Outline

1
Outline

• Announcement
• Deadlock
• Deadlock definition - review
• Conditions for a deadlock to occur - review
• Deadlock prevention review
• Deadlock avoidance
• Deadlock detection and recovery

2
Announcement

• Homework 4
• Is due on Nov. 13, 2003
• Not on Nov. 11, 2003 (given in the handout)

3
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 tape drives, one CD-ROM and one DAT
  drive.
• P1 and P2 each hold one tape drive and each needs
  another one.

4
Two-process deadlock
5
Deadlock Examples cont.
6
Deadlock Examples cont.
7
Deadlock Characterization

• Deadlock can arise only if four conditions hold
  simultaneously
• Mutual exclusion
• Hold and wait
• No preemption
• Circular wait

8
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.

9
Deadlock Characterization

• 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, , Pn1 is waiting for a
  resource that is held by Pn, and P0 is waiting
  for a resource that is held by P0.

10
A Model

• P p1, p2, , pn be a set of processes
• R R1, R2, , Rm be a set of resources
• cj number of units of Rj in the system
• S S0, S1, be a set of states representing
  the assignment of Rj to pi
• State changes when processes take action
• This allows us to identify a deadlock situation
  in the operating system

11
Resources
Resource Anything that a process can request,
then be blocked because that thing is not
available.
R Rj 0 ? j lt m resource types C cj ? 0
? Rj?R (0 ? j lt m) units of Rj available
Reusable resource After a unit of the resource
has been allocated, it must ultimately be
released back to the system. E.g., CPU, primary
memory, disk space, The maximum value for cj is
the number of units of that resource
Consumable resource There is no need to release
a resource after it has been acquired. E.g., a
message, input data, Notice that cj is
unbounded.
12
Using the Model

• There is a resource manager, Mgr(Rj) for every Rj

Mgr(Rj)
Process
13
A Generic Resource Manager
14
Using the Model cont.

• In most cases, we assume that each process
  utilizes a resource as follows
• request
• If the requested resources are not available, the
  calling process will be blocked
• use
• release
• Which implies that we are dealing with reusable
  resources

15
State Transitions

• The system changes state because of the action of
  some process, pi
• There are three pertinent actions
• Request (ri) request one or more units of a
  resource
• Allocation (ai) All outstanding requests from
  a process for a given resource are satisfied
• Deallocation (di) The process releases units
  of a resource

xi
Sj
Sk
16
Properties of States

• Want to define deadlock in terms of patterns of
  transitions
• Define pi is blocked in Sj if pi cannot cause a
  transition out of Sj

17
Properties of States - cont.

• If pi is blocked in Sj, and will also be blocked
  in every Sk reachable from Sj, then pi is
  deadlocked
• Sj is called a deadlock state

18
State Diagram cont.

• State diagram of one process with one resource
• of two units
• Under the single unit allocation/release
  assumption

19
State Diagram cont.
20
Resource-Allocation Graph

• 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

21
Resource-Allocation Graph - cont.

• Process
• Resource Type with 4 instances
• Pi requests instance of Rj
• Pi is holding an instance of Rj

22
Example of a Resource Allocation Graph
23
Another Example of a Resource Allocation Graph
24
Yet Another Example of Resource Allocation Graph
25
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.

26
Dealing with Deadlocks

• Three ways
• Prevention
• place restrictions on resource requests to make
  deadlock impossible
• Avoidance
• plan ahead to avoid deadlock.
• Recovery
• detect when deadlock occurs and recover from it

27
Deadlock Prevention

• Restrain the ways that request can be made.
• 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.

28
Deadlock Prevention cont.
- Requesting all resources before starting
29
Deadlock Prevention cont.
- Release of all resources before requesting more
30
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.

31
Deadlock Prevention - cont.

• Circular Wait
• Impose a total ordering of all resource types,
  and require that each process requests resources
  in an increasing order of enumeration
• In other words, assuming Ri lt Rj if i lt j, we
  only a process to acquire a resource Rj if it has
  acquired all other resources Ri, for i lt j
• Here we assume F(Ri)i
• Semaphore example
• semaphores A and B, initialized to 1
• P0 P1
• wait (A) wait(A)
• wait (B) wait(B)

32
Deadlock Prevention - cont.
33
Deadlock Prevention - cont.
34
Deadlock Avoidance

• 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

35
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 safe
  sequence of all processes.
• Sequence ltP1, P2, , Pngt is safe if 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 lt i.
• 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, Pi1 can obtain its needed
  resources, and so on.

36
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.

37
Comments on Safe State

• It is a worst case analysis
• If every process were to request its maximum
  claim, there would be a sequence of allocations
  and deallocations that could enable the system to
  satisfy every processs request in some order
• It does not mean that the system must have enough
  resources to simultaneously meet all the maximum
  claims

38
Safe State Strategy
39
Safe, unsafe , deadlock state spaces
40
Bankers Algorithm

• 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.

41
Data Structures for the Bankers Algorithm
Let n number of processes, and m number of
resources types.

• 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 Allocationi,j k then Pi is
  currently allocated k instances of Rj.
• Need
• n x m matrix. If Needi,j k, then Pi may need
  k more instances of Rj to complete its task.
• Need i,j Maxi,j Allocation i,j

42
Safety Algorithm

• 1. Let Work and Finish be vectors of length m and
  n, respectively. Initialize
• Work Available
• Finish i false for i - 1, 2, 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 AllocationiFinishi
  truego to step 2.
• 4. If Finish i true for all i, then the
  system is in a safe state.

43
Example of Bankers 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

44
Example - cont.

• The content of the matrix. Need is defined to be
  Max Allocation.
• Allocation Need Available
  Work
• A B C A B C A B C A B C
• P0 0 1 0 7 4 3 3 3 2
• P1 2 0 0 1 2 2
• P2 3 0 2 6 0 0
• P3 2 1 1 0 1 1
• P4 0 0 2 4 3 1
• The system is in a safe state since the sequence
  lt P1, P3, P4, P2, P0gt satisfies safety criteria.

45
Resource-Request Algorithm for Process Pi

• Requesti 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 Requesti
• 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

46
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
  ltP1, P3, P4, P0, P2gt satisfies safety
  requirement.

47
Example Continued

• 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
• Can an additional request for (3,3,0) by P4 be
  granted?
• Can an additional request for (0,2,0) by P0 be
  granted?

48
Bankers Algorithm

• Let maxci, j be the maximum claim for Rj by pi
• Let alloci, j be the number of units of Rj held
  by pi
• Can always compute
• availj cj - S0?ilt nalloci,j
• Then number of available units of Rj
• Should be able to determine if the state is safe
  or not using this info

49
Bankers Algorithm

• Copy the alloci,j table to alloci,j
• Given C, maxc and alloc, compute avail vector
• Find pi maxci,j - alloci,j ? availj
  for 0 ? j lt m and 0 ? i lt n.
• If no such pi exists, the state is unsafe
• If alloci,j is 0 for all i and j, the state is
  safe
• Set alloci,j to 0 deallocate all resources
  held by pi go to Step 2

50
Example
Maximum Claim
C lt8, 5, 9, 7gt
Process R0 R1 R2 R3 p0 3 2 1 4 p1 0 2 5 2 p2 5 1 0
5 p3 1 5 3 0 p4 3 0 3 3
Allocated Resources
Process R0 R1 R2 R3 p0 2 0 1 1 p1 0 1 2 1 p2 4 0 0
3 p3 0 2 1 0 p4 1 0 3 0 Sum 7 3 7 5
51
Example
Maximum Claim
C lt8, 5, 9, 7gt
Process R0 R1 R2 R3 p0 3 2 1 4 p1 0 2 5 2 p2 5 1 0
5 p3 1 5 3 0 p4 3 0 3 3
Allocated Resources
Process R0 R1 R2 R3 p0 2 0 1 1 p1 0 1 2 1 p2 0 0 0
0 p3 0 2 1 0 p4 1 0 3 0 Sum 3 3 7 2
52
Example
Maximum Claim
C lt8, 5, 9, 7gt
Process R0 R1 R2 R3 p0 3 2 1 4 p1 0 2 5 2 p2 5 1 0
5 p3 1 5 3 0 p4 3 0 3 3

• Can anyones maxc be met? (Yes, any of them can)

Allocated Resources
Process R0 R1 R2 R3 p0 2 0 1 1 p1 0 1 2 1 p2 0 0 0
0 p3 0 2 1 0 p4 0 0 0 0 Sum 2 1 4 2
53
Example
Maximum Claim
C lt8, 5, 9, 7gt
Process R0 R1 R2 R3 p0 3 2 1 4 p1 0 2 5 2 p2 5 1 0
5 p3 1 5 3 0 p4 3 0 3 3
Determine available units
avail lt8-8, 5-3, 9-7, 7-5gt lt0, 2, 2,
2gt

• Can anyones maxc be met?

Allocated Resources
Process R0 R1 R2 R3 p0 2 0 1 1 p1 0 1 2 1 p2 4 0 0
3 p3 1 2 1 0 p4 1 0 3 0 Sum 8 3 7 5
54
Deadlock Detection and Recovery

• Allow system to enter deadlock state
• Detection algorithm
• Recovery scheme

55
Deadlock Detection and Recovery cont.

• Check for deadlock (periodically or
  sporadically), then recover
• Can be far more aggressive with allocation
• No maximum claim, no safe/unsafe states
• Differentiate between
• Serially reusable resources A unit must be
  allocated before being released
• Consumable resources Never release acquired
  resources resource count is number currently
  available

56
Deadlock Detection Algorithm

• 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.

57
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
  Finishi falseotherwise, Finishi true.
• 2. Find an index i such that both
• (a) Finishi false
• (b) Requesti ? Work
• If no such i exists, go to step 4.
• 3. (a) Work Work Allocationi (b) Finishi
  true go to step 2.
• 4. If Finishi false, for some i, 1 ? i ? n,
  then the system is in deadlock state. Moreover,
  if Finishi false, then Pi is deadlocked.

Algorithm requires an order of m x n2 operations
to detect whether the system is in deadlocked
state.
58
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 ltP0, P2, P3, P1, P4gt will result in
  Finishi true for all i.

59
Example - cont.

• P2 requests an additional instance of type C.
• 
  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 1 0 0
• P3 2 1 1 1 0 0
• P4 0 0 2 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.

60
Reusable Resource Graphs

• Micro model to describe a single state
• Nodes p0, p1, , pn ? R1, R2, , Rm
• Edges connect pi to Rj, or Rj to pi
• (pi, Rj) is a request edge for one unit of Rj
• (Rj, pi) is an assignment edge of one unit of Rj
• For each Rj there is a count, cj of units Rj
• Number of units of Rj allocated to pi plus the
  number requested by pi cannot exceed cj

61
State Transitions due to Request

• In Sj, pi is allowed to request q?ch units of Rh,
  provided pi has no outstanding requests.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by adding q request edges from pi to Rh

q edges
Rh
pi
Rh
pi
pi request q units
State Sk
State Sj
of Rh
62
State Transition for Acquire

• In Sj, pi is allowed to acquire units of Rh, iff
  there is (pi, Rh) in the graph, and all can be
  satisfied.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by changing each request edge to an assignment
  edge.

Rh
pi
Rh
pi
pi acquires units
State Sk
State Sj
of Rh
63
State Transition for Release

• In Sj, pi is allowed to release units of Rh, iff
  there is (Rh, pi) in the graph, and there is no
  request edge from pi.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by deleting all assignment edges.

Rh
pi
Rh
pi
pi releases units
State Sk
State Sj
of Rh
64
Example
R
p
P holds one unit of R
P requests one unit of R
R
p
A Deadlock State
65
Example
Not a Deadlock State
No Cycle in the Graph
66
Example
p0
p1
S00
67
Example
p0
p0
p1
p1
S00
S01
68
Example
p0
p0
p0
p1
p1
p1
S00
S01
S11
69
Example
p0
p0
p0
p0
p1
p1
p1
p1
S00
S01
S11
S21
70
Example
p0
p0
p0
p0
p0
p1
p1
p1
p1
p1
S00
S01
S11
S21
S22
71
Example
p0
p0
p0
p0
p0
p0
. . .
p1
p1
p1
p1
p1
p1
S00
S01
S11
S21
S22
S33
72
Graph Reduction

• Deadlock state if there is no sequence of
  transitions unblocking every process
• A RRG represents a state can analyze the RRG to
  determine if there is a sequence
• A graph reduction represents the (optimal) action
  of an unblocked process. Can reduce by pi if
• pi is not blocked
• pi has no request edges, and there are (Rj, pi)
  in the RRG

73
Graph Reduction (cont)

• Transforms RRG to another RRG with all assignment
  edges into pi removed
• Represents pi releasing the resources it holds

pi
Reducing by pi
pi
74
Graph Reduction (cont)

• A RRG is completely reducible if there a sequence
  of reductions that leads to a RRG with no edges
• A state is a deadlock state if and only if the
  RRG is not completely reducible.

75
Example RRG
p0
A
C
p1
p2
B
76
Corresponding Detection Algorithm

• Three processes P0 through P2 three resource
  types A (2 instances), B (2 instances), and C (1
  instance).
• Snapshot at time T0
• Allocation Request Available
• A B C A B C A B C
• P0 1 0 1 1 0 0 1 0 0
• P1 0 2 0 2 0 0
• P2 0 0 0 0 1 1

77
Example RRG
Allocation Request Available A B C A B C A B
C P0 1 0 1 1 0 0 0 0 0 P1 1 0 0 0 1 0 P2 0 2
0 0 0 1
78
Consumable Resource Graphs (CRGs)

• Number of units varies, have producers/consumers
• Nodes p0, p1, , pn ? R1, R2, , Rm
• Edges connect pi to Rj, or Rj to pi
• (pi, Rj) is a request edge for one unit of Rj
• (Rj, pi) is an producer edge (must have at least
  one producer for each Rj)
• For each Rj there is a count, wj of units Rj

79
State Transitions due to Request

• In Sj, pi is allowed to request any number of
  units of Rh, provided pi has no outstanding
  requests.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by adding q request edges from pi to Rh

q edges
Rh
pi
Rh
pi
pi request q units
State Sk
State Sj
of Rh
80
State Transition for Acquire

• In Sj, pi is allowed to acquire units of Rh, iff
  there is (pi, Rh) in the graph, and all can be
  satisfied.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by deleting each request edge and decrementing wh.

Rh
pi
Rh
pi
pi acquires units
State Sk
State Sj
of Rh
81
State Transition for Release

• In Sj, pi is allowed to release units of Rh, iff
  there is (Rh, pi) in the graph, and there is no
  request edge from pi.
• Sj ? Sk, where the RRG for Sk is derived from Sj
  by incrementing wh.

Rh
pi
Rh
pi
pi releases 2 units
State Sk
State Sj
of Rh
82
Example
p0
p1
83
Deadlock Detection

• May have a CRG that is not completely reducible,
  but it is not a deadlock state
• For each process
• Find at least one sequence which leaves each
  process unblocked.
• There may be different sequences for different
  processes -- not necessarily an efficient approach

84
Deadlock Detection

• May have a CRG that is not completely reducible,
  but it is not a deadlock state
• Only need to find sequences, which leave each
  process unblocked.

p0
p1
85
Deadlock Detection

• May have a CRG that is not completely reducible,
  but it is not a deadlock state
• Only need to find a set of sequences, which
  leaves each process unblocked.

86
General Resource Graphs

• Have consumable and reusable resources
• Apply consumable reductions to consumables, and
  reusable reductions to reusables
• See Figure 10.29

87
GRG Example (Fig 10.29)
88
GRG Example (Fig 10.29)
p3
p2
Reduce by p3
R2
R0
R1
p0
p1
Reusable
Consumable
89
GRG Example (Fig 10.29)
p3
p2
R2
R0
?
R1
p0
p1
Reduce by p0
Reusable
Consumable
90
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?
• 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.

91
Recovery from Deadlock Process Termination

• Abort all deadlocked processes.
• Roll back to a previous checkpoint
• 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?

92
Recovery from Deadlock Resource Preemption

• Selecting a victim minimize cost.
• Rollback return to some safe state, restart
  process from that state.
• Starvation same process may always be picked
  as victim, include number of rollback in cost
  factor.

93
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.

94
Summary

• Deadlock is a situation where a set of blocked
  processes are waiting for each other
• Three ways to deal with deadlocks
• Deadlock prevention
• Deadlock avoidance
• Deadlock recovery