A deadlock is a situation in which two computer programs sharing the same resource are effectively preventing each other from accessing the resource, resulting in both programs ceasing to function.

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How to avoid Deadlocks

Deadlocks can be avoided by avoiding at least one of the four conditions, because all this four conditions are required simultaneously to cause deadlock.

  1. Mutual ExclusionResources shared such as read-only files do not lead to deadlocks but resources, such as printers and tape drives, requires exclusive access by a single process.
  2. Hold and WaitIn this condition processes must be prevented from holding one or more resources while simultaneously waiting for one or more others.
  3. No PreemptionPreemption of process resource allocations can avoid the condition of deadlocks, where ever possible.
  4. Circular WaitCircular wait can be avoided if we number all resources, and require that processes request resources only in strictly increasing(or decreasing) order.

Resource-Allocation Graph

  • In some cases deadlocks can be understood more clearly through the use of Resource-Allocation Graphs, having the following properties:
    • A set of resource categories, { R1, R2, R3, . . ., RN }, which appear as square nodes on the graph. Dots inside the resource nodes indicate specific instances of the resource. ( E.g. two dots might represent two laser printers. )
    • A set of processes, { P1, P2, P3, . . ., PN }
    • Request Edges – A set of directed arcs from Pi to Rj, indicating that process Pi has requested Rj, and is currently waiting for that resource to become available.
    • Assignment Edges – A set of directed arcs from Rj to Pi indicating that resource Rj has been allocated to process Pi, and that Pi is currently holding resource Rj.
    • Note that a request edge can be converted into an assignment edge by reversing the direction of the arc when the request is granted. ( However note also that request edges point to the category box, whereas assignment edges emanate from a particular instance dot within the box. )

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

Mutual Exclusion – not required for sharable resources; 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  sources before it begins execution, or allow process to request resources only when the process has none. Low resource utilization; starvation possible. Restrain the ways request can be made.

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

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.

Requires that the system has some additional a priori information available.

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 currently available resources + resources held by all the Pj, with j<I.

  1. If Pi resource needs are not immediately available, then Pi can wait until all Pj have finished.
  2. When Pj is finished, Pi can obtain needed resources, execute, return allocated resources, and  


  1. 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       

Resource-Allocation Graph Algorithm

Claim edge Pi Rj indicated that process Pj may request resource Rj; represented by a dashed     


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.

Resource-Allocation Graph For Deadlock Avoidance



Unsafe State In 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

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.

Safety Algorithm

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

       Work = Available

       Finish [i] = false for i – 1,3, …, n.

  1. Find and i such that both:

        (a)   Finish [i] = false

        (b)  Needi Work

       If no such i exists, go to step 4.

  1. Work = Work + Allocation i

       Finish [i] = true

       go to step 2.

  1. 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 Request i [j] = k

then process Pi wants k instances of resource type Rj.

  1. If Request i Need i go to step 2. Otherwise, raise  error condition, since process has

         exceeded its maximum claim.

  1. If Request i Available, go to step 3. Otherwise Pi must  wait, since resources are not available.
  2. 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;;

  • 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 Availabl

               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.


               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.

Check that Request ≤ Available (that is, (1,0,2) ≤ (3,3,2) _ 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.

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.

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 Allocation i ≠ 0, then

      Finish [i] = false; otherwise, Finish [i] = true.

  1. Find an index i such that both:

                (a) Finish [i] == false

                (b) Request i Work

          If no such i exists, go to step 4.

  1. Work = Work + Allocation i

             Finish [i] = true

             go to step 2.

  1. 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

            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

Sequence <P0, P2, P3, P1, P4> will result in Finish [i] = true for all i.

P2 requests an additional instance of type C.


           A      B     C

             P0     0       0      0

             P1     2       0      1

            P2      0       0      1

            P3      1       0      0

            P4      0       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.

Detection-Algorithm Usage

When, and how often, to invoke depends on:

  1. How often a deadlock is likely to occur?
  2. How many processes will need to be rolled back?
  3. 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.