Deadlock

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The deadlock problem

Deadlocks

Prevenzione statica: preemption
Prevenzione dinamica: deadlock avoidance

A deadlock is a set of blocked processes each holding a resource and waiting to acquire a resource held by another process in the set.

An arrow from $P_0$ to $A$ means the process $P_0$ called a wait(A).
An arrow from $B$ to $P_1$ means the process $P_1$ has control of the resource $B$.
If we map like this and we get a cycle, this means we currently have a deadlock.

System Model

A system has resource types $R_1,R_2,...,R_m$
These can be CPU cycles, memory space, I/O devices..

Each resource type $R_i$ has $W_i$ instances.

Each process utilizes a resource as follows:

• request
• use
• release

Deadlock Characterization

A deadlock can occur if these four conditions hold simultaneously:

• mutual exclusion
• hold and wait: a process holding at least one resource is waiting to acquire additional resources held by other processes
• no preemption
• circular wait (cycle)

Resource-Allocation Graph

An arrow from $P_0$ to $A$ means the process $P_0$ called a wait(A).
An arrow from $B$ to $P_1$ means the process $P_1$ has control of the resource $B$.

Basic Facts

• If a graph contains no cycles $⟹$ no deadlock.
• If a graph contains a cycle:
  • if only there is one instance per resource type $⟹$ deadlock
  • if several instances per resource type $⟹$ possibility of deadlock

Methods for handling Deadlocks

Methods can be:

• ensuring that the system will never enter a deadlock state
• allow the system to ender a deadlock and then recover
• ignore the problem and pretend that deadlock never occur in the system: this is used by most operating systems, including Unix

Deadlock Prevention

Prevention is done by restraining the ways requests can be made:

• mutual exclusion: this is not required for sharable resources, but must hold for nonsharable resources
• hold and wait: must guarantee that whenever a process request a resource it does not hold any other resource
  • require processes to request and get allocated all the resources it will need, before it begins execution, or only allow processes to request resources when they have none
  • low resource utilization: starvation possible
• no preemption:
  • if a process that is holding some resources request another resource that cannot be immediately allocated to it, then all the resource currently being held are released
  • preempted resources are added to the list of resource for which the process is waiting
  • the 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 reqeust resources in an increasing order of enumeration: “if $P$ already holds $R_k$, it cannot request $R_{k-i}$“

Deadlock Avoidance

Requires that the system has some additional a priori information available:

• the simplest and most useful model requires that each process declares the maximum number of resources of each type that it may need
• this avoidance algorithm dynamically examines the resource-allocation state to ensure that there can never be a circular-wait condition
• the resource-allocation state is defined by:
  • the number of available allocated resources
  • the maximum demands of the processes

Safe State

The System is in a safe state if there exists a sequence of ALL processes in the systems such that for each process, the resource that it can still request can be satisfied by the currently available resource or the resources held by all processes scheduled before it.

When a process requests an available resource, the system must decide if immediate allocation leaves the system in a safe state.

So if a processe’s resource needs cannot be immediately met, this process waits for all the processes before it that hold resources it would need. When these processes finish, their resources get returned to the system and the process that was waiting can be executed.

The deadlock state is a subset of the unsafe states set.

Basic Facts

• If a system is in safe state $⟹$ no deadlocks
• if a system is in unsafe state $⟹$ possibility of deadlocks
• avoidance $⟹$ ensuring that the system will never enter an unsafe 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

This algorithm is used when working with resource types with a single instance.

Graph Scheme

• Claim edge $P_i\to R_j$ indicates that process $P_j$ may request resource $R_j$; 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 is allocated to the process resource
• When a resource is released by a process, assignment edge reconverts to a claim edge
• Resources must be claimed a priori in the system

If a process has an outgoing request edge, it is bloccato.

Algorithm

Suppose that process $P_i$ requests a resource $R_j$: 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

This algorithm is used when having multiple instances of a resource type.

• Each process must a priori claim its maximum resource use
• when a process request 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

Let n = number of processes and m = number of resources type.

• Available: Vector of length m. If Available[j] = k, there are $k$
  instances of resource type $R_j$ available
• Max: $n\times m$ matrix. If Max[i,j] = k, then process $P_i$ may request at
  most $k$ instances of resource type
• Allocation: $n\times m$ matrix. If Allocation[i,j] = k then $P_i$ is currently
  allocated $k$ instances of $R_j$
• Need: $n\times m$ matrix. If Need[i,j] = k, then $P_i$ may need $k$ more
  instances of $R_j$ to complete its task

we have: $\text{Need}[i.j]=\text{Max}[i,j]-\text{Allocation}[i,j]$

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 $i$ such that both:
   • (a) $\text{Finish}[i]=\text{false}$
   • (b) ${\text{Need}}_i\le \text{Work}$
     If no such $i$ exists, go to step 4
3. $\text{Work}=\text{Work}+{\text{Allocation}}_i$
   $\text{Finish}[i]=\text{true}$
   go to step 2
4. If $\text{Finish}[i]==\text{true}\forall i$, then the system is in a safe state

Resource-Request Algorithm for Process $P_i$

Request = request vector for process Pi.

If ${\text{Request}}_i[j]=k$ then process $P_i$ wants $k$ instances of
resource type $R_j$

1. If ${\text{Request}}_i\le {\text{Need}}_i$ go to step 2.
   Otherwise, raise error condition, since process has exceeded its maximum claim
2. If ${\text{Request}}_i\le \text{Available}$, go to step 3. Otherwise $P_i$ must wait, since resources are not available
3. Assume to allocate requested resources to $P_i$ by modifying the state as follows:
   - $\text{Available}=\text{Available}–{\text{Request}}_i$;
   - ${\text{Allocation}}_i={\text{Allocation}}_i+{\text{Request}}_i$;
   - ${\text{Need}}_i={\text{Need}}_i–{\text{Request}}_i$;
   • If safe $⟹$ the resources are allocated to $P_i$
   • If unsafe $⟹$ $P_i$ must wait, and the old resource-allocation state is restored

Deadlock Detection

This strategy allows the system to enter deadlock state, detects it and tries to recover from it.

Single instance of each resource type

The system maintains a wait-for graph:

• nodes are processes
• $P_i\to P_j$ if $P_i$ is waiting for $P_j$

The system periodically invokes an algorithm that detects cycles in the wait-for graph, if one is found, a deadlock is detected.

Note that an algorithm of cycle detection on a graph of $n$ vertices (nodes) requires an order of $n^2$ operations.

Multiple instances of a resource type

We keep:

• available: a vector of length $m$ that indicates the number of available resources of each type
• allocation: a $n\times n$ matrix that defines the number of resources of each type currently allocated to each process
• request: a $n\times m$ matrix that indicates the current requests of each process.
  If $Request[i][j]=k$, the process $P_i$ is requesting $k$ more instances of resource type $R_j$

Detection algorithm

This algorithm requires an order of $O(m\times n^2)$ operations to detect a deadlock state.

1. Let Work and Finish be vectors of length $m$ and $n$, respectively initialize:
   • Work = Available
   • For i = 1,2, …, n, if ${\text{Allocation}}_i\ne 0$, then Finish[i] = false; otherwise, Finish[i] = true
2. Find an index $i$ such that both:
   • Finish[i] == false
   • ${\text{Request}}_i\le \text{Work}$
     If no such $i$ exists, go to step 4
3. $\text{Work}=\text{Work}+{\text{Allocation}}_i$
   • Finish[i] = true
   • go to step 2
4. If Finish[i] == false, for some $i$, $1\le i\le n$, then the system is in deadlock state.
   Moreover, if Finish[i] == false, then $P_i$ is deadlocked

When to invoke the detection algorithm

When and how often to invoke this algorithm depends on:

• how often can a deadlock occur
• how many processes will need to be rolled back for recovery: one for each disjoint cycle

Possibilities:

• every time a request cannot be satisfied
• every hour
• when CPU usage goes below 40%

Recovery from Deadlock

Possibilities of recovery are:

• abort all deadlocked processes
• abort one process at a time until the deadlock cycle is eliminated

Order of abortion of process:

• priority of processes
• how long processes have computed, and how much time is needed until completion
• number of resources processes have used
• number of resources processes need until completion
• how many processes will need to be aborted
• wether a process is interactive or batch

Resource Preemption

Instead of aborting processes we can select a “victim” process and roll it back to a safe state.

Starvation: there is the possibility of always the same processes being picked as victim. We solve this by including the number of rollbacks executed on every process when computing the cost of rolling back.