DEADLOCKS

System Model Deadlock Characterization Methods for Handling Deadlocks Deadlock Prevention Deadlock Avoidance Deadlock Detection Recovery from Deadlock Combined Approach to Deadlock Handling

The Deadlock Problem

A set of blocked processes each holding a resource and waiting to acquire a resource held by another process in the set. Example o System has 2 tape drives. o P1 and P2 each hold one tape drive and each needs another one. Example

semaphores A and B , initialized to 1

P0 P1 ------ -----wait(A) wait(B) wait(B) wait(A)

Example: bridge crossing

o o o o o

Traffic only in one direction. Each section of a bridge can be viewed as a resource. 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.

System Model

Resource types R1 , R2 , ..., Rm-1 Examples of resource types - CPU cycles, memory space, I/O devices Each resource type Ri has Wi instances. e.g. 2 CPUs, 1 Floppy Disk, 2 Hard Disks Each process utilizes a resource (using system calls) as follows: o request o use o release

Deadlock Characterization - deadlock can arise if four conditions hold simultaneously.

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 , ..., Pn } 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 P 0 .

Resource-Allocation Graph - a diagram showing allocations

A set of vertices V and a set of edges E.

V is partitioned into two types: o P = {P1 , P2 , ..., Pn }, the set consisting of all the processes in the system. o R = {R 1 , R 2 , ..., Rm }, the set consisting of all resource types in the system. request edge - directed edge Pi -> Rj assignment edge - directed edge Rj -> Pi

Example

Process

Resource type with 4 instances

Pi requests instance of R j

Pi is holding an instance of R j

Example of a resource-allocation graph with no cycles.

Example of a resource-allocation graph with a cycle.

If graph contains no cycles -> no deadlock. If graph contains a cycle -> o if only one instance per resource type, then deadlock. o if several instances per resource type, possibility of deadlock.

e.g. R={1r1,2r2,1r3},E={(p1,r1),(p2,r3),(r1,p2),(r2,p2),(r2,p1),(r3,p3),(p3,r2)} e.g. R={2r1,2r2},E={(p1,r1),(r1,p2),(r1,p3),(r2,p1),(p3,r2),(r2,p4)}

Methods for Handling Deadlocks

Ensure that the system will never enter a deadlock state. (traffic lights) Allow the system to enter a deadlock state and then recover. (back up cars) Ignore the problem and pretend that deadlocks never occur in the system; used by most operating systems, including UNIX.

Deadlock Prevention - restrain the ways resource requests can be made.

Mutual Exclusion - not required for sharable resources; must hold for nonsharable resources. Hold and Wait - must guarantee that whenever a process requests a resource, it does not hold any other resources. o Require process to request and be allocated all its resources before it begins execution, or allow process to request resources only when the process has none. o Low resource utilization; starvation possible. No Preemption o 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. o Preempted resources are added to the list of resources for which the process is waiting. o 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.

Deadlock Avoidance - requires that the system has some additional a priori information available.

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.

Safe State - when a process requests an available resource, system must decide if immediate allocation leaves the system in a safe state.

System is in safe state if there exists a safe sequence of all processes. Sequence <P1 , P2 , ..., Pn > is safe if for each Pi , the resources that Pi can still request can be satisfied by the currently available resources plus the resources held by all the Pj , with j < i. o If 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. o When Pi terminates, Pi+1 can obtain its needed resources, and so on. 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.
o Max Needs 10 4 9 Current Needs 5 2 2

e.g. 12 instances of a resource.

p0 p1 p2

systems is safe because <p1, p0, p2> satisfies safety condition. The following diagram shows how deadlock can occur. At point t, any move upwards would enter an unsafe state.

Resource-Allocation Graph Algorithm

Claim edge Pi -> Rj indicates that process Pi may request resource Rj ; represented by a dashed line. Claim edge converts to request edge when a process requests a resource. When a resource is released by a process, assignment edge reconverts to a claim edge.

Resources must be claimed a priori in the system.

Example
E={(r1,p1)} C={(p1,r2),(p2,r1),(p2,r2)} no cycles -> system is safe now if p2 requests r2 -> system is unsafe.

Banker's Algorithm (Dijkstra 1965)

Multiple resource types. 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. Data Structures for the Banker's algorithm where n = number of processes, and m = number of resource types. o Available: Vector of length m. If Available[j] = k, there are k instances of resource type Rj available. o Max: n x m matrix. If Max[i,j] = k, then process Pi may request at most k instances of resource type R j . o Allocation: n x m matrix. If Allocation[i,j] = k, then Pi is currently allocated k instances of R j . o 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].

Example: consider the following: A banker 10 thousand dollars and four customers Florence, Dougal, Dylan and Zebedee. each customer has a maximum need and and starts owing nothing. Name Used Max Florence 0 6 Dougal 0 5 Dylan 0 4 Zebedee 0 7 Available = 10 Safe Name Used Max Florence 1 6 Dougal 1 5 Dylan 2 4 Zebedee 4 7

Available = 2 Safe, because any requests for loans, except to Dylan, can wait until Dylan repays his loan. Name Used Max Florence 1 6 Dougal 2 5 Dylan 2 4 Zebedee 4 7 Available = 1 Unsafe, since if all customers ask for their maximum, none will get it, causing deadlock.

Safety Algorithm
1. Let Work and Finish be vectors of length m and n, respectively. Initialize:
Work := Available Finish[i] := false for i = 1, 2, ..., n.

2. Find an i such that both: 1. Finish[i] = false 2. Need i <= Work (every element in Needi < every element in Work) If no such i exists, go to step 4. 3. Work := Work + Allocation i Finish[i] := true go to step 2. 4. If Finish[i] = true for all i, then the system is in a safe state. May require an order of m x n 2 operations to decide whether a state is safe.

Resource-Request Algorithm for process Pi

Request i = request vector for process Pi . If Request i [ j ] = k , then process Pi wants k instances of resource type R j . 1. If Request i <= Need i , go to step 2. Otherwise, raise error condition, since process has exceeded its maximum claim. 2. If Request i <= Available, go to step 3. Otherwise, Pi must wait, since resources are not available. 3. Pretend to allocate requested resources to Pi by modifying the state as follows:

Available := Available - Request i ; Allocation i := Allocation i + Request i ; Need i := Need i - Request i ;

o o

If safe -> the resources are allocated to Pi . If unsafe -> Pi must wait, and the old resource-allocation state is restored.

Example of Banker's algorithm

5 processes P 0 through P4 ; 3 resource types A (10 instances), B (5 instances), and C (7 instances). Snapshot at time T 0 :
Allocation ---------A B C P0 0 1 0 P1 2 0 0 P2 3 0 2 P3 2 1 1 P4 0 0 2 4 Max --A B 7 5 3 2 9 0 2 2 3 3 C 3 2 2 2 Available --------A B C 3 3 2 Need ----A B C 7 4 3 1 2 2 6 0 0 0 1 1 4 3 1

Sequence <P1, P3, P4, P2, P0> satisfies safety criteria. P1 now requests resources. Request 1 = (1,0,2). o Check that Request 1 <= Available (that is, (1,0,2) <= (3,3,2)) -> true.
o o o o o o o Allocation Need -----------A B C A B C P0 0 1 0 7 4 3 P1 3 0 2 0 2 0 P2 3 0 2 6 0 0 P3 2 1 1 0 1 1 0 0 2 4 3 1 Available --------A B C 2 3 0

P4 o

Executing safety algorithm shows that sequence <P1, P3, P4, P0, P2> satisfies safety requirement. From this state, can request for (3,3,0) by P4 be granted? From this state, can request for (0,2,0) by P0 be granted?

Deadlock Detection

Allow system to enter deadlock state Detection algorithm Recovery scheme

Single Instance of Each Resource Type

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Maintain wait-for graph o Nodes are processes. o Pi ->Pj if Pi is waiting for Pj . Periodically invoke an algorithm that searches for a cycle in the graph. 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.

Several Instances of a Resource Type

Data structures o Available: A vector of length m indicates the number of available resources of each type. o Allocation: An n x m matrix defines the number of resources of each type currently allocated to each process. o Request: An n x m matrix indicates the current request of each process. If Request[i,j] = k, then process Pi is requesting k more instances of resource type Rj .

Detection Algorithm
1. Let Work and Finish be vectors of length m and n, respectively. Initialize: Work := Available. For i = 1, 2, ..., n, if Allocationi <> 0, then Finish[i] := false; otherwise, Finish[i] := true. 2. Find an index i such that both: 1. Finish[i] = false. 2. Request i <= Work. If no such i exists, go to step 4. 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 a deadlock state. Moreover, if Finish[i] = false, then Pi is deadlocked. Algorithm requires an order of m x n2 operations to detect whether the system is in a deadlocked state.

Example of Detection algorithm

Five processes P 0 through P4 ; three resource types A (7 instances), B (2 instances), and C (6 instances). Snapshot at time T 0 :
Allocation Request Available

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 P4

---------- ------A B C A B C P0 0 1 0 0 0 0 2 0 2 P1 2 0 0 P2 3 0 3 0 0 0 P3 2 1 1 1 0 0 0 0 2 0 0 2

--------A B C 0 0 0

Sequence <P0, P2, P3, P1, P4> will result in Finish[i] = true for all i. P2 requests an additional instance of type C.
Request ------A B C 0 0 0 2 0 2 0 0 1 1 0 0 0 2

P4

P0 P1 P2 P3 0

State of system? o Can reclaim resources held by process P0 , but insufficient resources to fulfill other processes' requests. o Deadlock exists, consisting of processes P1 , P2 , P3 , and P4 .

Detection-Algorithm Usage

When, and how often, to invoke depends on: o How often a deadlock is likely to occur? o How many processes will need to be rolled back? one for each disjoint cycle If detection algorithm is invoked arbitrarily, there may be many cycles in the resource graph and so we would not be able to tell which of the many deadlocked processes ``caused'' the deadlock.

Recovery from Deadlock

Process termination o Abort all deadlocked processes. o Abort one process at a time until the deadlock cycle is eliminated. o 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.

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Is process interactive or batch? Resource Preemption o Selecting a victim - minimize cost. o Rollback - return to some safe state, restart process from that state. o Starvation - same process may always be picked as victim; include number of rollback in cost factor.

Combined Approach to Deadlock Handling

Combine the three basic approaches (prevention, avoidance, and detection), allowing the use of the optimal approach for each class of resources in the system. Partition resources into hierarchically ordered classes. Use most appropriate technique for handling deadlocks within each class.

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