Deadlock
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Deadlock. 10. Example. Process 1. Process 2. Resource 1. Resource 2. Process holds the resource. Process requests the resource. Three Deadlocked Processes. Process 1. Process 2. Process 3. Resource 1. Resource 2. Resource 3. Process holds the resource.

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Deadlock

Deadlock

10


Deadlock

Example

Process 1

Process 2

Resource 1

Resource 2

Process holds the resource

Process requests the resource


Three deadlocked processes

Three Deadlocked Processes

Process 1

Process 2

Process 3

Resource 1

Resource 2

Resource 3

Process holds the resource

Process requests the resource


A model

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


State transitions

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


Properties of states

a1

r3

Sj

r1

p2 is blocked in Sj

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


Properties of states cont

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


A simple process resource model instance

A Simple Process-Resource Model Instance

P1

P2

P3

R1

R2

R3

Process holds resource

Process requests resource


Example

Example

  • One process, two units of one resource

  • Can request one unit at a time

d

d

r

a

r

a

S0

S1

S2

S3

S4


Extension of example

Extension of Example

d0

d0

r0

a0

r0

a0

S00

S10

S20

S30

S40

r1

r1

r1

r1

r1

d0

d0

r0

a0

r0

a0

S01

S11

S21

S31

S41

d1

d1

d1

d1

a1

a1

a1

a1

d0

r0

a0

r0

S02

S12

S22

S32

r1

r1

d0

r1

r1

r0

a0

r0

S03

S13

S23

S33

d1

d1

a1

a1

r0

S04

S14


Figure 10 10 a model of a state with a circular wait

Figure 10‑10: A Model of a State with a Circular Wait

R

P

Ri

P holds R

Pi

P

R

P requests R


Dining philosophers revisited

Dining Philosophers Revisited

philosopher(int i){

while (TRUE) {

// Think

// Eat

P(fork[i]); /* Pick up left fork */

P(fork[(i+1) mod 5]); /* Pick up right fork */

eat();

V(fork[(i+1) mod 5]);

V(fork[i]);

}

}

philosopher4(){

while (TRUE) {

// Think

// Eat

P(fork[0]); /* Pick up right fork */

P(fork[4]); /* Pick up left fork */

eat();

V(fork[4]);

V(fork[0]);

}

}

semaphore fork[5];

fork[0] = fork[1] = fork[2] = fork[3] = fork[4] = 1;

fork(philosopher, 1, 0);

fork(philosopher, 1, 1);

fork(philosopher, 1, 2);

fork(philosopher, 1, 3);

fork(philosopher4, 0);


Addressing deadlock

Addressing Deadlock

  • Prevention: Design the system so that deadlock is impossible

  • Avoidance: Construct a model of system states, then choose a strategy that will not allow the system to go to a deadlock state

  • Detection & Recovery: Check for deadlock (periodically or sporadically), then recover

  • Manual intervention: Have the operator reboot the machine if it seems too slow


Prevention

Prevention

  • Necessary conditions for deadlock

    • Mutual exclusion

    • Hold and wait

    • Circular waiting

    • No preemption

  • Ensure that at least one of the necessary conditions is false at all times

    • Mutual exclusion must hold at all times


Hold and wait

Hold and Wait

  • Need to be sure a process does not hold one resource while requesting another

  • Approach 1: Force a process to request all resources it needs at one time

  • Approach 2: If a process needs to acquire a new resource, it must first release all resources it holds, then reacquire all it needs

  • What does this say about state transition diagrams?


Circular wait

Circular Wait

  • Have a situation in which there are K processes holding units of K resources

R

P

Ri

P holds R

Pi

P

R

P requests R


Deadlock

Circular Wait (cont)

  • There is a cycle in the graph of processes and resources

  • Choose a resource request strategy by which no cycle will be introduced

  • Total order on all resources, then can only ask for Rj if Ri < Rj for all Ri the process is currently holding


Circular wait cont

Circular Wait (cont)

  • There is a cycle in the graph of processes and resources

  • Choose a resource request strategy by which no cycle will be introduced

  • Total order on all resources, then can only ask for Rj if Ri < Rj for all Ri the process is currently holding

  • This is how we noticed the easy solution for the dining philosophers


Allowing preemption

Allowing Preemption

  • Allow a process to time-out on a blocked request -- withdrawing the request if it fails

ru

Si

Sj

wu

dv

ru

Sk


Avoidance

Avoidance

  • Define a model of system states, then choose a strategy that will guarantee that the system will not go to a deadlock state

  • Requires extra information, e.g., the maximum claim for each process

  • Allows resource manager to see the worst case that could happen, then to allow transitions based on that knowledge


Safe vs unsafe states

Safe vs Unsafe States

  • Safe state: one in which the system can assure that any sequence of subsequent transitions leads back to the initial state

    • Even if all exercise their maximum claim, there is an allocation strategy by which all claims can be met

  • Unsafe state: one in which the system cannot guarantee that the system will transition back to the initial state

    • Unsafe state can lead to a deadlock state if too many processes exercise their maximum claim at once


More on safe unsafe states

Likely to be in a safe state

Probability of being in unsafe state increases

More on Safe & Unsafe States

Normal

Execution

No

Request

Max Claim

Yes

Execute, then

release


More on safe unsafe states1

More on Safe & Unsafe States

I

Disallow

Safe States

Unsafe States

Deadlock States


Banker s algorithm

Banker’s Algorithm

  • Let maxc[i, j] be the maximum claim for Rj by pi

  • Let alloc[i, j] be the number of units of Rj held by pi

  • Can always compute

    • avail[j] = cj - S0i< nalloc[i,j]

    • Then number of available units of Rj

  • Should be able to determine if the state is safe or not using this info


Banker s algorithm1

Banker’s Algorithm

  • Copy the alloc[i,j] table to alloc’[i,j]

  • Given C, maxc and alloc’, compute avail vector

  • Find pi: maxc[i,j] - alloc’[i,j]  avail[j] for 0  j < m and 0  i < n.

    • If no such pi exists, the state is unsafe

    • If alloc’[i,j] is 0 for all i and j, the state is safe

  • Set alloc’[i,j] to 0; deallocate all resources held by pi; go to Step 2


Deadlock

  • Compute total allocated

  • Determine available units

avail = <8-7, 5-3, 9-7, 7-5>

= <5, 2, 2, 5>

  • Can anyone’s maxc be met?

maxc[4,0]-alloc’[4,0] = 5-1 = 45 = avail[0]

maxc[4,1]-alloc’[4,1] = 0-0 = 02 = avail[1]

maxc[4,2]-alloc’[4,2] = 3-3 = 02 = avail[2]

maxc[4,3]-alloc’[4,3] = 3-0 = 35 = avail[3]

  • P4 can exercise max claim

avail[0] = avail[0]+alloc’[4,0] = 5+1 = 6

avail[1] = avail[1]+alloc’[4,1] = 2+0 = 2

avail[2] = avail[2]+alloc’[4,2] = 2+3 = 5

avail[3] = avail[3]+alloc’[4,3] = 5+0 = 5

Example

Maximum Claim

C = <8, 5, 9, 7>

ProcessR0R1R2R3

p03214

p10252

p25105

p31530

p43033

Allocated Resources

ProcessR0R1R2R3

p02011

p10121

p20000

p30210

p41030

Sum3372


Deadlock

  • Compute total allocated

  • Determine available units

avail = <8-7, 5-3, 9-7, 7-5>

= <6, 2, 5, 5>

Example

Maximum Claim

C = <8, 5, 9, 7>

ProcessR0R1R2R3

p03214

p10252

p25105

p31530

p43033

  • Can anyone’s maxc be met? (Yes, any of them can)

Allocated Resources

ProcessR0R1R2R3

p02011

p10121

p20000

p30210

p40000

Sum2142


Detection recovery

Detection & Recovery

  • 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


Recovery

Recovery

  • No magic here

    • Choose a blocked resource

    • Preempt it (releasing its resources)

    • Run the detection algorithm

    • Iterate if until the state is not a deadlock state


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