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Solution of CS604 Assignment no 3:

Question:

a. Consider a system with five processes: P₁, P₂, P₃, P₄, P₅and four resource types: R₁, R₂, R₃, R₄ with single instance. From the given below information, you are required to determine whether the deadlock exists in the system though deadlock detection strategy for resources with single instance.

P = {P₁, P₂, P₃, P₄, P₅}

R = {R₁, R₂, R₃, R₄}

E = {P₁®R₁, R₁®P₂, P₂®R₂, R₂®P₃, P₃®R₃, R₃®P₄, P₄®R₄, R₄®P₅, P₅®R₅, R₅®P₁}           

b. Consider a system with five processes: P₁, P₂, P₃, P₄, P₅ and four resource types: R1, R2, R3 and R4 with multiple instances. From the given below information, you are required to determine whether the deadlock occurs in a system though deadlock detection strategy for resources with multiple instances.

P = {P₁, P₂, P₃, P₄, P₅}

R = {R₁, R₂, R₃, R₄}

R1: 5 instances

R2: 3 instances

R3: 2 instances

R4: 4 instances

Consider the system in following state:

Processes	Allocation				Request				Work
	R1	R2	R3	R4	R1	R2	R3	R4	R1	R2	R3	R4
P1	0	0	0	0	0	1	0	0	0	0	1	1
P2	0	1	0	1	0	0	1	1
P3	2	0	0	2	0	0	1	1
P4	1	1	0	0	2	1	2	0
P5	2	1	1	0	1	0	0	1

Note: There can be many sequences so you are required to start from top to bottom for “Processes” column. i.e. P₁ to P₅.

Solution:

a)

P = {P₁, P₂, P₃, P₄, P₅}

R = {R₁, R₂, R₃, R₄}

E = {P₁®R₁, R₁®P₂, P₂®R₂, R₂®P₃, P₃®R₃, R₃®P₄, P₄®R₄, R₄®P₅, P₅®R₅, R₅®P₁}           

****Image is in File below****

Deadlock Detection:

Single instance of each resource type

A deadlock exists in the system if and only if the wait for graph contains a cycle. To detect deadlocks the system needs to maintain the wait-for graph and periodically to invoke algorithm that searches for a cycle in the graph.

b)

R1:5 instances, R2:3instances, R3:2instances, R4:4instances

Processes	Allocation				Request				Work
	R1	R2	R3	R4	R1	R2	R3	R4	R1	R2	R3	R4
P1	0	0	0	0	0	1	0	0	0	0	1	1
P2	0	1	0	1	0	0	1	1	0	1	1	2
P3	2	0	0	2	0	0	1	1	2	1	1	4
P4	1	1	0	0	2	1	2	0
P5	2	1	1	0	1	0	0	1	4	2	2	4

After execution in system:

Processes	Allocation				Request				Work
	R1	R2	R3	R4	R1	R2	R3	R4	R1	R2	R3	R4
P1	0	0	0	0	0	1	0	0	4	2	2	4
P2	0	1	0	1	0	0	1	1	0	1	1	2
P3	2	0	0	2	0	0	1	1	2	1	1	4
P4	1	1	0	0	2	1	2	0	5	3	2	4
P5	2	1	1	0	1	0	0	1	4	2	2	4

Possible Processes are:

< P2, P3, P5, P1, P4 >

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