Safe, Unsafe , Deadlock 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

line.

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.

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 + 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.

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.

2. If Request i ≤ 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 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.

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.

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.

2. Find an index i such that both:

(a) Finish [i] == false

(b) 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.

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.

Request

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.