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Chapter 8 · Final syllabus · Lectures 21–25

Deadlocks

The system model, the four necessary conditions, resource-allocation graphs, prevention, avoidance with safe states and the Banker’s algorithm, detection with wait-for graphs and the detection algorithm, and recovery by termination or preemption.

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Before we start

Why this matters

Two threads each hold one lock and wait for the other’s. Nothing crashes — everything just stops, forever.

A deadlock needs four conditions at once. Break any one and it cannot happen; or check every request so the system never gets close; or let it happen and clean up.

This chapter covers all three strategies, including the Banker’s algorithm you can run step by step.

Chapter 8 · Lectures 21–25

Outline

Select a topic to jump to the slide that explains it.

  1. System model
  2. Deadlock characterization
  3. Methods for handling deadlocks
  4. Deadlock prevention
  5. Deadlock avoidance
  6. Banker’s algorithm
  7. Deadlock detection
  8. Recovery from deadlock

System model

System model

  • System consists of resources
  • 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
request→use→release

Deadlock characterization

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 held by P1, P1 for one held by P2, …, Pn–1 for one held by Pn, and Pn for one held by P0

Deadlock characterization

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 Pi → Rj
  • assignment edge – directed edge Rj → Pi
SymbolMeaning
circleprocess
rectangle with dotsresource type with one dot per instance
Pi → RjPi requests an instance of Rj
Rj (dot) → PiPi holds an instance of Rj

Deadlock characterization

Resource allocation graph example

  • One instance of R1
  • Two instances of R2
  • One instance of R3
  • Three instances of R4
  • T1 holds one instance of R2 and is waiting for an instance of R1
  • T2 holds one instance of R1, one instance of R2, and is waiting for an instance of R3
  • T3 holds one instance of R3

Deadlock characterization

Resource allocation graph example (cont.)

Resource-allocation graph.

Deadlock characterization

Graphs with and without deadlock

With a deadlock: T3 also requests R2. Cycles T1 → R1 → T2 → R3 → T3 → R2 → T1 and T2 → R3 → T3 → R2 → T2.
A cycle but no deadlock: T1 → R1 → T3 → R2 → T1, but T2 and T4 can finish and release an instance each.

Deadlock characterization

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

Deadlock characterization

Basic facts (cont.)

Methods for handling deadlocks

Methods for handling deadlocks

  • Ensure that the system will never enter a deadlock state:
    • Deadlock prevention
    • Deadlock avoidance
  • Allow the system to enter a deadlock state and then recover
  • Ignore the problem and pretend that deadlocks never occur in the system.

Deadlock prevention

Deadlock prevention

Invalidate one of the four necessary conditions for deadlock:

  • Mutual exclusion – not required for sharable resources (e.g., read-only files); must hold for non-sharable 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 allocated to it.
    • Low resource utilization; starvation possible

Deadlock prevention

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 prevention

Circular wait

  • Invalidating the circular wait condition is most common.
  • Simply assign each resource (i.e., mutex locks) a unique number.
  • Resources must be acquired in order.
  • If: first_mutex = 1, second_mutex = 5, code for thread_two could not be written as follows:
/* thread_one runs in this function */
void *do_work_one(void *param)
{
   pthread_mutex_lock(&first_mutex);
   pthread_mutex_lock(&second_mutex);
   /** Do some work */
   pthread_mutex_unlock(&second_mutex);
   pthread_mutex_unlock(&first_mutex);
   pthread_exit(0);

Deadlock prevention

Circular wait (cont.)

}

/* thread_two runs in this function */
void *do_work_two(void *param)
{
   pthread_mutex_lock(&second_mutex);
   pthread_mutex_lock(&first_mutex);
   /** Do some work */
   pthread_mutex_unlock(&first_mutex);
   pthread_mutex_unlock(&second_mutex);
   pthread_exit(0);
}
If thread_one holds first_mutex and thread_two holds second_mutex, each waits for the other forever. Locking in increasing order (first, then second) in both threads removes the cycle.

Interactive

Step two threads into a deadlock

Code and output

The deadlock, for real

deadlock.c
#include <pthread.h>
#include <stdio.h>
#include <unistd.h>

pthread_mutex_t first_mutex  = PTHREAD_MUTEX_INITIALIZER;
pthread_mutex_t second_mutex = PTHREAD_MUTEX_INITIALIZER;

void *do_work_one(void *param)
{
    pthread_mutex_lock(&first_mutex);
    printf("thread_one: holds first_mutex, wants second_mutex\n");
    sleep(1);                                 /* let thread_two run */
    pthread_mutex_lock(&second_mutex);        /* blocks forever */
    printf("thread_one: got both\n");

Code and output

The deadlock, for real (cont.)

    return NULL;
}

void *do_work_two(void *param)
{
    pthread_mutex_lock(&second_mutex);
    printf("thread_two: holds second_mutex, wants first_mutex\n");
    sleep(1);
    pthread_mutex_lock(&first_mutex);         /* blocks forever */
    printf("thread_two: got both\n");
    return NULL;
}

int main(void)
{
    pthread_t one, two;

Code and output

The deadlock, for real (cont.)

    pthread_create(&one, NULL, do_work_one, NULL);
    pthread_create(&two, NULL, do_work_two, NULL);
    pthread_join(one, NULL);                  /* never returns: deadlock */
    pthread_join(two, NULL);
    printf("done\n");
    return 0;
}
Output
Terminal
$ gcc deadlock.c -o deadlock -pthread && ./deadlock
thread_one: holds first_mutex, wants second_mutex
thread_two: holds second_mutex, wants first_mutex
(no more output: both threads wait forever, the program never ends)

Each thread gets its first mutex, sleeps, then asks for the other one. Both wait forever: the program has to be killed. Locking both mutexes in the same order in both threads removes the circular wait.

Deadlock avoidance

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

Deadlock avoidance

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 in the system 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

Deadlock avoidance

Safe state (cont.)

  • 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 spaces.

Deadlock avoidance

Avoidance algorithms

Single instance of a resource type

Use a resource-allocation graph

Multiple instances of a resource type

Use the Banker’s algorithm

Deadlock avoidance

Resource-allocation graph scheme

  • 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
  • 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 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

Deadlock avoidance

Resource-allocation graph scheme (cont.)

Resource-allocation graph with claim edges.
Unsafe state: giving R2 to T2 creates a cycle with T1’s claim edge.

Banker’s algorithm

Banker’s algorithm

  • Multiple instances of resources
  • 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

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

Banker’s algorithm

Banker’s algorithm (cont.)

  • Available: vector of length m. If Available[j] = k, there are k instances of resource type Rj available
  • Max: n × m matrix. If Max[i, j] = k, then process Pi may request at most k instances of resource type Rj
  • Allocation: n × m matrix. If Allocation[i, j] = k then Pi is currently allocated k instances of Rj
  • Need: n × 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]

Banker’s algorithm

Safety algorithm and resource-request algorithm

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) 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

Banker’s algorithm

Safety algorithm and resource-request algorithm (cont.)

Resource-request algorithm for process Pi

Requesti = 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 – Requesti;
    • 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

Banker’s algorithm

Example of Banker’s algorithm

  • 5 processes P0 through P4;
  • 3 resource types: A (10 instances), B (5 instances), and C (7 instances)
  • Snapshot at time T0:
Allocation
A B C		Max
A B C		Available
A B C
P00 1 07 5 33 3 2
P12 0 03 2 2
P23 0 29 0 2
P32 1 12 2 2
P40 0 24 3 3

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

Need
A B C
P07 4 3
P11 2 2
P26 0 0
P30 1 1
P44 3 1
The system is in a safe state since the sequence <P1, P3, P4, P0, P2> satisfies safety criteria

Banker’s algorithm

Example: P1 requests (1, 0, 2)

  • Check that Request ≤ Available (that is, (1, 0, 2) ≤ (3, 3, 2) → true)
Allocation
A B C		Need
A B C		Available
A B C
P00 1 07 4 32 3 0
P13 0 20 2 0
P23 0 26 0 0
P32 1 10 1 1
P40 0 24 3 1
  • 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?
Answer them with the tool on the next slide: choose the second snapshot, then press P4 (3, 3, 0) and P0 (0, 2, 0).

Interactive

Banker’s algorithm, step by step

Code and output

The safety algorithm in C

bankers.c
#include <stdbool.h>
#include <stdio.h>

#define N 5   /* processes */
#define M 3   /* resource types A, B, C */

int alloc[N][M] = {{0,1,0},{2,0,0},{3,0,2},{2,1,1},{0,0,2}};
int max[N][M]   = {{7,5,3},{3,2,2},{9,0,2},{2,2,2},{4,3,3}};
int avail[M]    = {3,3,2};

int main(void)
{
    int need[N][M], work[M], seq[N], count = 0;
    bool finish[N] = {false};

Code and output

The safety algorithm in C (cont.)

    for (int i = 0; i < N; i++)
        for (int j = 0; j < M; j++)
            need[i][j] = max[i][j] - alloc[i][j];   /* Need = Max - Allocation */
    for (int j = 0; j < M; j++) work[j] = avail[j]; /* Work = Available */

    for (int i = 0, idle = 0; idle < N; i = (i + 1) % N) {
        bool ok = !finish[i];
        for (int j = 0; ok && j < M; j++) ok = need[i][j] <= work[j];
        if (!ok) { idle++; continue; }
        for (int j = 0; j < M; j++) work[j] += alloc[i][j];
        finish[i] = true; seq[count++] = i; idle = 0;
        printf("P%d finishes, Work = (%d, %d, %d)\n", i, work[0], work[1], work[2]);
    }
    if (count == N) {

Code and output

The safety algorithm in C (cont.)

        printf("Safe. Safe sequence:");
        for (int k = 0; k < N; k++) printf(" P%d", seq[k]);
        printf("\n");
    } else printf("Unsafe state\n");
    return 0;
}
Output
Terminal
$ gcc bankers.c -o bankers -pthread && ./bankers
P1 finishes, Work = (5, 3, 2)
P3 finishes, Work = (7, 4, 3)
P4 finishes, Work = (7, 4, 5)
P0 finishes, Work = (7, 5, 5)
P2 finishes, Work = (10, 5, 7)
Safe. Safe sequence: P1 P3 P4 P0 P2

The same snapshot as the slides. The scan continues from the next process after each success, which gives the slide’s sequence <P1, P3, P4, P0, P2>.

Deadlock detection

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

Deadlock detection

Resource-allocation graph and wait-for graph

Remove the resource nodes and collapse the edges: Pi → Rq → Pj becomes Pi → Pj.

Deadlock detection

Several instances of a resource type

  • Available: a vector of length m indicates the number of available resources of each type
  • Allocation: an n × m matrix defines the number of resources of each type currently allocated to each process
  • Request: an n × 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

Deadlock detection

Several instances of a resource type (cont.)

  1. Find an index i such that both:
    • Finish[i] == false
    • Requesti ≤ Work
    • If no such i exists, go to step 4
  2. Work = Work + Allocationi; Finish[i] = true; go to step 2
  3. 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 × n2) operations to detect whether the system is in deadlocked state

Deadlock detection

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
A B C		Request
A B C		Available
A B C
P00 1 00 0 00 0 0
P12 0 02 0 2
P23 0 30 0 0
P32 1 11 0 0
P40 0 20 0 2

Deadlock detection

Example of detection algorithm (cont.)

  • 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

Deadlock detection

Example of detection algorithm (cont.)

Request
A B C
P00 0 0
P12 0 2
P20 0 1
P31 0 0
P40 0 2
  • 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

Interactive

Detection algorithm, step by step

Deadlock detection

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

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?

  1. Priority of the process
  2. How long process has computed, and how much longer to completion
  3. Resources the process has used
  4. Resources process needs to complete
  5. How many processes will need to be terminated
  6. Is process interactive or batch?

Recovery from deadlock

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 rollbacks in cost factor

Worked example 1 of 3

Worked example 1

Using the T0 snapshot, show step by step that <P1, P3, P4, P0, P2> is a safe sequence.
Show the solution
StepNeed ≤ Work?Work after
start(3, 3, 2)
P1(1, 2, 2) ≤ (3, 3, 2) ✓(5, 3, 2)
P3(0, 1, 1) ≤ (5, 3, 2) ✓(7, 4, 3)
P4(4, 3, 1) ≤ (7, 4, 3) ✓(7, 4, 5)
P0(7, 4, 3) ≤ (7, 4, 5) ✓(7, 5, 5)
P2(6, 0, 0) ≤ (7, 5, 5) ✓(10, 5, 7)

Every process can finish, so the state is safe. Work ends at the total (10, 5, 7).

Worked example 2 of 3

Worked example 2

After P1’s request (1, 0, 2) is granted, can P4’s request (3, 3, 0) and P0’s request (0, 2, 0) be granted?
Show the solution

P4 (3, 3, 0): Request ≤ Need (4, 3, 1) ✓, but Request ≤ Available (2, 3, 0)? 3 > 2 ✗ → P4 must wait; the resources are not available.

P0 (0, 2, 0): ≤ Need (7, 4, 3) ✓ and ≤ Available (2, 3, 0) ✓. Pretend: Available = (2, 1, 0), Need0 = (7, 2, 3). Safety: no process has Need ≤ (2, 1, 0) (P1 needs (0, 2, 0), P3 needs (0, 1, 1)), so the state is unsafe → P0 must wait and the old state is restored.

Worked example 3 of 3

Worked example 3

Why does the second detection example deadlock P1, P2, P3 and P4?
Show the solution

Work = (0, 0, 0). Only P0 requests nothing, so it finishes and Work = (0, 1, 0). Now P1 needs (2, 0, 2), P2 (0, 0, 1), P3 (1, 0, 0), P4 (0, 0, 2): none is ≤ (0, 1, 0). They can never finish, so all four are deadlocked.

Practice

Practice (1 of 2)

Try each one on paper first, then check your answer.

1. Name the four necessary conditions for deadlock.
Show the answer
Mutual exclusion, hold and wait, no preemption and circular wait — all four must hold simultaneously.
2. A resource-allocation graph has a cycle. Is there a deadlock?
Show the answer
If every resource type has only one instance, yes. If some have several instances, there may or may not be a deadlock.
3. How can hold and wait be prevented, and what is the cost?
Show the answer
Require a process to request all its resources before it starts, or to request only when it holds none. Resource utilization is low and starvation is possible.

Practice

Practice (2 of 2)

Try each one on paper first, then check your answer.

4. What is the most common prevention method, and how does it work?
Show the answer
Invalidating circular wait: number every resource type and require each process to request resources in increasing order.
5. Compute Need for P2 with Max (9, 0, 2) and Allocation (3, 0 ,2).
Show the answer
Need = Max − Allocation = (6, 0, 0).
6. Give three factors for choosing which deadlocked process to abort.
Show the answer
Any three of: priority; how long it has computed and how long it still needs; resources it has used; resources it needs to complete; how many processes must be terminated; interactive or batch.

Check yourself

Quiz

Resources

Further learning

Free material to go deeper. Links open in a new tab.

Free bookOSTEP: Common Concurrency Problems ↗Deadlock conditions, lock ordering and avoidance in real code.ArticleBanker’s algorithm ↗Safety and request algorithms with examples.ArticleDeadlock ↗The Coffman conditions and handling strategies.ArticleWait-for graph ↗Detecting deadlock with single-instance resources.ArticleDining philosophers problem ↗The classic deadlock puzzle and its solutions.Referencepthread_mutex_lock(3p) ↗The mutex calls used in the lock-ordering example.

Summary · End of Chapter 8

Summary

  • Processes request, use and release resources; deadlock needs mutual exclusion, hold and wait, no preemption and circular wait at once.
  • Resource-allocation graphs: no cycle → no deadlock; a cycle → deadlock with single instances, possible deadlock otherwise.
  • Prevention breaks a condition — most often circular wait, by acquiring resources in a fixed order.
  • Avoidance keeps the system in a safe state: the RAG algorithm with claim edges for single instances, the Banker’s algorithm (Need = Max − Allocation) for several.
  • Detection finds cycles in a wait-for graph or runs the detection algorithm with the Request matrix.
  • Recovery aborts processes or preempts resources, choosing victims by cost and avoiding starvation.
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