![Data Structures for the Banker’s Algorithm
• Available: Vector of length m. If available [j] = k, there are k
instances of resource type Rj available.
• Max: n x m matrix. If Max [i,j] = k, then process Pi may
request at most k instances of resource type Rj.
• Allocation: n x m matrix. If Allocation[i,j] = k then Pi is
currently allocated k instances of Rj.
• Need: n x m matrix. If Need[i,j] = k, then Pi may need k more
instances of Rj to complete its task.
Need [i,j] = Max[i,j] – Allocation
[i,j]
Let n = number of processes, and m = number of resources types.](https://image.slidesharecdn.com/ch07-deadlocks-191104080347/85/Ch07-deadlocks-31-320.jpg)
![Multiple 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 [ij] = k, then
process Pi is requesting k more instances of
resource type. Rj.
Required data structures:](https://image.slidesharecdn.com/ch07-deadlocks-191104080347/85/Ch07-deadlocks-40-320.jpg)
Ch07 deadlocks
- 2. Chapter 7: Deadlocks • 7.1 System Model • 7.2 Deadlock Characterization • 7.3 Methods for Handling Deadlocks • 7.4 Deadlock Prevention • 7.5 Deadlock Avoidance • 7.6 Deadlock Detection • 7.7 Recovery from Deadlock
- 3. Chapter Objectives • To develop a description of deadlocks, which prevent sets of concurrent processes from completing their tasks • To present a number of different methods for preventing, avoiding, or detecting deadlocks in a computer system
- 5. The Deadlock Problem • A deadlock consists of a set of blocked processes, each holding a resource and waiting to acquire a resource held by another process in the set • Example #1 – A system has 2 disk drives – P1 and P2 each hold one disk drive and each needs the other one • Example #2 – Semaphores A and B, initialized to 1 P0 P1 wait (A); wait(B) wait (B); wait(A)
- 6. Bridge Crossing Example • Traffic only in one direction • The resource is a one-lane bridge • If a deadlock occurs, it can be resolved if one car backs up (preempt resources and rollback) • Several cars may have to be backed up if a deadlock occurs • Starvation is possible
- 7. System Model • Resource types R1, R2, . . ., Rm CPU cycles, memory space, I/O devices • Each resource type Ri has 1 or more instances • Each process utilizes a resource as follows: – request – use – release
- 9. Deadlock Characterization • Mutual exclusion: only one process at a time can use a resource • Hold and wait: a process holding at least one resource is waiting to acquire additional resources held by other processes • No preemption: a resource can be released only voluntarily by the process holding it after that process has completed its task • Circular wait: there exists a set {P0, P1, …, P0} of waiting processes such that P0 is waiting for a resource that is held by P1, P1 is waiting for a resource that is held by P2, …, Pn–1 is waiting for a resource that is held by Pn, and Pn is waiting for a resource that is held by P0 Deadlock can arise if four conditions hold simultaneously.
- 10. Resource-Allocation Graph • V is partitioned into two types: – P = {P1, P2, …, Pn}, the set consisting of all the processes in the system – R = {R1, R2, …, Rm}, the set consisting of all resource types in the system • request edge – directed edge P1 Rj • assignment edge – directed edge Rj Pi A set of vertices V and a set of edges E.
- 11. Resource-Allocation Graph (Cont.) • Process • Resource Type with 4 instances • Pi requests instance of Rj • Pi is holding an instance of Rj Pi Pi Rj Rj
- 12. Resource Allocation Graph With A Deadlock Before P3 requested an instance of R2 After P3 requested an instance of R2
- 13. Graph With A Cycle But No Deadlock Process P4 may release its instance of resource type R2. That resource can then be allocated to P3, thereby breaking the cycle.
- 14. Relationship of cycles to deadlocks • If a resource allocation graph contains no cycles no deadlock • If a resource allocation graph contains a cycle and if only one instance exists per resource type deadlock • If a resource allocation graph contains a cycle and and if several instances exists per resource type possibility of deadlock
- 15. 7.3 Methods for Handling Deadlocks
- 16. Methods for Handling Deadlocks • Prevention – Ensure that the system will never enter a deadlock state • Avoidance – Ensure that the system will never enter an unsafe state • Detection – Allow the system to enter a deadlock state and then recover • Do Nothing – Ignore the problem and let the user or system administrator respond to the problem; used by most operating systems, including Windows and UNIX
- 18. Deadlock Prevention • Mutual Exclusion – The mutual-exclusion condition must hold for non-sharable resources • Hold and Wait – we must guarantee that whenever a process requests a resource, it does not hold any other resources – Require a process to request and be allocated all its resources before it begins execution, or allow a process to request resources only when the process has none – Result: Low resource utilization; starvation possible To prevent deadlock, we can restrain the ways that a request can be made
- 19. Deadlock Prevention (Cont.) • No Preemption – – If a process that is holding some resources requests another resource that cannot be immediately allocated to it, then all resources currently being held are released – Preempted resources are added to the list of resources for which the process is waiting – A process will be restarted only when it can regain its old resources, as well as the new ones that it is requesting • Circular Wait – impose a total ordering of all resource types, and require that each process requests resources in an increasing order of enumeration. For example: F(tape drive) = 1 F(disk drive) = 5 F(printer) = 12
- 21. 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 • A 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. a priori: formed or conceived beforehand
- 22. Safe State • When a process requests an available resource, the 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 • A sequence of processes <P1, P2, …, Pn> is a safe sequence for the current allocation state if, for each Pi, the resource requests that Pi can still make, can be satisfied by currently available resources plus resources held by all Pj, with j < i. • That is: – If the Pi resource needs are not immediately available, then Pi can wait until all Pj have finished – When Pj is finished, Pi can obtain needed resources, execute, return allocated resources, and terminate – When Pi terminates, Pi +1 can obtain its needed resources, and so on
- 23. Safe State (continued) • 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
- 24. Safe, Unsafe , Deadlock State
- 25. Avoidance algorithms • For a single instance of a resource type, use a resource-allocation graph • For multiple instances of a resource type, use the banker’s algorithm
- 26. Resource-Allocation Graph Scheme • Introduce a new kind of edge called a claim edge • Claim edge Pi Rj indicates that process Pj may request resource Rj; which is represented by a dashed line • A claim edge converts to a request edge when a process requests a resource
- 27. Resource-Allocation Graph with Claim Edges Request edge Assignment edge Claim edge Claim edge
- 28. Unsafe State In Resource-Allocation Graph Assignment edge Request edge Assignment edgeClaim edge
- 29. Resource-Allocation Graph Algorithm • Suppose that process Pi requests a resource Rj • 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
- 30. Banker’s Algorithm • Used when there exists multiple instances of a resource type • Each process must a priori claim maximum use • 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
- 31. Data Structures for the Banker’s Algorithm • Available: Vector of length m. If available [j] = k, there are k instances of resource type Rj available. • Max: n x m matrix. If Max [i,j] = k, then process Pi may request at most k instances of resource type Rj. • Allocation: n x m matrix. If Allocation[i,j] = k then Pi is currently allocated k instances of Rj. • Need: n x m matrix. If Need[i,j] = k, then Pi may need k more instances of Rj to complete its task. Need [i,j] = Max[i,j] – Allocation [i,j] Let n = number of processes, and m = number of resources types.
- 32. Safty Algo
- 34. e.g
- 35. E.g
- 37. Deadlock Detection • For deadlock detection, the system must provide – An algorithm that examines the state of the system to detect whether a deadlock has occurred – And an algorithm to recover from the deadlock • A detection-and-recovery scheme requires various kinds of overhead – Run-time costs of maintaining necessary information and executing the detection algorithm – Potential losses inherent in recovering from a deadlock
- 38. Single Instance of Each Resource Type • Requires the creation and maintenance of a wait-for graph – Consists of a variant of the resource-allocation graph – The graph is obtained by removing the resource nodes from a resource-allocation graph and collapsing the appropriate edges – Consequently; all nodes are processes – Pi Pj if Pi is waiting for Pj. • 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 n2 operations, where n is the number of vertices in the graph
- 39. Resource-Allocation Graph and Wait-for Graph Resource-Allocation Graph Corresponding wait-for graph
- 40. Multiple 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 [ij] = k, then process Pi is requesting k more instances of resource type. Rj. Required data structures:
- 41. Detection-Algorithm Usage • When, and how often, to invoke the detection algorithm depends on: – How often is a deadlock likely to occur? – How many processes will be affected by deadlock when it happens? • If the detection algorithm is invoked arbitrarily, there may be many cycles in the resource graph and so we would not be able to tell which one of the many deadlocked processes “caused” the deadlock • If the detection algorithm is invoked for every resource request, such an action will incur a considerable overhead in computation time • A less expensive alternative is to invoke the algorithm when CPU utilization drops below 40%, for example – This is based on the observation that a deadlock eventually cripples system throughput and causes CPU utilization to drop
- 42. 7.7 Recovery From Deadlock
- 43. Recovery from Deadlock • Two Approaches – Process termination – Resource preemption
- 44. Recovery from Deadlock: Process Termination • Abort all deadlocked processes – This approach will break the deadlock, but at great expense • Abort one process at a time until the deadlock cycle is eliminated – This approach incurs considerable overhead, since, after each process is aborted, a deadlock- detection algorithm must be re-invoked to determine whether any processes are still deadlocked • Many factors may affect which process is chosen for termination – What is the priority of the process? – How long has the process run so far and how much longer will the process need to run before completing its task? – How many and what type of resources has the process used? – How many more resources does the process need in order to finish its task? – How many processes will need to be terminated? – Is the process interactive or batch?
- 45. Recovery from Deadlock: Resource Preemption • With this approach, we successively preempt some resources from processes and give these resources to other processes until the deadlock cycle is broken • When preemption is required to deal with deadlocks, then three issues need to be addressed: – Selecting a victim – Which resources and which processes are to be preempted? – Rollback – If we preempt a resource from a process, what should be done with that process? – Starvation – How do we ensure that starvation will not occur? That is, how can we guarantee that resources will not always be preempted from the same process?
- 46. Summary • Four necessary conditions must hold in the system for a deadlock to occur – Mutual exclusion – Hold and wait – No preemption – Circular wait • Four principal methods for dealing with deadlocks – Use some protocol to (1) prevent or (2) avoid deadlocks, ensuring that the system will never enter a deadlock state – Allow the system to enter a deadlock state, (3) detect it, and then recover • Recover by process termination or resource preemption – (4) Do nothing; ignore the problem altogether and pretend that deadlocks never occur in the system (used by Windows and Unix) • To prevent deadlocks, we can ensure that at least one of the four necessary conditions never holds
- 47. End of Chapter 7