Operating Systems - CS604 Power Point Slides Lecture 28

Operating Systems

Lecture 28Syed Mansoor Sarwar

January 27, 2016 Copyright Virtual University of Pakistan

Agenda for TodayReview of previous lectureDeadlock avoidanceBankers algorithmsSafety algorithmSafe SequenceRecap of lecture


Review of Lecture 27Deadlock handlingDeadlock preventionDeadlock avoidance


RAG AlgorithmClaim edge Pi Rj indicates

that process Pi may request an instance of resource Rj; represented by a dashed line.

Claim edge converts to request edge when a process requests a resource.


When a resource is assigned to a process, request edge reconverts to an assignment edge.

When a resource is released by a process, assignment edge reconverts to a claim edge.

Resources must be claimed a priori in the system.

RAG Algorithm


RAG For Deadlock Avoidance


Unsafe State In RAG


Bankers 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 for the Bankers Algorithm

n = number of processesm = number of resource typesAvailable: 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 = AvailableFinish[i] = false; i = 1, 2, , n.


Safety Algorithm2. 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 + AllocationiFinish[i] = truego to step 2.

4. If Finish [i] == true for all i, then the system is in a safe state.

Safety Algorithm


Requesti = request vector for Pi. If Requesti [j] = k then process Pi

wants k instances of resource type Rj.

1. If Requesti Needi go to step 2. Otherwise, report error since process has exceeded its maximum claim.

Resource-Request Algorithm for Pi



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 Requestj;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 System

Five processes: P0 P4 Three resource types: A (10 instances)B (5 instances)C (7 instances)


Example System

Process

P0P1P2P3P4

AvailableA B C3 3 2

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

MaxA B C7 5 33 2 29 0 22 2 24 3 3

System state: Is it safe?


Needi = Maxi AllocationiNeed matrix

Process A B CP0 7 4 3P1 1 2 2P2 6 0 0P3 0 1 1P4 4 3 1

Example System


Safe Sequence:

Process

P0P1P2P3P4

WorkA B C3 3 2

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1

Example System


Process

P0P1P2P3P4

WorkA B C3 3 25 3 2

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1

Safe Sequence: < P1>

Example System


Process

P0P1P2P3P4

WorkA B C3 3 25 3 27 4 3

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1

Safe Sequence: < P1, P3>

Example System


Process

P0P1P2P3P4

WorkA B C3 3 25 3 27 4 37 4 5

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1

Safe Sequence: < P1, P3, P4 >

Example System


Process

P0P1P2P3P4

WorkA B C3 3 25 3 27 4 37 4 57 5 5

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1

Safe Sequence:

Example System


Final safe sequence:

Not a unique sequence Possible safe sequences for the this

example:, , , , ,

Example System


Example P1 requests (1,0,2). Can this

request be granted immediately?

1. Is Request1 Need1? (1,0,2) (1,2,2) true

2. Is Request1 Available? (1,0,2) (3,3,2) true


Example

Process

P0P1P2P3P4

AvailableA B C3 3 2

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1


Safe Sequence:

Example

Process

P0P1P2P3P4

WorkA B C2 3 0

AllocationA B C0 1 03 0 23 0 22 1 10 0 2

NeedA B C7 4 30 2 06 0 00 1 14 3 1


Example

Process

P0P1P2P3P4

WorkA B C2 3 05 3 2

AllocationA B C0 1 03 0 23 0 22 1 10 0 2

NeedA B C7 4 30 2 06 0 00 1 14 3 1

Safe Sequence: < P1 >


Example

Process

P0P1P2P3P4

WorkA B C2 3 05 3 27 4 3

AllocationA B C0 1 03 0 23 0 22 1 10 0 2

NeedA B C7 4 30 2 06 0 00 1 14 3 1

Safe Sequence: < P1, P3 >


Example

Process

P0P1P2P3P4

WorkA B C2 3 05 3 27 4 37 4 5

AllocationA B C0 1 03 0 23 0 22 1 10 0 2

NeedA B C7 4 30 2 06 0 00 1 14 3 1

Safe Sequence: < P1, P3, P4 >


Example

Process

P0P1P2P3P4

WorkA B C2 3 05 3 27 4 37 4 57 4 5

AllocationA B C0 1 03 0 23 0 22 1 10 0 2

NeedA B C7 4 30 2 06 0 00 1 14 3 1

Safe Sequence:


Executing safety algorithm shows that sequence satisfies safety requirement.

Yes, P1s request may be granted immediately.

Example


Can request for (0,2,0) by P0 be granted?

1. Is Request0 Need0? (0,2,0) (7,4,3) true

2. Is Request1 Available? (0,2,0) (3,3,2) true

More Examples


Example

Process

P0P1P2P3P4

AvailableA B C3 3 2

AllocationA B C0 1 02 0 03 0 22 1 10 0 2

NeedA B C7 4 31 2 26 0 00 1 14 3 1


Safe Sequence:

Example

Process

P0P1P2P3P4

WorkA B C3 1 2

AllocationA B C0 3 02 0 03 0 22 1 10 0 2

NeedA B C7 2 31 2 26 0 00 1 14 3 1


Safe Sequence: < P3 >

Example

Process

P0P1P2P3P4

WorkA B C3 1 25 2 3

AllocationA B C0 3 02 0 03 0 22 1 10 0 2

NeedA B C7 2 31 2 26 0 00 1 14 3 1


Safe Sequence: < P3,P1 >

Example

Process

P0P1P2P3P4

WorkA B C3 1 25 2 37 2 3

AllocationA B C0 3 02 0 03 0 22 1 10 0 2

NeedA B C7 2 31 2 26 0 00 1 14 3 1


Safe Sequence: < P3,P1,P2 >

Example

Process

P0P1P2P3P4

WorkA B C3 1 25 2 37 2 3

10 2 5

AllocationA B C0 3 02 0 03 0 22 1 10 0 2

NeedA B C7 2 31 2 26 0 00 1 14 3 1


Safe Sequence:

Example

Process

P0P1P2P3P4

WorkA B C3 1 25 2 37 2 3

10 2 510 5 5

AllocationA B C0 3 02 0 03 0 22 1 10 0 2

NeedA B C7 2 31 2 26 0 00 1 14 3 1


Executing safety algorithm shows that sequence satisfies safety requirement.

Yes, P0s request may be granted immediately.

Example


Can request for (3,3,0) by P4 be granted?

Do it yourself!

More Examples


Recap of Lecture

Deadlock avoidance Bankers algorithm Safety algorithm Safe state Safe sequence

Operating Systems

Lecture 28Syed Mansoor Sarwar

Operating SystemsSlide 2Slide 3Slide 4Slide 5Slide 6Slide 7Bankers AlgorithmData Structures for the Bankers AlgorithmSlide 10Slide 11Safety AlgorithmSlide 13Slide 14Resource-Request Algorithm for PiSlide 16Slide 17Example SystemSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26ExampleSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34More ExamplesSlide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43Slide 44Slide 45

Operating Systems - CS604 Power Point Slides Lecture 28

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