v   Definition & Basics:

A set of blocked processes each holding a resource and

waiting to acquire a resource held by another process in the set.

Example 1

System has 2 disk drives

Processes P1 and P2 each hold one disk drive and each needs another one

Example 2

Semaphores A and B, initialized to 1

P0                 P1

wait (A);                wait(B)

wait (B);                wait(A)

Deadlock can arise if   four conditions  hold simultaneously:

·        Mutual exclusion:  only one process at a time can use a resource

·        Hold and wait:  holding at least one resource and  is waiting to acquire additional resources held by others

·        No preemption:  a resource can be released only voluntarily by the process holding it.

·        Circular wait:  there exists a set {P0, P1, …, Pn} 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.

v   Resource-Allocation Graph

A set of vertices V and a set of edges E

·       V is partitioned into two types:

o   P = {P1, P2, …, Pn}, the set consisting of all the processes in the system

o   R = {R1, R2, …, Rm}, the set consisting of all resource types in the system

·       E is partitioned into two types:

o   request edge – directed edge Pi ® Rj

o   assignment edge – directed edge Rj ® Pi

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 Ž no deadlock

·       If graph contains a cycle Ž

o   if only one instance per resource type, then deadlock

o   if several instances per resource type, possibility of deadlock

Restrain the ways request can be made

·        Hold and Wait –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.

·        No Preemption – If a process holding some resources requests another resource that cannot be immediately allocated to it, all resources currently being held are released. 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.

Requires that the system has a priori information available.

·       Simplest 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.

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

·       If a system is in safe state Ž no deadlocks

·       If a system is in unsafe state Ž possibility of deadlock

·       Avoidance Ž ensure that a system will never enter an unsafe state.

v   Avoidance algorithms

Resource-Allocation Graph Scheme:  Used for Single instance of resource types

Resources must be claimed a priori in the system.

·       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

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

Used for Multiple instances of a resource type

Each process must a priori claim maximum use.

Ų Data Structures

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 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]

ą   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 an index  i such that:

Finish [i] = false  AND 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,

otherwise it is unsafe

The Algorithm requires m x n2 operations to detect whether the system is in deadlocked state

ą   Resorce-Request for a Process

Request = request vector for process Pi

If Requesti [j] = k then process Pi wants k instances of resource type Rj

·       If Requesti > Needi

Raise error condition, since process has exceeded its maximum claim.

·       If Requesti > Available

Pi  must wait, since resources are not available

Pretend to allocate requested resources to Pi by modifying the state as follows:

Available   = Available   Requesti

Allocationi = Allocationi + Requesti

Needi = Needi Requesti

·       If state is  safe Ž the resources are allocated to Pi

·       If state is unsafe Ž Pi must wait, and the old resource-allocation state is restored

ą   Example of Banker’s Algorithm

·       5 processes P0  through P4;

·       3 resource types:

A    B    C

10    5    7

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

·       The content of the matrix Need is defined to be MaxAllocation

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) Ž 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

Allow system to enter deadlock state then: Detect & Recover.

Single Instance of Each Resource Type

·       Maintain wait-for graph

o   Nodes are processes

o   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:

Work = Available

For i = 1,2, …, n, if Allocationi ¹ 0, then
Finish[i] = false; otherwise, Finish[i] = true

2.  Find an index i such that both:

Finish[i] == false AND Requesti £ 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] == false, for some i, 1 £ i £  n, then the system is in deadlock state.

Moreover, if Finish[i] == false, then Pi is deadlocked

The Algorithm requires 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  B  C

7  2   6

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

System is not deadlocked, sequence <P0, P2, P3, P1, P4> will result in Finish[i] = true for all i

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?

o   Can reclaim resources held by process P0,

but insufficient resources to fulfill other processes requests

o   Deadlock exists, consisting of processes P1,  P2, P3, and P4

·        Abort one process at a time until the deadlock cycle is eliminated

·        In which order should we choose to abort?

o   Priority of the process

o   How long process has computed, and how much longer to completion

o   Resources the process has used

o   Resources process needs to complete

o   How many processes will need to be terminated

o   Is process interactive or batch?

·       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