2.) All Graphs in Chapter 8 (Deadlock) with their explanation

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

EXPLANATION:
A set of vertices V and a set of edges E.
● V is partitioned into two types:
- P = {P1, P2, …, Pn}, the set consisting of all the processes in the system.
- R = {R1, R2, …, Rm}, the set consisting of all resource types in the system.
● request edge – directed edge P1  Rj
● assignment edge – directed edge Rj  Pi
----
● Process
● Resource Type with 4 instances
● Pi requests instance of Rj
● Pi is holding an instance of Rj

● The Resource Allocation Graph (RAG) above is composed of 3 processes and four resources.
● R1 or resource 1 is composed of only one instance
● R2 has 2 instances
● R3 has one instance
● R4 has 3 instances
● P1 requests instance of R1
● P2 is holding an instance of R1
● P2 requests instance of R3
● P3 holds an instance of R3
● There is no deadlock found

------------------------

Resource Allocation Graph With A Deadlock

EXPLANATION:
If graph contains a cycle
=> if only one instance per resource type, then deadlock.
=> if several instances per resource type, possibility of deadlock.

● The Resource Allocation Graph (RAG) above is composed of 3 processes and four resources.
● R1 or resource 1 is composed of only one instance
● R2 has 2 instances
● R3 has one instance
● R4 has 3 instances
● P1 requests instance of R1
● P2 is holding an instance of R1
● P2 requests instance of R3
● P3 holds an instance of R3
● P3 requests an instance of R1
● There is deadlock based of the RAG no. 2 because all of the instances of R2 are held by the P1 and P2, then P3 is requesting for instances of R2. R2 cannot give any instances to P3 that is why a deadlock occurred.

------------------------

Resource Allocation Graph With A Cycle But No Deadlock

EXPLANATION:
If graph contains no cycles => no deadlock.

● The Resource Allocation Graph (RAG) above is composed of4 processes and 2 resources.
● R1 and R2 has composed of 2 instances
● P1 requests instance of R1
● P2 is holding an instance of R1
● P3 also holds an instance of R1
● P3 requests an instance of R2
● P4 holds an instance of R2
● P1 also holds an instance of R2
● There is no deadlock.

------------------------

Safe, Unsafe , Deadlock State

EXPLANATION:
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.

------------------------

Resource-Allocation Graph For Deadlock Avoidance

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

● The Resource Allocation Graph (RAG) above is composed of 2 processes and 2 resources.
● P1 holds an instance of R1
● P2 requests an instance of R1
● P1 and P2 may request an instance of R2

------------------------

Unsafe State In Resource-Allocation Graph

EXPLANATION:
● Basic fact:
If a system is in unsafe state => possibility of deadlock.
● The RAG above is compose of 2 resources and 2 processes
● P1 holds an instance of R1
● P2 is requesting an instance of R1
● P2 holds an instance of R2
● P1 may request an instance of R2

------------------------

Resource-Allocation Graph and Wait-for Graph

EXPLANATION:
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 n^2 operations, where n is the number of vertices in the 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.

additional...
A Wait-For Graph in computer science is a directed graph used for deadlock detection in operating systems and relational database systems.
In Computer Science, a system that allows concurrent operation of multiple processes and locking of resources and which does not provide mechanisms to avoid or prevent deadlock must support a mechanism to detect deadlocks and an algorithm for recovering from them.
One such deadlock detection algorithm makes use of a Wait-For Graph to track which other processes a process is currently blocking on. In a Wait-for Graph, processes are represented as nodes, and an edge from process Pi to Pj implies Pj is holding a resource that Pi needs and thus Pi is waiting for Pj to release its lock on that resource.

1.) Resource Allocation Graph

Example of a Resource Allocation Graph


Resource Allocation Graph With A Deadlock


Resource Allocation Graph With A Cycle But No Deadlock


Resource-Allocation Graph For Deadlock Avoidance


Unsafe State In Resource-Allocation Graph


Resource-Allocation Graph and Wait-for Graph


Resource-Allocation Graph
● Process


● Resource Type with 4 instances


● Pi requests instance of Rj


● Pi is holding an instance of Rj


---------------------------------

QUESTION:
=>How would you know if there's a DEADLOCK based on the resource allocation graph?

ANSWER:
If graph contains no cycles => no deadlock.
If graph contains a cycle
=> if only one instance per resource type, then deadlock (meaning if the cycle goes on a single path, it will result to a DEALOCK).
=> if several instances per resource type, possibility of deadlock (meaning if the resource allocation graph has several cycles it has a POSSIBILITY for DEADLOCK).

Recovery from Deadlock

Recovery from Deadlock: Process Termination
• Abort all deadlocked processes.
• Abort one process at a time until the deadlock cycle is eliminated.
• In which order should we choose to abort?
– Priority of the process.
– How long process has computed, and how much longer to completion.
– Resources the process has used.
– Resources process needs to complete.
– How many processes will need to be terminated.
– Is process interactive or batch?

Recovery from Deadlock: Resource Preemption
• Selecting a victim – minimize cost
• Rollback – return to some safe state, restart process from that state
– Require the system to keep more information about the state of all the running processes
• Starvation – same process may always be picked as victim, include number of rollback in cost factor

Deadlock Detection

Overview
• Allow system to enter a deadlock state
• Detection algorithm: examine the system state to determine whether a deadlock has occurred
• Recovery scheme: recover from the deadlock

Single Instance of Each Resource Type
• Maintain wait-for graph
– Nodes are processes.
– This graph is obtained from the resource-allocation graph by removing the nodes of type resource and collapsing the appropriate edges
– 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


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 [i,j] = k, then process Pi is requesting k more instances of resource type Rj

Combined Approach to Deadlock Handling
• Combine the three basic approaches
– Prevention
– Avoidance
– Detection
• Allowing the use of the optimal approach for each of resources in the system
• Partition resources into hierarchically ordered classes.
• Use most appropriate technique for handling deadlocks within each class
• Group resources into a number of different resource classes
• Use the linear ordering strategy defined previously for the prevention of circular wait to prevent deadlocks between resource classes
• Within a resource class, use the algorithm that is most appropriate for that class
• Swappable space
Hold-and-Wait prevention strategy + avoidance
• Process resources: Assignable devices such as tape drives, files…
Avoidance + Resource ordering
• Main memory: assignable in pages or segments
Preemption
• Internal resources: PCB, I/O channels…
Resource ordering

Deadlock Prevention

Ensure that at least one of the necessary conditions cannot hold
Prevent deadlocks by constraining how requests for resources can be made

• 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.
– Method 1: require each process to request and be allocated all its resources before it begins execution
– Method 2: allow a process to request resources only when the process has none
– Example: copy data from tape drive to disk file, sort disk file, print
Disadvantage
• Low resource utilization
• Starvation possible
• No Preemption – if process A holding resources requests another resource that cannot be immediately allocated to it
– Method 1: All resources currently being held by A are preempted
• Preempted resources are added to A’s waiting resource list
• A will be restarted only when it can regain its old resources, as well as the new ones that it is requesting.
– Method 2: Check the requested resources for following conditions
• If it is allocated to a process waiting for additional resources, preempt it from the waiting process and allocate it to A
• If it is held by a process not waiting, A must wait
– A’s resources may be preempted, but only if another process requests them

Often applied to resources whose state can be easily saved and restored later, such as CPU registers and memory space

• Circular Wait – impose a total ordering of all resource types
– Example: F(tape drive) = 1, F(disk drive) = 5, F(Printer) = 12
• F is defined according to the normal order of resource usage
– Method 1: require that each process requests resources in an increasing order of enumeration
• OK if tape drive  disk drive  Printer
• Not OK if disk drive  tape drive  Printer
– Method 2: Whenever a process requests an instance of Rj, it has released any resources Ri such that F(Ri) > F(Rj)

Methods for Handling Deadlock

Methods for Handling Deadlocks
• Use a protocol to prevent or avoid deadlocks, ensuring that the system will never enter a deadlock state
– Deadlock prevention
– Deadlock avoidance
• Allow the system to enter a deadlock state, detect it and then recover
• Ignore the problem and pretend that deadlocks never occur in the system
– Used by most operating systems, including UNIX
– The undetected deadlock will result in the deterioration of the system performance. Eventually, the system will stop functioning and will need to be restarted manually

Deadlock Characterization

Necessary Conditions
• Mutual exclusion: At least one resource must be held in a non-sharable mode
• Hold and wait: a process holding at least one resource is waiting to acquire additional resources held by others
• No preemption: a resource can be released only voluntarily by the process holding it, after it has completed its task
• Circular wait: there exists a set {P0, P1, …, P0} of waiting processes such that P0 is waiting for a resource that is held by P1, P1 is waiting for a resource that is held by P2, …, Pn–1 is waiting for a resource that is held by Pn, and Pn is waiting for a resource that is held by P0.

Deadlock can arise if four conditions hold simultaneously.

Resource-Allocation Graph
• A set of vertices V and a set of edges E.
• V is partitioned into two types:
– P = {P1, P2, …, Pn} (All processes in the system)
– R = {R1, R2, …, Rm} (All resources in the system)
• Two kinds of edges
– Request edge – directed edge P1  Rj
– Assignment edge – directed edge Rj  Pi

continuation..
• Process

• Resource Type with 4 instances

• Pi requests instance of Rj

• Pi is holding an instance of Rj

Example of a Resource Allocation Graph


Resource Allocation Graph With A Cycle But No Deadlock


RAG And Deadlock
• If graph contains no cycles  no deadlock.
• If graph contains a cycle 
– If only one instance per resource type, then deadlock.
– If several instances per resource type, possibility of deadlock.