Operating System | Banker’s Algorithm

The banker’s algorithm is a resource allocation and deadlock avoidance algorithm that tests for safety by simulating the allocation for predetermined maximum possible amounts of all resources, then makes an “s-state” check to test for possible activities, before deciding whether allocation should be allowed to continue.

Following Data structures are used to implement the Banker’s Algorithm:

Let ‘n’ be the number of processes in the system and ‘m’ be the number of resources types.

Available : 

  • It is a 1-d array of size ‘m’ indicating the number of available resources of each type.
  • Available[ j ] = k means there are ‘k’ instances of resource type Rj

Max :

  • It is a 2-d array of size ‘n*m’ that defines the maximum demand of each process in a system.
  • Max[ i, j ] = k means process Pi may request at most ‘k’ instances of resource type Rj.

Allocation :

  • It is a 2-d array of size ‘n*m’ that defines the number of resources of each type currently allocated to each process.
  • Allocation[ i, j ] = k means process Pi is currently allocated ‘k’ instances of resource type Rj

Need :

  •  It is a 2-d array of size ‘n*m’ that indicates the remaining resource need of each process.
  • Need [ i,  j ] = k means process Pi currently allocated ‘k’ instances of resource type Rj
  • Need [ i,  j ] = Max [ i,  j ] – Allocation [ i,  j ]

Allocationi specifies the resources currently allocated to process Pi and Needi specifies the additional resources that process Pi may still request to complete its task.

Banker’s algorithm consist of Safety algorithm and Resource request algorithm

Safety Algorithm

The algorithm for finding out whether or not a system is in a safe state can be described as follows:

1) Let Work and Finish be vectors of length ‘m’ and ‘n’ respectively.
Initialize: Work = Available
Finish[i] = false; for i=1, 2, 3, 4….n

2) Find an i such that both
a) Finish[i] = false
b) Needi <= Work if no such i exists goto step (4)

3) Work = Work + Allocation
Finish[i] = true
goto step (2)

4) if finish [i] = true for all i
then the system is in a safe state

Resource-Request Algorithm

Let Requesti be the request array for process Pi. Requesti [j] = k means process Pi wants k instances of resource type Rj. When a request for resources is made by process Pi, the following actions are taken:

1) If Requesti <= Needi
Goto step (2) ; otherwise, raise an error condition, since the process has exceeded its maximum claim.

2) If Requesti <= Available Goto step (3); otherwise, Pi must wait, since the resources are not available.

3) Have the system pretend to have allocated the requested resources to process Pi by modifying the state as
Available = Available – Requesti
Allocationi = Allocationi + Requesti
Needi = Needi– Requesti


Considering a system with five processes P0 through P4 and three resources types A, B, C. Resource type A has 10 instances, B has 5 instances and type C has 7 instances. Suppose at time t0 following snapshot of the system has been taken:


Question1. What will be the content of the Need matrix?

Need [i, j] = Max [i, j] – Allocation [i, j]

So, the content of Need Matrix is:


Question2.  Is the system in safe state? If Yes, then what is the safe sequence?

Applying the Safety algorithm on the given system,


Question3. What will happen if process Prequests one additional instance of resource type A and two instances of resource type C?


We must determine whether this new system state is safe. To do so, we again execute Safety algorithm on the above data structures.


Hence the new system state is safe, so we can immediately grant the request for process  P1 .

GATE question:

Operating System Concepts 8th Edition by Abraham Silberschatz, Peter B. Galvin, Greg Gagne

This article has been contributed by Vikash Kumar. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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