1. Chapter 7: Deadlocks (Continuation)

2. 7.2 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Chapter 7: Deadlocks The Deadlock Problem System Model Deadlock Characterization Methods for Handling Deadlocks Deadlock Prevention Deadlock Avoidance Deadlock Detection Recovery from Deadlock

3. 7.3 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Deadlock Avoidance Simplest and most useful model requires that each process declare the maximum number of resources of each type that it may need. The deadlock-avoidance algorithm dynamically examines the resource-allocation state to ensure that there can never be a circular-wait condition. Resource-allocation state is defined by the number of available and allocated resources, and the maximum demands of the processes. Requires that the system has some additional a priori information available.

4. 7.4 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Safe State When a process requests an available resource, system must decide if immediate allocation leaves the system in a safe state. A system is in a safe state only if there exists a safe sequence for the current allocation state such that for each P i, the resource requests that P i can still make can be satisfied by currently available resources + resources held by all the P j, with j < i. That is: If P i resource needs are not immediately available, then P i can wait until all P j have finished. When P j is finished, P i can obtain needed resources, execute, return allocated resources, and terminate. When P i terminates, P i +1 can obtain its needed resources, and so on.

5. 7.5 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Basic Facts If a system is in safe state  no deadlocks. If a system is in unsafe state  possibility of deadlock. Avoidance  ensure that a system will never enter an unsafe state.

6. 7.6 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Safe, Unsafe, Deadlock State

7. 7.7 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Avoidance algorithms Single instance of a resource type. Use a resource-allocation graph Multiple instances of a resource type. Use the banker’s algorithm

8. 7.8 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Allocation Graph Scheme Claim edge P i  R j indicates that process P j may request resource R j ; represented by a dashed line. Claim edge converts to request edge when a process requests a resource. Request edge converted to an assignment edge when the resource is allocated to the process. When a resource is released by a process, assignment edge reconverts to a claim edge. Resources must be claimed a priori in the system.

9. 7.9 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Allocation Graph

10. 7.10 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Allocation Graph Algorithm Suppose that process P i requests a resource R j The request can be granted only if converting the request edge to an assignment edge does not result in the formation of a cycle in the resource allocation graph If n is the number of processes in the system then an algorithm for detecting a cycle in the resource allocation graph requires an order of n 2 operations.

11. 7.11 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Allocation Graph

12. 7.12 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Unsafe State In Resource-Allocation Graph Cycle: if R 2 is allocated to P 2 and at the same time R 2 is requested by P 1, a deadlock may occur

13. 7.13 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Banker’s Algorithm The resource-allocation graph algorithm is not applicable to a resource-allocation system with multiple instances of each resource type. The Banker’s algorithm got its name because it could be used in a banking system to ensure that the bank never allocated its available cash in such a way that it could no longer satisfy the needs of all its customers.

14. 7.14 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Banker’s Algorithm Background: Each process must a priori claim maximum use: it must declare the maximum number of instances of each resource type that it may need. When a process requests a resource it may have to wait. When a process gets all its resources it must return them in a finite amount of time.

15. 7.15 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Data Structures for the Banker’s Algorithm Available: Vector of length m. If Available [j] = k, there are k instances of resource type R j available. Max: n x m matrix. If Max [i,j] = k, then process P i may request at most k instances of resource type R j. Allocation: n x m matrix. If Allocation [i,j] = k then P i is currently allocated k instances of R j. Need: n x m matrix. If Need [i,j] = k, then P i may need k more instances of R j to complete its task. Need [i,j] = Max[i,j] – Allocation [i,j] Let n = number of processes, and m = number of resources types.

16. 7.16 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Safety Algorithm 1.Let Work and Finish be vectors of length m and n, respectively. Initialize: Work = Available Finish [i] = false for i = 0, 1, …, n- 1. 2.Find an i such that both: (a) Finish [i] = false (b) Need [i]  Work (i th row of Need is component-wise less then or equal to Work) If no such i exists, go to step 4. 3.Work = Work + Allocation [i] (component-wise addition of Work and i th row of Allocation) Finish[i] = true Put P i to the safety sequence go to step 2. 4. If Finish [i] = true for all i, then the system is in a safe state. The efficiency of this algorithm is of order O( mn 2 )

17. 7.17 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example of Banker’s Algorithm 5 processes P 0 through P 4 ; 3 resource types: A (10 instances), B (5instances), and C (7 instances). Suppose the following snapshot at time T 0 : AllocationMaxAvailable A B CA B C A B C P 0 0 1 07 5 3 3 3 2 P 1 2 0 0 3 2 2 P 2 3 0 2 9 0 2 P 3 2 1 1 2 2 2 P 4 0 0 24 3 3

18. 7.18 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example (Cont.) The content of the matrix Need is defined to be Max – Allocation. Need A B C P 0 7 4 3 P 1 1 2 2 P 2 6 0 0 P 3 0 1 1 P 4 4 3 1 Work (initial) 3 3 2

19. 7.19 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example (Cont.) The content of the matrix Need is defined to be Max – Allocation. Allocation Need Available A B CA B C A B C P 0 0 1 07 4 3 3 3 2 P 1 2 0 0 1 2 2 P 2 3 0 2 6 0 0 P 3 2 1 1 0 1 1 P 4 0 0 24 3 1 Work 3 3 2  5 3 2  7 4 3  7 4 5  7 5 5  10 5 7 P1  P3  P4  P0  P2 The system is in a safe state since the sequence satisfies safety criteria.

20. 7.20 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Request Algorithm for Process P i Request i = request vector for process P i. If Request i [j] = k then process P i wants k instances of resource type R j. 1.If Request i  Need [ i ] (component-wise comparison with the i th row of Need), go to step 2. Otherwise, raise error condition, since process has exceeded its maximum claim. 2.If Request i  Available (component-wise comparison with Available), go to step 3. Otherwise P i must wait, since resources are not available. 3.Pretend to allocate requested resources to P i by modifying the state as follows: Available = Available – Request i ; Allocation[i] = Allocation[i] + Request i ; Need [i] = Need [i] – Request i ; If safe  the resources are allocated to P i. If unsafe  P i must wait, and the old resource-allocation state is restored

21. 7.21 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example: P 1 Request (1,0,2) Check that Request  Available (that is, (1,0,2)  (3,3,2)  true. AllocationNeedAvailable A B CA B CA B C P 0 0 1 0 7 4 3 3 3 2 P 1 2 0 01 2 2 P 2 3 0 2 6 0 0 P 3 2 1 1 0 1 1 P 4 0 0 2 4 3 1 Executing safety algorithm shows that sequence satisfies safety requirement.

22. 7.22 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example: P 1 Request (1,0,2) (cont.) After P 1 Request (1,0,2) was satisfied, we obtain: AllocationNeedAvailable A B CA B CA B C P 0 0 1 0 7 4 3 2 3 0 P 1 3 0 20 2 0 P 2 3 0 2 6 0 0 P 3 2 1 1 0 1 1 P 4 0 0 2 4 3 1 Is the system still in a safe state?

23. 7.23 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example: P 1 Request (1,0,2) (cont.) After P 1 Request (1,0,2) was satisfied, we obtain: AllocationNeedAvailable A B CA B CA B C P 0 0 1 0 7 4 3 2 3 0 P 1 3 0 20 2 0 P 2 3 0 2 6 0 0 P 3 2 1 1 0 1 1 P 4 0 0 2 4 3 1 Work 2 3 0  5 3 2  7 4 3  7 4 5  7 5 5  10 5 7 P1  P3  P4  P0  P2 Request (1,0,2) can be granted because the system will still be in a safe state

24. 7.24 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Homework Assignment AllocationNeedAvailable A B CA B CA B C P 0 0 1 0 7 4 3 3 3 2 P 1 2 0 01 2 2 P 2 3 0 2 6 0 0 P 3 2 1 1 0 1 1 P 4 0 0 2 4 3 1 HOMEWORK ASSIGNMENT: Can request for (3,3,0) by P 4 be granted? Can request for (0,2,0) by P 0 be granted? Can request for (2,2,3) by P 2 be granted?

25. 7.25 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Deadlock Detection Allow system to enter deadlock state Detection algorithm Recovery scheme

26. 7.26 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Deadlock Detection Algorithm: Single Instance of Each Resource Type Maintain wait-for graph Nodes are processes. P i  P j if P i is waiting for P j. Periodically invoke an algorithm that searches for a cycle in the graph. If there is a cycle, there exists a deadlock. An algorithm to detect a cycle in a graph requires an order of n 2 operations, where n is the number of vertices in the graph.

27. 7.27 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Resource-Allocation Graph and Wait-for Graph Resource-Allocation GraphCorresponding wait-for graph

28. 7.28 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Deadlock Detection Algorithm: Several Instances of a Resource Type Available: A vector of length m indicates the number of available resources of each type. Allocation: An n x m matrix defines the number of resources of each type currently allocated to each process. Request: An n x m matrix indicates the current request of each process. If Request [I,j] = k, then process P i is requesting k more instances of resource type. R j.

29. 7.29 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Detection Algorithm 1. Let Work and Finish be vectors of length m and n, respectively Initialize: (a) Work = Available (b)For i = 1,2, …, n, if Allocation [i, j]  0 for some j, then Finish[ i ] = false; otherwise, Finish[ i ] = true. 2.Find an index i such that both: (a)Finish[i] == false (b)Request [ i ]  Work (component-wise comparison of the i th row of matrix Request and vector Work. If no such i exists, go to step 4.

30. 7.30 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Detection Algorithm (Cont.) 3. Work = Work + Allocation[i] Finish[ i ] = true go to step 2. 4.If Finish[ i ] == false, for some i, 1  i  n, then the system is in deadlock state. Moreover, if Finish [i ] == false, then P i is deadlocked. Algorithm requires an order of O( mn 2 ) operations to detect whether the system is in a deadlocked state.

31. 7.31 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example of Detection Algorithm Five processes P 0 through P 4 ; three resource types A (7 instances), B (2 instances), and C (6 instances). Snapshot at time T 0 : AllocationRequestAvailable A B C A B C A B C P 0 0 1 0 0 0 0 0 0 0 P 1 2 0 0 2 0 2 P 2 3 0 30 0 0 P 3 2 1 1 1 0 0 P 4 0 0 2 0 0 2 Is the system in the safe state or there is a deadlock?

32. 7.32 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example of Detection Algorithm Five processes P 0 through P 4 ; three resource types A (7 instances), B (2 instances), and C (6 instances). Snapshot at time T 0 : AllocationRequestAvailable A B C A B C A B C P 0 0 1 0 0 0 0 0 0 0 P 1 2 0 0 2 0 2 P 2 3 0 30 0 0 P 3 2 1 1 1 0 0 P 4 0 0 2 0 0 2 Work 0 0 0  0 1 0  3 1 3  5 2 4  5 2 6  7 2 6 P0  P2  P3  P4  P1 Sequence will result in Finish[i] = true for all i.

33. 7.33 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Example (Cont.) P 2 requests an additional instance of type C. Request A B C P 0 0 0 0 P 1 2 0 1 P 2 0 0 1 P 3 1 0 0 P 4 0 0 2 State of system? We can reclaim resources held by process P 0, but the number of available resources is to fulfill the requests of the other processes. Deadlock exists, consisting of processes P 1, P 2, P 3, and P 4.

34. 7.34 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Detection-Algorithm Usage When, and how often, to invoke depends on: How often a deadlock is likely to occur? How many processes will be affected by deadlock when it happens? If deadlocks occur frequently, the detection algorithm should be invoked frequently; otherwise resources allocated to deadlocked processes will be idle until the deadlock can be broken

35. 7.35 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Detection-Algorithm Usage In the extreme, we can invoke the deadlock detection algorithm every time a request for allocation can not be granted immediately (this will make it possible even to identify the specific process that caused the deadlock. However, if the deadlock-detection algorithm is invoked for every resource request, this will incur a considerable overhead in computation time. The best solution is to invoke the algorithm either at some fixed time (once per hour or 30 minutes, or 15 minutes) or whenever CPU utilization drops below 40 %.

36. 7.36 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Recovery from Deadlock: Process Termination Abort all deadlocked processes. Abort one process at a time until the deadlock cycle is eliminated. In which order should we choose to abort? Priority of the process. How long process has computed, and how much longer to completion. Resources the process has used. Resources process needs to complete. How many processes will need to be terminated. Is process interactive or batch?

37. 7.37 Silberschatz, Galvin and Gagne ©2005 Operating System Concepts - 7 th Edition, Feb 14, 2005 Recovery from Deadlock: Resource Preemption To eliminate deadlocks using resource preemption, we successively preempt some resources from processes and give these resources to other processes until the deadlock cycle is broken. Selecting a victim – minimize cost. Rollback – return to some safe state, restart process for that state. Starvation – same process may always be picked as victim, include number of rollback in cost factor.

38. End of Chapter 7