 2 m 1 m 2

41 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n m whenever α(n) m for two calls in the same node. n 1 n 2 m 1 m 2 n depends on m if there is a path from n to m containing a dependency cycle is close path with a

42 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n m whenever α(n) m for two calls in the same node. n 1 n 2 m 1 m 2 DependencyCycle n depends on m if there is a path from n to m containing a dependency cycle is close path with a

43 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n m whenever α(n) m for two calls in the same node. 1 n 1 n 2 m 1 1 m 2 DependencyCycle n depends on m if there is a path from n to m containing a dependency cycle is close path with a

44 nnotations nnotations are computed statically n 1 n 2 m 1 m 2 Dependency edges n m whenever α(n) m for two calls in the same node. 1 n 1 n 2 m 1 m 2 DependencyCycle n depends on m if there is a path from n to m containing a dependency cycle is close path with a

45 asic Solution Deadlock voidance Protocol asic-p: n 1 α [ ] when α < t do t n 1 () t ++

46 asic Solution Deadlock voidance Protocol asic-p: n 1 α [ ] when α < t do t n 1 () t ++ Theorem: If α has no cyclic dependencies, then asic-p guarantees absence of deadlock.

47 asic Solution Deadlock voidance Protocol asic-p: n 1 α [ ] when α < t do t n 1 () t ++ Theorem: If α has no cyclic dependencies, then asic-p guarantees absence of deadlock. Lemma: The following is an invariant: The number of processes running methods with annotation i or higher is at most T i.

48 The nnotation Theorem Theorem: If α has no cyclic dependencies, then asic-p guarantees absence of deadlock. Lemma: The following is an invariant: The number of processes running methods with annotation i or higher is at most T i. annotation α Max num of procs T 1 T T 1 1

49 The nnotation Theorem Theorem: If α has no cyclic dependencies, then asic-p guarantees absence of deadlock. Lemma: The following is an invariant: The number of processes running methods with annotation i or higher is at most T i. Lemma: If a request n 1 is disabled, then α 2 there is an active process running with α 2 α. α n 2

50 nnotations Two immediate questions: 1. How to compute acyclic annotations 2. What if annotations are not acyclic?

51 nnotations Two immediate questions: 1. How to compute acyclic annotations Visit nodes following some reverse topological order. When visiting n, compute the set of nodes S previously visited and reachable following ( ). Set α(n) to 1 plus the largest node in S that resides in the same site. 2. What if annotations are not acyclic?

52 nnotations Two immediate questions: 1. How to compute acyclic annotations Visit nodes following some reverse topological order. When visiting n, compute the set of nodes S previously visited and reachable following ( ). Set α(n) to 1 plus the largest node in S that resides in the same site. 2. What if annotations are not acyclic? n 1 m 1 C C n 2 m 2 n 3 m 3 T = 1 T = 1 T C = 1

53 nnotations Two immediate questions: 1. How to compute acyclic annotations Visit nodes following some reverse topological order. When visiting n, compute the set of nodes S previously visited and reachable following ( ). Set α(n) to 1 plus the largest node in S that resides in the same site. 2. What if annotations are not acyclic? n 1 m 1 C C n 2 m 2 n 3 m 3 FCT: Given enough resources, a deadlock is reachable T = 1 T = 1 T C = 1

54 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = 2 t = 2 and the call graph: n 1 n 2 m 1 1 m 2

55 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = 2 t = 2 and the call graph: n 1 n 2 m 1 1 m 2

56 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = 2 and the call graph: n 1 n 2 m 1 1 m 2

57 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = 2 and the call graph: n 1 n 2 m 1 1 m 2

58 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = and the call graph: n 1 n 2 m 1 1 m 2

59 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = 1 and the call graph: n 1 n 2 m 1 1 m 2

60 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = 1 t = 1 and the call graph: n 1 n 2 m 1 1 m 2

61 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = 1 and the call graph: n 1 n 2 m 1 1 m 2

62 How about liveness? Consider two nodes, with two resource each (T = T = 2): t = t = and the call graph: n 1 n 2 m 1 1 m 2

63 Revisiting the Invariant Lemma: The following is an invariant: The number of processes running methods with annotation i or higher is at most T i. act, i T i for all notes and i where act,i : number of active processes in with annotation i act, i = k i act,i

64 Revisiting the Invariant Lemma: The following is an invariant: The number of processes running methods with annotation i or higher is at most T i. act, i T i for all notes and i where act,i : number of active processes in with annotation i act, i = k i act,i The weakest precondition on allowing a request for n i ϕ = k { act, k T k if k > i act, k + 1 T k if k i

65 The Protocol Live-P i To execute n : [ ] when ϕ do act,i ++ n() act,i Theorem (Deadlock voidance): If α is acyclic, then Live-P guarantees absence of deadlock. Theorem (Liveness): If α is acyclic, then Live-P guarantees that every waiting process is eventually enabled.

66 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = 2 t = 2 Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

67 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = 2 t = 2 Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

68 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = t = 2 Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

69 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = t = 2 Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

70 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = t = Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

71 Live-P provides liveness Consider two nodes, with two resource each (T = T = 2): t = t = 1 Live-P asic-p n 1 n 2 n 1 n 2 m 1 1 m 2 m 1 1 m 2 act, act, 1

72 Conclusions Distributed Deadlock voidance is possible without communication... provided call-graphs are known Using static annotations + runtime protocols If cycles are allowed (e.g. by uncontrolled resource allocation), then deadlocks are unavoidable, provided enough resources Individual liveness is also enforceable Future work: is deadlock avoidance enforceable for any amount of initial resources? can this be adapted to composable conveyor systems?

73 Conclusions Distributed Deadlock voidance is possible without communication... provided call-graphs are known Using static annotations + runtime protocols If cycles are allowed (e.g. by uncontrolled resource allocation), then deadlocks are unavoidable, provided enough resources Individual liveness is also enforceable Future work: is deadlock avoidance enforceable for any amount of initial resources? can this be adapted to composable conveyor systems?

74 Distributed Dinning Philosphers Distributed voidance:???

75 Distributed Dinning Philosphers Distributed voidance:?? SOLUTION:?

76 Distributed Dinning Philosphers Distributed voidance:? 3 2 1?? SOLUTION: For your first pick, do not the take last fork if going in increasing order. For your second pick, do as you wish.

77 Questions Thank you for your attention!