Deadlocks

êDefinition & Basics:

Deadlock:

A set of blocked processes each holding a resource & waiting

to acquire a resource held by another process in the set.

Ex1

System has 2 disk drives

Processes P1 and P2 each hold one disk drive and each needs another one

Ex2

Semaphores A and B, initialized to 1

P0 P1

wait (A); wait(B)

wait (B); wait(A)

Deadlock can arise if 4 conditions hold simultaneously:

1. Mutual exclusion: only one process at a time can use a resource

2. Hold and Wait: holding at least one resource and is waiting to acquire additional resources held by others

3. No preemption: a resource can be released only voluntarily by the process holding it.

4. 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, …,

P_n–1 is waiting for a resource that is held by P_n, and

P_n is waiting for a resource that is held by P₀.

êResource-Allocation Graph

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

· V is partitioned into two types:

o P = {P₁, P₂, …, P_n}, the set consisting of all the Processes in the system

o R = {R₁, R₂, …, R_m}, the set consisting of all Resource types in the system

· E is partitioned into two types:

o request edge – directed edge P_i ® R_j

o assignment edge – directed edge R_j ® P_i

Resource Allocation Graph with No Deadlock (no cycle)

Resource Allocation Graph with Deadlock (cycle)

Resource Allocation Graph with No Deadlock (cycle)

Basic Facts

· If graph contains no cycles Þ no deadlock

· If graph contains a cycle Þ

o if only one instance per resource type, then deadlock

o if several instances per resource type, possibility of deadlock

êDeadlock Prevention

Restrain the ways request can be made.

Any of the following polices will prevent deadlock:

1. Hold and Wait –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.

2. No Preemption – If a process holding some resources and requests another resource that cannot be immediately allocated to it:

ALL resources currently being held are released.

Process will be restarted only when it can regain its old resources, as well as the new ones that it is requesting.

3. Circular Wait – impose a total ordering of all resource types, and require process requests resources in an increasing order of enumeration.

êDeadlock Avoidance

Requires that the system has a priori information available.

· Simplest model requires that each process declare the maximum number of

resources of each type that it may need.

· The deadlock-avoidance algorithm dynamically examines resource-allocation state to

ensure there is no circular-wait.

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 sequence <_P1, _P2, …, _Pn> of ALL processes

in the systems such that:

For each Pi , the resources that Pi can still request can be satisfied by currently available resources

+ resources held by all the Pj , with j < i

· If a system is in safe state Þ no deadlocks

· If a system is in unsafe state Þ possibility of deadlock

· Avoidance Þ ensure that a system will never enter an unsafe state.

Safe, Unsafe & Deadlock State

êAvoidance algorithms

v Resource-Allocation Graph Scheme:

(Used for Single instance of resource types)

Resources must be claimed a priori in the system.

· Claim edge P_i ® R_j indicated that process P_i 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

Resource-Allocation Graph

Unsafe State In Resource-Allocation Graph

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

v Banker’s Algorithm ( by Dijkstra)

(Used for Multiple instances of a resource type)

Each process must a priori claim maximum use.

o Data Structures

Let n = number of processes, and

m = number of resources types

ü Available: vector of length m.

If Available [j] = k, there are k instances of resource type R_j available

ü 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

ü Allocation: n x m matrix.

If Allocation [i,j] = k then P_i is currently allocated k instances of R_j

ü 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]

o 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 index i such that:

Finish [i] = false AND Need_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] == true for all i, then the system is in a safe state,

otherwise it is unsafe

The Algorithm requires m x n² operations to detect whether the system is in deadlocked state

o Resource-Request for a Process

Request = request vector for process P_i

If Request_i [j] = k then process P_i wants k instances of resource type R_j

· If Request_i > Need_i

Raise error condition, since process has exceeded its maximum claim.

· If Request_i > Available

P_i must wait, since resources are not available

· If Request_i <= Available

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 state is safe Þ the resources are allocated to Pi

· If state is unsafe Þ Pi must wait, and the old resource-allocation state is restored

o Example of Banker’s Algorithm

· 5 processes P₀ through P₄;

· 3 resource types:

A B C

10 5 7

Snapshot at time T₀:

Allocation Max Available

A B C A B C A B C

P₀ 0 1 0 7 5 3 3 3 2

P₁ 2 0 0 3 2 2

P₂ 3 0 2 9 0 2

P₃ 2 1 1 2 2 2

P₄ 0 0 2 4 3 3

· The content of the matrix Need is defined to be Max – Allocation

Need

A B C

P₀ 7 4 3

P₁ 1 2 2

P₂ 6 0 0

P₃ 0 1 1

P₄ 4 3 1

· The system is in a safe state since the sequence < P₁, P₃, P₄, P₂, P₀> satisfies safety criteria

Example:

P₁ Request (1,0,2)

· Check that Request £ Available that is, (1,0,2) £ (3,3,2) Þ true

Allocation Need Available

A B C A B C A B C

P₀ 0 1 0 7 4 3 2 3 0

P₁ 3 0 2 0 2 0

P₂ 3 0 1 6 0 0

P₃ 2 1 1 0 1 1

P₄ 0 0 2 4 3 1

· Executing safety algorithm shows that sequence < P₁, P₃, P₄, P₀, P₂> satisfies safety requirement

êDeadlock Detection

Allow system to enter deadlock state then: Detect & Recover.

o Single Instance of Each Resource Type

· Maintain wait-for graph

o Nodes are processes

o 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 n² operations,

where n is the number of vertices in the graph

Resource-Allocation Graph & Wait-for Graph

Resource-Allocation Graph Corresponding wait-for graph

o Several Instances of a Resource Type

ü Available: A vector of length m indicates the number of available resources of each type.

ü Allocation: An n x m matrix defines the number of resources of each type currently allocated to each process.

ü 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.

Detection Algorithm

1. Let Work and Finish be vectors of length m and n, respectively

Initialize:

Work = Available

For i = 1,2, …, n: if Allocation_i ¹ 0, then Finish[i] = false; else Finish[i] = true

2. Find an index i such that both:

Finish[i] == false AND 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 deadlock state.

and P_i is deadlocked

The Algorithm requires m x n² operations to detect whether the system is in deadlocked state

Example of Detection Algorithm

· Five processes P₀ through P₄;

· Three resource types
A B C

7 2 6

Snapshot at time T₀:

Allocation Request Available

A B C A B C A B C

P₀ 0 1 0 0 0 0 0 0 0

P₁ 2 0 0 2 0 2

P₂ 3 0 3 0 0 0

P₃ 2 1 1 1 0 0

P₄ 0 0 2 0 0 2

System is not deadlocked, sequence <P₀, P₂, P₃, P₁, P₄> will result in Finish[i] = true for all i

P₂ requests an additional 1 instance of type C

Request

A B C

P₀ 0 0 0

P₁ 2 0 2

P₂ 0 0 1

P₃ 1 0 0

P₄ 0 0 2

· 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

êRecovery from Deadlock:

Options:

· Abort all deadlocked processes

· Abort one process at a time until the deadlock cycle is eliminated

· In which order should we choose to abort?

o Priority of the process

o How long process has computed, and how much longer to completion

o Resources the process has used

o Resources process needs to complete

o How many processes will need to be terminated

o Is process interactive or batch?

· Selecting a victim to minimize cost

· Rollback – return to some safe state, restart process from that state

· Starvation – same process may always be picked as victim, include number of rollback in cost factor