Deadlocks

1
Deadlocks

• Chapter 8
• (continued)

2
Chapter 8 Deadlocks

• System Model
• Deadlock Characterization
• Methods for Handling Deadlocks
• Deadlock Prevention
• Deadlock Avoidance
• Deadlock Detection
• Deadlock Recovery
• Combined Approach

3
Process Resource Trajectory
u
B
Printer
I8 I7 I6 I5
t
r
Plotter
s
A
p
q
I1 I2 I3 I4
Printer
Plotter
4
Process Resource Trajectory

• Every point in the diagram represents a joint
  state of the two processes
• With a single processor, all progress is vertical
  or horizontal, never diagonal
• At I1, task A got the printer
• when B reaches q, it requests the plotter.
• Should it be given the plotter?
• Box I1-I2, I5-I6 is unsafe if the process
  arrives at I2-I6 it will deadlock.
• At point p, the only safe route is to run Process
  A until it gets to I4.

5
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 it is not deadlocked,
  and there is some scheduling order in which every
  process can run to completion even if all of them
  suddenly request their maximum number of
  resources immediately.
• 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

6
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.

7
Safe State Example
Ten instances of the one resource exist
(a)
The state of (a) is safe because there exists a
sequence of allocations that allows all processes
to complete.
8
Unsafe State Example
Ten instances of the resource exist
Dead lock
(b)
The state of (b) is unsafe because there is no
sequence that guarantees completion.
9
Bankers Algorithm Single Resource
Ten instances of the credit resource
exist Customers have maximum credit totaling 22
Dead lock ?
(b)
(c)
The state of (b) is safe because with two units
left, the banker grant Cs request, delaying
others until C pays back the loan. (c) is unsafe
not enough for any.
10
Bankers Algorithm Single Resource

• Consider each request as it occurs, and see if
  granting it leads to a safe state.
• If safe, the request is granted.
• If unsafe, the request is postponed.
• To see if a state is safe, the banker checks to
  see if he has enough resources to satisfy some
  customer.
• If so, the loan is assumed to be repaid, and the
  customer now closest to the limit is checked,
• If all loans can eventually be repaid, the state
  is safe and the initial request can be granted.

11
Bankers Algorithm Multiple Resources
Multiple instances of multiple resources exist.
Tape Drives
CD Drives
Plotters
Scanners
E ( 6 4 4 2) P ( 5 4 2 2) A ( 1 0 2 0 )
E total P possessed A available
C R
12
Bankers Algorithm Multiple Resources
Multiple instances of multiple resources exist.
Tape Drives
CD Drives
Plotters
Scanners
E ( 6 4 4 2) P ( 5 4 3 2) A ( 1 0 1 0 )
E total P possessed A available
C R

• 1. Satisfy Process D, as its needs fit in
  Available A

13
Bankers Algorithm Multiple Resources
Multiple instances of multiple resources exist.
Tape Drives
CD Drives
Plotters
Scanners
E ( 6 4 4 2) P ( 4 2 2 1) A ( 2 2 2 1 )
E total P possessed A available
C R

• 2. Assume D completed, add to Available A

14
Bankers Algorithm Multiple Resources
Multiple instances of multiple resources exist.
Tape Drives
CD Drives
Plotters
Scanners
E ( 6 4 4 2) P ( 6 3 3 1) A ( 0 1 1 1 )
E total P possessed A available
C R

• 3. Satisfy Process E, as its needs fit in
  Available A

15
Bankers Algorithm Multiple Resources
Multiple instances of multiple resources exist.
Tape Drives
CD Drives
Plotters
Scanners
E ( 6 4 4 2) P ( 4 2 2 1) A ( 2 2 2 1 )
E total P possessed A available
C R

• 4. Assume E completed, add to Available A

16
Bankers Safety Algorithm

• Look for a row, R, whose unmet resource needs are
  all smaller than or equal to A.
• If no such row exists, the system will deadlock
  since no process can run to completion.
• If such a row does exist, assume the process
  requests its maximum number of resources and
  finishes. Mark that process as terminated and
  add all its resources to A.
• Repeat Steps 1 and 2 until either all processes
  are marked terminated (in which case the initial
  state was safe), or until a deadlock occurs (in
  which case it was unsafe).

17
Bankers Resource-Request Algorithm

• Check that request R lt maximum request M
• If true, proceed if false, flag error and exit.
• Check that request R ? available A.
• If true, proceed if false, wait for resources.
• Pretend to allocate resources by adding them to
  correct row in Assignment Matrix C, and removing
  them from available Vector A
• Check safety of the resulting system
• If safe, allocate resources
• If unsafe, refuse request and wait for resources.

18
Example of Bankers Algorithm

• Suppose E (10, 5, 7), with five processes
• Snapshot at time T0
• Allocation Max Available Need
• A B C A B C A B C ABC
• P0 0 1 0 7 5 3 3 3 2 7 4 3
• P1 2 0 0 3 2 2 1 2 2
• P2 3 0 2 9 0 2 6 0 0
• P3 2 1 1 2 2 2 0 1 1
• P4 0 0 2 4 3 3 4 3 1

• The system is in a safe state since the sequence
• lt P1, P3, P4, P2, P0gt satisfies safety
  criteria.

19
Example of Bankers Algorithm

• Suppose P1 requests (1,0,2)
• Check that Request ? Available
• that is, (1,0,2) ? (3,3,2) ? true.
• If granted, then
• Allocation Max Available Need
• A B C A B C A B C A B C
• P0 0 1 0 7 5 3 2 3 0 7 4 3
• P1 3 0 2 3 2 2 0 2 0
• P2 3 0 2 9 0 2 6 0 0
• P3 2 1 1 2 2 2 0 1 1
• P4 0 0 2 4 3 1 4 3 1
• Executing safety algorithm shows that sequence
• ltP1, P3, P4, P0, P2gt satisfies safety
  requirement.
• ? The request can be granted.

20
Example of Bankers Algorithm

• Can request for (3,3,0) by P4 be granted?
• Can request for (0,2,0) by P0 be granted?
• Starting from
• Allocation Max Available Need
• A B C A B C A B C A B C P0 0 1 0 7 5 3
  2 3 0 7 4 3 P1 3 0 2 3 2 2 0 2 0 P2 3 0 2
  9 0 2 6 0 0
• P3 2 1 1 2 2 2 0 1 1
• P4 0 0 2 4 3 3 4 3 1

21
Bankers Algorithm Practicalities

• In theory, Bankers Algorithm works well.
• However,
• In practice, processes rarely know in advance
  what their maximum resource needs will be
• The number of processes is not fixed, but
  dynamically varying as new users log in and out.
• Resources that were thought to be available can
  suddenly vanish (tape drives can break).
• Thus, in practice, few existing systems use the
  bankers algorithm for avoiding deadlocks.

22
Resource-Allocation Graph Algorithm

• Processes indicate all needed resources before
  they begin executing.
• Claim edge Pi ? Rj indicates that process Pj may
  at some time 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.

23
Resource-Allocation Graph for Deadlock Avoidance
Safe Unsafe
Good for single instances of multiple resources.
24
Resource-Allocation Graph Algorithm

• Suppose that Process Pi requests Resource Rj.
• The request can be granted only if converting the
  request edge Pi ? Rj does not result in the
  formation of a cycle in the resource-allocation
  graph.
• If no cycle exists, then the allocation of the
  resource will leave the system in a safe state.
• If a cycle is found, then the allocation will put
  the system in an unsafe state.
• (Process Pi will have to wait.)

25
3. Deadlock Detection and Recovery

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

26
Resource-Allocation Graph and Wait-for Graph
Resource-Allocation Graph
Corresponding wait-for graph
Good for single instances of multiple resources.
27
Wait-for Graph

• Applicable to single instance of each resource
  type
• To detect deadlocks, 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 n2 operations, where n is
  the number of vertices in the graph.

28
Deadlock Detection
Multiple instances of each resource
Resources in existence
Resources available
(E1 , E2, E3 , Em)
(A1 , A2, A3 , Am)
Request matrix
Current allocation matrix
R11 R12 R13 R1m R21 R22 R23 R2m
.. .. .. .. .. Rn1 Rn2 Rn3 Rnm

• C11 C12 C13 C1m
• C21 C22 C23 C2m
• .. .. .. .. ..
• Cn1 Cn2 Cn3 Cnm

Row n is current allocation to process n
Row n is what process n needs.
29
Resource Allocation Example
Tape Drives
Scanners
Tape Drives
Scanners
CD Drives
Plotters
CD Drives
Plotters
E ( 4 2 3 1 )
A ( 2 1 0 0 )
Resources in existence
Resources available to be allocated

• 0 0 1 0
• 2 0 0 1
• 0 1 2 0

C
Request matrix
Current allocation matrix
30
Deadlock Detection
Multiple instances of each resource

• Define A ? B to mean that each element of vector
  A is less than or equal to each element of vector
  B.
• Look for an unmarked process Pi for which the
  i-th row of R is less than or equal to A
• If such a process is found, add the i-th row of C
  to A, mark the process and go back to Step 1
• If no such process exists, the algorithm
  terminates.
• On termination, all unmarked processes are
  deadlocked.

31
Several Instances of a Resource Type

• Available A vector of length m indicates the
  number of available resources of each type.
• Allocation An n ? m matrix defines the number
  of resources of each type currently allocated to
  each process.
• Request An n ? 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.

32
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.

33
Detection Algorithm

• 3. Work Work AllocationiFinishi trueGo
  to step 2.
• If Finishi false, for some i, 1 ? i ? n,
  then the system is in deadlock state.
• Moreover, if Finishi false, then Pi is
  deadlocked.

Reclaim resources, assume its finished
Algorithm requires an order of O(m x n2)
operations to detect whether the system is in
deadlocked state.
34
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. This state is not
  deadlocked.

35
Example of Detection Algorithm

• Suppose P2 requests an additional instance of
  type C.
• Then state is
• 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 1
• 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 requests of
  other processes.
• Deadlock exists, consisting of processes P1, P2,
  P3, and P4.

36
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.

37
Recovery from Deadlock Process Termination

• Abort all deadlocked processes. ? lose their
  results
• Abort one process at a time until the deadlock
  cycle is eliminated, invoking deadlock detection
  each time.
• 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. (e.g. Simple to
  preempt?)
• Resources process needs to complete.
• How many processes will need to be terminated.
• Is process interactive or batch?

38
Recovery from Deadlock Resource Preemption

• Successively preempt some resources and give them
  to other processes until deadlock is broken.
• Issues
• Selecting a victim minimize cost
• (eg. Take into account time spent so far).
• Rollback return to some safe state, restart
  process from that state.
• Starvation same process may always be picked
  as victim, so include number of rollbacks in cost
  factor.

39
Combined Approach to Deadlock Handling

• Combine the three basic approaches
• prevention
• avoidance
• detection
• allowing the use of the optimal approach for
  each resource in the system.
• Partition resources into hierarchically ordered
  classes.
• Use most appropriate technique for handling
  deadlocks within each class.

40
Traffic Deadlock
41
Traffic Deadlock

• Show that the four necessary conditions for
  deadlock indeed hold in this example.
• Mutual exclusion
• Hold and wait
• No preemption
• Circular wait
• State a simple rule that will avoid deadlocks in
  this system.