APznzaZenBvMrFxaXzEJxdrVUNNyE0fr00QtsSxUlaP4S8BlbdSE_Orvlh8uM-L7GkOENfMiqmxPmFCZrasYhForPFDqQ2YJiGbKwP884VNUmLPA1EBFgyHxL1RBHz8Hmn9N2iCGLGwKybDvLHNzRvFnCJFma3rNajyukK5QLLo85-u.pdf

7.2 Silberschatz, Galvin and Gagne ©2005
Operating System Concepts - 7th
Edition, Feb 14, 2005
Chapter 7: Deadlocks
● The Deadlock Problem
● System Model
● Deadlock Characterization
● Methods for Handling Deadlocks
● Deadlock Prevention
● Deadlock Avoidance
● Deadlock Detection
● Recovery from Deadlock

Chapter Objectives
● To develop a description of deadlocks, which prevent sets of
concurrent processes from completing their tasks
● To present a number of different methods for preventing or
avoiding deadlocks in a computer system.

The Deadlock Problem
● A set of blocked processes each holding a resource and waiting to
acquire a resource held by another process in the set.
● Example
● System has 2 disk drives.
● P1
and P2
each hold one disk drive and each needs another one.
● Example
● semaphores A and B, initialized to 1
P0
P1
wait (A); wait(B)
wait (B); wait(A)

Bridge Crossing Example
● Traffic only in one direction.
● Each section of a bridge can be viewed as a resource.
● If a deadlock occurs, it can be resolved if one car backs up
(preempt resources and rollback).
● Several cars may have to be backed up if a deadlock occurs.
● Starvation is possible.

System Model
● Resource types R1
, R2
, . . ., Rm
CPU cycles, memory space, I/O devices
● Each resource type Ri
has Wi
instances.
● Each process utilizes a resource as follows:
● request
● use
● release

Deadlock Characterization
● Mutual exclusion: only one process at a time can use a resource.
● Hold and wait: a process holding at least one resource is waiting
to acquire additional resources held by other processes.
● No preemption: a resource can be released only voluntarily by
the process holding it, after that process 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 P0
is waiting for a resource that is held by P0
.
Deadlock can arise if four conditions hold simultaneously.

Resource-Allocation Graph
● 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
A set of vertices V and a set of edges E.

Resource-Allocation Graph (Cont.)
● Process
● Resource Type with 4 instances
● Pi
requests instance of Rj
● Pi
is holding an instance of Rj
P
i
P
i
Rj
Rj

Example of a Resource Allocation Graph

Resource Allocation Graph With A Deadlock

Graph With A Cycle But No Deadlock

Basic Facts
● 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.

Methods for Handling Deadlocks
● Ensure that the system will never enter a deadlock state.
● Allow the system to enter a deadlock state and then recover.
● Ignore the problem and pretend that deadlocks never occur in the
system; used by most operating systems, including UNIX.

Deadlock Prevention
● Mutual Exclusion – not required for sharable resources; must
hold for nonsharable resources.
● Hold and Wait – must guarantee that whenever a process
requests a resource, it does not hold any other resources.
● Require process to request and be allocated all its resources
before it begins execution, or allow process to request
resources only when the process has none.
● Low resource utilization; starvation possible.
Restrain the ways request can be made.

Deadlock Prevention (Cont.)
● No Preemption –
● If a process that is holding some resources requests another
resource that cannot be immediately allocated to it, then all
resources currently being held are released.
● Preempted resources are added to the list of resources for which
the process is waiting.
● Process will be restarted only when it can regain its old
resources, as well as the new ones that it is requesting.
● Circular Wait – impose a total ordering of all resource types, and
require that each process requests resources in an increasing order of
enumeration.

Deadlock Avoidance
● 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.
Requires that the system has some additional a priori information
available.

Safe State
● When a process requests an available resource, system must decide if
immediate allocation leaves the system in a safe state.
● System is in safe state if there exists a sequence <P1
, P2
, …, Pn
> of ALL
the processes is the systems such that for each Pi
, the resources that Pi
can still request can be satisfied by currently available resources +
resources held by all the Pj
, with j < i.
● That is:
● If Pi
resource needs are not immediately available, then Pi
can wait
until all Pj
have finished.
● When Pj
is finished, Pi
can obtain needed resources, execute, return
allocated resources, and terminate.
● When Pi
terminates, Pi +1
can obtain its needed resources, and so on.

Basic Facts
● 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.

Safe, Unsafe , Deadlock State

Avoidance algorithms
● Single instance of a resource type. Use a resource-allocation
graph
● Multiple instances of a resource type. Use the banker’s algorithm

Resource-Allocation Graph Scheme
● 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.
● Request edge converted to an assignment edge when the resource
is allocated to the process.
● 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

Unsafe State In Resource-Allocation Graph

Resource-Allocation Graph Algorithm
● Suppose that process Pi
requests a resource Rj
● The request can be granted only if converting the request
edge to an assignment edge does not result in the formation
of a cycle in the 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 = 0, 1, …, n- 1.
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 + Allocationi
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 Requesti
[j] = k then process
Pi
wants k instances of resource type Rj.
1. If Requesti
≤ Needi
go to step 2. Otherwise, raise error condition,
since process has exceeded its maximum claim.
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 – Request;
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 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 Available
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

Example (Cont.)
● 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.

Example: P1
Request (1,0,2)
● 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. If there is a cycle, there exists a deadlock.
● 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 Allocationi
≠ 0, then
Finish[i] = false;otherwise, Finish[i] = true.
2. Find an index i such that both:
(a)Finish[i] == false
(b)Requesti
≤ Work
If no such i exists, go to step 4.

Detection Algorithm (Cont.)
3. Work = Work + Allocationi
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.

Example (Cont.)
● 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:
● How often a deadlock is likely to occur?
● How many processes will need to be rolled back?
4 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.

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 for that state.
● Starvation – same process may always be picked as victim, include
number of rollback in cost factor.

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