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Chapter 7: Deadlocks

The Deadlock Problem
System Model
Deadlock Characterization
Methods for Handling Deadlocks
Deadlock Prevention
Deadlock Avoidance
Deadlock Detection
Recovery from Deadlock

Operating System Concepts - 7 th Edition, Feb 14, 2005 7.2 Silberschatz, Galvin and Gagne

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
or avoiding deadlocks in a computer system.


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
System has 2 disk drives.
P1 and P2 each hold one disk drive and each needs another
one.
Example
semaphores A and B, initialized to 1

P0 P1
wait (A); wait(B)
wait (B); wait(A)


Bridge Crossing Example

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
CPU cycles, memory space, I/O devices
Each resource type Ri has Wi instances.
Each process utilizes a resource as follows:
request
use
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, …, 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 P0 is waiting for a resource that is held by P0.


Resource-Allocation Graph

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

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


Resource-Allocation Graph (Cont.)

Process

Resource Type with 4 instances

Pi requests instance of Rj

Pi
Rj
Pi is holding an instance of Rj

Pi
Rj


Example of a Resource Allocation
Graph


Resource Allocation Graph With A Deadlock


Graph With A Cycle But No Deadlock


Basic Facts

If graph contains no cycles ⇒ no deadlock.

If graph contains a cycle ⇒
if only one instance per resource type, then deadlock.
if several instances per resource type, possibility of
deadlock.


Methods for Handling Deadlocks

Ensure that the system will never enter a deadlock state.

Allow the system to enter a deadlock state and then
recover.

Ignore the problem and pretend that deadlocks never occur
in the system; used by most operating systems, including
UNIX.


Deadlock Prevention

Restrain the ways request 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.
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.
Low resource utilization; starvation possible.


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.
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 sequence <P1, P2, …, Pn>
of ALL the processes is 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.
That is:
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.
When Pi terminates, Pi +1 can obtain its needed resources, and
so on.


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.


Safe, Unsafe , Deadlock State


Avoidance algorithms

Single instance of a resource type. Use a resource-
allocation graph

Multiple instances of a resource type. Use the banker’s
algorithm


Resource-Allocation Graph Scheme

Claim edge Pi → Rj indicated that process Pj may request
resource Rj; 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.


Resource-Allocation Graph


Unsafe State In Resource-Allocation Graph


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


Banker’s Algorithm

Multiple instances.

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

Let n = number of processes, and m = number of resources types.

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].


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 and i such that both:
(a) Finish [i] = false
(b) Needi ≤ Work
If no such i exists, go to step 4.
3. Work = Work + Allocationi
Finish[i] = true
go to step 2.
4. If Finish [i] == true for all i, then the system is in a safe
state.


Resource-Request Algorithm for Process
Pi

Request = request vector for process Pi. If Requesti [j] = k then
process Pi wants k instances of resource type Rj.
1. If Requesti ≤ Needi go to step 2. Otherwise, raise error
condition, since process has exceeded its maximum claim.
2. If Requesti ≤ 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;
Allocationi = Allocationi + Requesti;
Needi = Needi – Requesti;
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 P0 through P4;
3 resource types:
A (10 instances), B (5instances), and C (7 instances).
Snapshot at time T0:
Allocation Max Available
ABC ABC ABC
P0 010 753 332
P1 200 322
P2 302 902
P3 211 222
P4 002 433


Example (Cont.)

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

Need
ABC
P0 743
P1 122
P2 600
P3 011
P4 431

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


Example: P 1 Request (1,0,2)

Check that Request ≤ Available (that is, (1,0,2) ≤ (3,3,2) ⇒ true.
Allocation Need Available
ABC ABC ABC
P0 010 743 230
P1 302 020
P2 301 600
P3 211 011
P4 002 431
Executing safety algorithm shows that sequence < P1, P3, P4, P0, P2>
satisfies safety requirement.
Can request for (3,3,0) by P4 be granted?
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

Maintain wait-for graph
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.


Resource-Allocation Graph and Wait-for
Graph

Resource-Allocation Graph Corresponding wait-for graph


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 [ij] = 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:
(a) Work = Available
(b) For i = 1,2, …, n, if Allocationi ≠ 0, then
Finish[i] = false;otherwise, Finish[i] = true.
2. Find an index i such that both:
(a) Finish[i] == false
(b) Requesti ≤ Work

If no such i exists, go to step 4.


Detection Algorithm (Cont.)

3. Work = Work + Allocationi
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 Pi is deadlocked.

Algorithm requires an order of O( 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 (7 instances), B (2 instances), and C (6 instances).
Snapshot at time T0:
Allocation Request Available
ABC ABC ABC
P0 010 000 000
P1 200 202
P2 303 000
P3 211 100
P4 002 002
Sequence <P0, P2, P3, P1, P4> will result in Finish[i] = true for all i.


Example (Cont.)

P2 requests an additional instance of type C.
Request
ABC
P0 000
P1 201
P2 001
P3 100
P4 002
State of system?
Can reclaim resources held by process P0, but insufficient
resources to fulfill other processes; requests.
Deadlock exists, consisting of processes P1, P2, P3, and P4.


Detection-Algorithm Usage

When, and how often, to invoke depends on:
How often a deadlock is likely to occur?
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

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?


Recovery from Deadlock: Resource
Preemption

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.


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