Detection Algorithm Usage

• When, and how often, to invoke depends on:

1. How often a deadlock is likely to occur?
2. 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.

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.

Resource-Allocation Graph and Wait-for Graph

Single Instance of Each Resource Type

• Maintain wait-for graph

1. Nodes are processes.
2. 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.

Deadlock Detection

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

Resource-Request Algorithm for Process Pi

   Request = 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 Þ the resources are allocated to Pi.

•If unsafe Þ Pi must wait, and the old resource-allocation state is restored

Safety Algorithm

• Let Work and Finish be vectors of length m and n, respectively.  Initialize:

Work = Available

Finish [i] = false for i - 1,3, …, n.

• Find and i such that both:

1.  Finish [i] = false
2.  Needi £ Work

      If no such i exists, go to step 4.

• Work = Work + Allocationi

                      Finish[i] = true
             go to step 2.

• If Finish [i] == true for all i, then the system is in a safe state.

Data Structures for the Banker’s 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 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].

Banker's Algorithm

• Multiple instances.
• 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.

Unsafe State In Resource-Allocation Graph

Resource-Allocation Graph For Deadlock Avoidance

Resource-Allocation Graph Algorithm

• 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.
• When a resource is released by a process, assignment edge reconverts to a claim edge.
• Resources must be claimed a priori in the system. 

Safe, Unsafe , Deadlock State

Basic Facts

• If a system is in safe state Þ no deadlocks.
• If a system is in unsafe state Þ possibility of deadlock.
• Avoidance Þ ensure that a system will never enter an unsafe state. 

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 <P1, P2, …, Pn> 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<I.

1. If Pi resource needs are not immediately available, then Pi can wait until all Pj have finished.
2. When Pj is finished, Pi can obtain needed resources, execute, return allocated resources, and terminate.
3. When Pi terminates, Pi+1 can obtain its needed resources, and so on. 

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.

Deadlock Prevention

Restrain the ways 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.

1. 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.
2. Low resource utilization; starvation possible.

• No Preemption – 

1. 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.
2. Preempted resources are added to the list of resources for which the process is waiting.
3. 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.

1. 
   

Methods for Handling Deadlocks

• Ensure that the system will never enter a deadlock state.
• Allow the system to enter a deadlock state and then recover.
• Ignore the problem and pretend that deadlocks never occur in the system; used by most operating systems, including UNIX.

Basic Facts

• If graph contains no cycles Þ no deadlock.
• If graph contains a cycle Þ 

1. if only one instance per resource type, then deadlock.
2. if several instances per resource type, possibility of deadlock.

Resource Allocation Graph With A Cycle But No Deadlock

Resource Allocation Graph With A Deadlock

Example of a Resource Allocation Graph

Resource-Allocation Graph

A set of vertices V and a set of edges E.

• V is partitioned into two types:

1. P = {P1, P2, …, Pn}, the set consisting of all the processes in the system.
2. 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 
• Process

• Resource Type with 4 instances

Deadlock Characterization

Deadlock can arise if four conditions hold simultaneously.

• 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.
• 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, …, Pn–1 is waiting for a resource that is held by
                         Pn, and P0 is waiting for a resource that is held by P0.

System Model

• Resource types R1, R2, . . ., Rm 

CPU cycles, memory space, I/O devices

• Each resource type Ri has Wi instances.
• Each process utilizes a resource as follows:

1. request
2. use
3. release

Bridge Crossing Example

• Traffic only in one direction.
• Each section of a bridge can be viewed as a resource.
• If a deadlock occurs, it can be resolved if one car backs up (preempt resources and rollback).
• Several cars may have to be backed up if a deadlock occurs.
• Starvation is possible.

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

1. System has 2 tape drives.
2. P1 and P2 each hold one tape drive and each needs another one.

• Example

1. semaphores A and B, initialized to 1

    P0     P1

wait (A);  wait(B)

wait (B);  wait(A)

Windows 2000 Synchronization

• Uses interrupt masks to protect access to global resources on uniprocessor systems.
• Uses spinlocks on multiprocessor systems.
• Also provides dispatcher objects which may act as wither mutexes and semaphores.
• Dispatcher objects may also provide events. An event acts much like a condition variable.

Solaris 2 Synchronization

• Implements a variety of locks to support multitasking, multithreading (including real-time threads), and multiprocessing.
• Uses adaptive mutexes for efficiency when protecting data from short code segments.
• Uses condition variables and readers-writers locks when longer sections of code need access to data. 
• Uses turnstiles to order the list of threads waiting to acquire either an adaptive mutex or reader-writer lock.

Monitor Implementation

• Conditional-wait construct: x.wait(c);

1. c – integer expression evaluated when the wait operation is executed.
2. value of c (a priority number) stored with the name of the process that is suspended.
3. when x.signal is executed, process with smallest associated priority number is resumed next.

• Check two conditions to establish correctness of system:

1. User processes must always make their calls on the monitor in a correct sequence.
2. Must ensure that an uncooperative process does not ignore the mutual-exclusion gateway provided by the monitor, and try to access the shared resource directly, without using the access protocols.

Monitor Implementation Using Semaphores

•           Variables

                         semaphore mutex;  // (initially  = 1)

                         semaphore next;     // (initially  = 0)

                         int next-count = 0;

•           Each external procedure F will be replaced by

                         wait(mutex);

                         …

                         body of F;

                         …

                         if (next-count > 0)

                         signal(next)

                         else

                         signal(mutex);

•          Mutual exclusion within a monitor is ensured.
• For each condition variable x, we  have:

                semaphore x-sem; // (initially  = 0)

                int x-count = 0;

• The operation x.wait can be implemented as: 

                x-count++;

                if (next-count > 0)

                signal(next);

                else

                signal(mutex);

                wait(x-sem);

                x-count--;

• The operation x.signal can be implemented as:

                if (x-count > 0)

                {

                next-count++;

                signal(x-sem);

                wait(next);

                next-count--;

                }