Outline Announcement Deadlock Deadlock definition review Conditions for

Outline • Announcement • Deadlock – Deadlock definition - review – Conditions for a deadlock to occur - review – Deadlock prevention – review – Deadlock avoidance – Deadlock detection and recovery 3/2/2021 COP 4610 1

Announcement • Homework #4 – Is due on Nov. 13, 2003 – Not on Nov. 11, 2003 (given in the handout) 3/2/2021 COP 4610 2

The 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 – System has 2 tape drives, one CD-ROM and one DAT drive. – P 1 and P 2 each hold one tape drive and each needs another one. 3/2/2021 COP 4610 3

Two-process deadlock 3/2/2021 COP 4610 4

Deadlock Examples – cont. 3/2/2021 COP 4610 5

Deadlock Examples – cont. 3/2/2021 COP 4610 6

Deadlock Characterization • Deadlock can arise only if four conditions hold simultaneously – – Mutual exclusion Hold and wait: No preemption Circular wait 3/2/2021 COP 4610 7

Deadlock Characterization • 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. 3/2/2021 COP 4610 8

Deadlock Characterization • 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 {P 0, P 1, …, P 0} of waiting processes such that P 0 is waiting for a resource that is held by P 1, P 1 is waiting for a resource that is held by P 2, …, Pn– 1 is waiting for a resource that is held by Pn, and P 0 is waiting for a resource that is held by P 0. 3/2/2021 COP 4610 9

A Model • • P = {p 1, p 2, …, pn} be a set of processes R = {R 1, R 2, …, Rm} be a set of resources cj = number of units of Rj in the system S = {S 0, S 1, …} 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 3/2/2021 COP 4610 10

Resources Resource: Anything that a process can request, then be blocked because that thing is not available. R = {Rj | 0 j < m} = resource types C = {cj 0 | Rj R (0 j < m)} = units of Rj available Reusable resource: After a unit of the resource has been allocated, it must ultimately be released back to the system. E. g. , CPU, primary memory, disk space, … The maximum value for cj is the number of units of that resource Consumable resource: There is no need to release a resource after it has been acquired. E. g. , a message, input data, … Notice that cj is unbounded. 3/2/2021 COP 4610 11

Using the Model • There is a resource manager, Mgr(Rj) for every Rj • Process pi can request units of Rj if it is currently running pi can only request ni cj units of reusable Rj pi can request unbounded # of units of consumable Rj • Mgr(Rj) can allocate units of Rj to pi request Mgr(Rj) Process allocate 3/2/2021 COP 4610 12

A Generic Resource Manager Blocked Processes Policy Process request() Process release() Resource Pool 3/2/2021 COP 4610 13

Using the Model – cont. • In most cases, we assume that each process utilizes a resource as follows – request • If the requested resources are not available, the calling process will be blocked – use – release – Which implies that we are dealing with reusable resources 3/2/2021 COP 4610 14

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 Sj 3/2/2021 xi Sk COP 4610 15

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 a 1 r 3 Sj r 1 3/2/2021 COP 4610 p 2 is blocked in Sj 16

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 3/2/2021 COP 4610 17

State Diagram – cont. - State diagram of one process with one resource of two units Under the single unit allocation/release assumption 3/2/2021 COP 4610 18

State Diagram – cont. 3/2/2021 COP 4610 19

Resource-Allocation Graph • A set of vertices V and a set of edges E. – V is partitioned into two types: • P = {P 1, P 2, …, Pn}, the set consisting of all the processes in the system • R = {R 1, R 2, …, Rm}, the set consisting of all resource types in the system – request edge – directed edge P 1 Rj – assignment edge – directed edge Rj Pi 3/2/2021 COP 4610 20

Resource-Allocation Graph - cont. • Process • Resource Type with 4 instances • Pi requests instance of Rj • Pi is holding an instance of Rj Pi Rj 3/2/2021 COP 4610 21

Example of a Resource Allocation Graph 3/2/2021 COP 4610 22

Another Example of a Resource Allocation Graph 3/2/2021 COP 4610 23

Yet Another Example of Resource Allocation Graph 3/2/2021 COP 4610 24

Basic Facts • If graph contains no cycles no deadlock. • If graph contains a cycle – if only one instance per resource type, then deadlock. – if several instances per resource type, possibility of deadlock. 3/2/2021 COP 4610 25

Dealing with Deadlocks • Three ways – Prevention • place restrictions on resource requests to make deadlock impossible – Avoidance • plan ahead to avoid deadlock. – Recovery • detect when deadlock occurs and recover from it 3/2/2021 COP 4610 26

Deadlock Prevention • Restrain the ways that 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. – 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. – Low resource utilization; starvation possible. 3/2/2021 COP 4610 27

Deadlock Prevention – cont. - Requesting all resources before starting 3/2/2021 COP 4610 28

Deadlock Prevention – cont. - Release of all resources before requesting more 3/2/2021 COP 4610 29

Deadlock Prevention - cont. • No Preemption – – 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. – Preempted resources are added to the list of resources for which the process is waiting. – Process will be restarted only when it can regain its old resources, as well as the new ones that it is requesting. 3/2/2021 COP 4610 30

Deadlock Prevention - cont. • Circular Wait – Impose a total ordering of all resource types, and require that each process requests resources in an increasing order of enumeration • In other words, assuming Ri < Rj if i < j, we only a process to acquire a resource Rj if it has acquired all other resources Ri, for i <j – Here we assume F(Ri)=i – Semaphore example • semaphores A and B, initialized to 1 P 0 P 1 wait (A); wait(A) wait (B); wait(B) 3/2/2021 COP 4610 31

Deadlock Prevention - cont. 3/2/2021 COP 4610 32

Deadlock Prevention - cont. 3/2/2021 COP 4610 33

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 3/2/2021 COP 4610 34

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 <P 1, P 2, …, 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. – 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. – When Pi terminates, Pi+1 can obtain its needed resources, and so on. 3/2/2021 COP 4610 35

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. 3/2/2021 COP 4610 36

Comments on Safe State • It is a worst case analysis – If every process were to request its maximum claim, there would be a sequence of allocations and deallocations that could enable the system to satisfy every process’s request in some order • It does not mean that the system must have enough resources to simultaneously meet all the maximum claims 3/2/2021 COP 4610 37

Safe State Strategy 3/2/2021 COP 4610 38

Safe, unsafe , deadlock state spaces 3/2/2021 COP 4610 39

Banker’s Algorithm • 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. 3/2/2021 COP 4610 40

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] 3/2/2021 COP 4610 41

Safety Algorithm 1. Let Work and Finish be vectors of length m and n, respectively. Initialize: Work : = Available Finish [i] = false for i - 1, 2, 3, …, n. 2. Find and i such that both: (a) Finish [i] = false (b) 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. 3/2/2021 COP 4610 42

Example of Banker’s Algorithm • 5 processes P 0 through P 4; 3 resource types A (10 instances), B (5 instances, and C (7 instances). • Snapshot at time T 0: Allocation Max Available ABC ABC P 0 010 753 332 P 1 200 322 P 2 302 902 P 3 211 222 P 4 002 433 3/2/2021 COP 4610 43

Example - cont. • The content of the matrix. Need is defined to be Max – Allocation Need Available Work ABC ABC P 0 010 743 332 P 1 200 122 P 2 302 600 P 3 211 011 P 4 002 431 • The system is in a safe state since the sequence < P 1, P 3, P 4, P 2, P 0> satisfies safety criteria. 3/2/2021 COP 4610 44

Resource-Request Algorithm for Process Pi Requesti = 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: • • 3/2/2021 Available : = Available = Requesti; Allocationi : = Allocationi + Requesti; Needi : = Needi – Requesti; ; If safe the resources are allocated to Pi. If unsafe Pi must wait, and the old resource-allocation state is restored COP 4610 45

Example: P 1 request (1, 0, 2) • Check that Request Available (that is, (1, 0, 2) (3, 3, 2) true. ) Allocation Need Available ABC ABC P 0 010 743 230 P 1 302 020 P 2 301 600 P 3 211 011 P 4 002 431 • Executing safety algorithm shows that sequence <P 1, P 3, P 4, P 0, P 2> satisfies safety requirement. 3/2/2021 COP 4610 46

Example Continued Allocation Need Available A B CA B C P 0 010 743 230 P 1 302 020 P 2 301 600 P 3 211 011 P 4 002 431 • Can an additional request for (3, 3, 0) by P 4 be granted? • Can an additional request for (0, 2, 0) by P 0 be granted? 3/2/2021 COP 4610 47

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 - S 0 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 3/2/2021 COP 4610 48

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 3/2/2021 COP 4610 49

Example Maximum Claim Process p 0 p 1 p 2 p 3 p 4 R 0 3 0 5 1 3 R 1 2 2 1 5 0 C = <8, 5, 9, 7> R 2 1 5 0 3 3 R 3 4 2 5 0 3 Allocated Resources Process p 0 p 1 p 2 p 3 p 4 Sum 3/2/2021 R 0 2 0 4 0 1 7 R 1 0 2 0 3 R 2 1 2 0 1 3 7 R 3 1 1 3 0 0 5 • Compute total allocated • Determine available units avail = <8 -7, 5 -3, 9 -7, 7 -5> = <1, 2, 2, 2> • Can anyone’s maxc be met? maxc[2, 0]-alloc’[2, 0] = 5 -4 = 1 1 = avail[0] maxc[2, 1]-alloc’[2, 1] = 1 -0 = 1 2 = avail[1] maxc[2, 2]-alloc’[2, 2] = 0 -0 = 0 2 = avail[2] maxc[2, 3]-alloc’[2, 3] = 5 -3 = 2 2 = avail[3] • P 2 can exercise max claim avail[0] = avail[0]+alloc’[2, 0] = 1+4 = 5 avail[1] = avail[1]+alloc’[2, 1] = 2+0 = 2 avail[2] = avail[2]+alloc’[2, 2] = 2+0 = 2 COP 4610 avail[3] = avail[3]+alloc’[2, 3] = 2+3 50 = 5

Example Maximum Claim Process p 0 p 1 p 2 p 3 p 4 R 0 3 0 5 1 3 R 1 2 2 1 5 0 C = <8, 5, 9, 7> R 2 1 5 0 3 3 R 3 4 2 5 0 3 Allocated Resources Process p 0 p 1 p 2 p 3 p 4 Sum 3/2/2021 R 0 2 0 0 0 1 3 R 1 0 2 0 3 R 2 1 2 0 1 3 7 R 3 1 1 0 0 0 2 • 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] • P 4 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 COP 4610 avail[3] = avail[3]+alloc’[4, 3] = 5+0 51 = 5

Example Maximum Claim Process p 0 p 1 p 2 p 3 p 4 R 0 3 0 5 1 3 R 1 2 2 1 5 0 C = <8, 5, 9, 7> R 2 1 5 0 3 3 R 3 4 2 5 0 3 R 2 1 2 0 1 0 4 R 3 1 1 0 0 0 2 Allocated Resources Process p 0 p 1 p 2 p 3 p 4 Sum 3/2/2021 R 0 2 0 0 2 R 1 0 2 0 1 COP 4610 • Compute total allocated • Determine available units avail = <8 -7, 5 -3, 9 -7, 7 -5> = <6, 2, 5, 5> • Can anyone’s maxc be met? (Yes, any of them can) 52

Example Maximum Claim Process p 0 p 1 p 2 p 3 p 4 R 0 3 0 5 1 3 R 1 2 2 1 5 0 R 2 1 5 0 3 3 R 3 4 2 5 0 3 R 2 1 2 0 1 3 7 R 3 1 1 3 0 0 5 C = <8, 5, 9, 7> Determine available units avail = <8 -8, 5 -3, 9 -7, 7 -5> = <0, 2, 2, 2> • Can anyone’s maxc be met? Allocated Resources Process p 0 p 1 p 2 p 3 p 4 Sum 3/2/2021 R 0 2 0 4 1 1 8 R 1 0 2 0 3 COP 4610 53

Deadlock Detection and Recovery • Allow system to enter deadlock state • Detection algorithm • Recovery scheme 3/2/2021 COP 4610 54

Deadlock Detection and Recovery – cont. • 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 3/2/2021 COP 4610 55

Deadlock Detection Algorithm • 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. 3/2/2021 COP 4610 56

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 Finish[i] : = false; otherwise, Finish[i] : = true. 2. Find an index i such that both: (a) Finish[i] = false (b) Requesti Work If no such i exists, go to step 4. 3. (a) Work : = Work + Allocationi; (b) 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. Algorithm requires an order of m x n 2 operations to detect whether the system is in deadlocked state. 3/2/2021 COP 4610 57

Example of Detection Algorithm • Five processes P 0 through P 4; three resource types A (7 instances), B (2 instances), and C (6 instances). • Snapshot at time T 0: Allocation Request Available ABC ABC P 0 010 000 P 1 200 202 P 2 303 000 P 3 211 100 P 4 002 • Sequence <P 0, P 2, P 3, P 1, P 4> will result in Finish[i] = true for all i. 3/2/2021 COP 4610 58

Example - cont. • P 2 requests an additional instance of type C. Allocation Request ABC P 0 010 P 1 200 P 2 303 P 3 211 P 4 002 • State of system? Available ABC 000 202 100 002 – Can reclaim resources held by process P 0, but insufficient resources to fulfill other processes; requests. – Deadlock exists, consisting of processes P 1, P 2, P 3, and P 4. 3/2/2021 COP 4610 59

Reusable Resource Graphs • Micro model to describe a single state • Nodes = {p 0, p 1, …, pn} {R 1, R 2, …, Rm} • Edges connect pi to Rj, or Rj to pi – (pi, Rj) is a request edge for one unit of Rj – (Rj, pi) is an assignment edge of one unit of Rj • For each Rj there is a count, cj of units Rj • Number of units of Rj allocated to pi plus the number requested by pi cannot exceed cj 3/2/2021 COP 4610 60

State Transitions due to Request • In Sj, pi is allowed to request q ch units of Rh, provided pi has no outstanding requests. • Sj Sk, where the RRG for Sk is derived from Sj by adding q request edges from pi to Rh q edges pi Rh State Sj 3/2/2021 pi request q units of Rh COP 4610 pi Rh State Sk 61

State Transition for Acquire • In Sj, pi is allowed to acquire units of Rh, iff there is (pi, Rh) in the graph, and all can be satisfied. • Sj Sk, where the RRG for Sk is derived from Sj by changing each request edge to an assignment edge. pi Rh State Sj 3/2/2021 pi acquires units of Rh COP 4610 pi Rh State Sk 62

State Transition for Release • In Sj, pi is allowed to release units of Rh, iff there is (Rh, pi) in the graph, and there is no request edge from pi. • Sj Sk, where the RRG for Sk is derived from Sj by deleting all assignment edges. pi Rh State Sj 3/2/2021 pi releases units of Rh COP 4610 pi Rh State Sk 63

Example R p P holds one unit of R P requests one unit of R p R A Deadlock State 3/2/2021 COP 4610 64

Example Not a Deadlock State 3/2/2021 No Cycle in the Graph COP 4610 65

Example p 0 p 1 S 00 3/2/2021 COP 4610 66

Example 3/2/2021 p 0 p 1 S 00 S 01 COP 4610 67

Example 3/2/2021 p 0 p 0 p 1 p 1 S 00 S 01 S 11 COP 4610 68

Example 3/2/2021 p 0 p 0 p 1 p 1 S 00 S 01 S 11 S 21 COP 4610 69

Example 3/2/2021 p 0 p 0 p 0 p 1 p 1 p 1 S 00 S 01 S 11 S 22 COP 4610 70

Example p 0 p 0 p 0 . . . 3/2/2021 p 1 p 1 p 1 S 00 S 01 S 11 S 22 S 33 COP 4610 71

Graph Reduction • Deadlock state if there is no sequence of transitions unblocking every process • A RRG represents a state; can analyze the RRG to determine if there is a sequence • A graph reduction represents the (optimal) action of an unblocked process. Can reduce by pi if – pi is not blocked – pi has no request edges, and there are (Rj, pi) in the RRG 3/2/2021 COP 4610 72

Graph Reduction (cont) • Transforms RRG to another RRG with all assignment edges into pi removed • Represents pi releasing the resources it holds pi Reducing by pi pi 3/2/2021 COP 4610 73

Graph Reduction (cont) • A RRG is completely reducible if there a sequence of reductions that leads to a RRG with no edges • A state is a deadlock state if and only if the RRG is not completely reducible. 3/2/2021 COP 4610 74

Example RRG p 0 A C p 1 p 2 B p 0 p 1 3/2/2021 p 0 p 1 p 2 COP 4610 p 2 75

Corresponding Detection Algorithm • Three processes P 0 through P 2; three resource types A (2 instances), B (2 instances), and C (1 instance). • Snapshot at time T 0: Allocation P 0 P 1 P 2 3/2/2021 Request ABC 101 100 020 200 011 COP 4610 Available ABC 76

Example RRG p 0 A C p 1 p 2 B 3/2/2021 Allocation Request Available ABC ABC P 0 101 100 P 1 100 010 P 2 020 001 COP 4610 000 77

Consumable Resource Graphs (CRGs) • Number of units varies, have producers/consumers • Nodes = {p 0, p 1, …, pn} {R 1, R 2, …, Rm} • Edges connect pi to Rj, or Rj to pi – (pi, Rj) is a request edge for one unit of Rj – (Rj, pi) is an producer edge (must have at least one producer for each Rj) • For each Rj there is a count, wj of units Rj 3/2/2021 COP 4610 78

State Transitions due to Request • In Sj, pi is allowed to request any number of units of Rh, provided pi has no outstanding requests. • Sj Sk, where the RRG for Sk is derived from Sj by adding q request edges from pi to Rh q edges pi Rh State Sj 3/2/2021 pi request q units of Rh COP 4610 pi Rh State Sk 79

State Transition for Acquire • In Sj, pi is allowed to acquire units of Rh, iff there is (pi, Rh) in the graph, and all can be satisfied. • Sj Sk, where the RRG for Sk is derived from Sj by deleting each request edge and decrementing wh. pi Rh State Sj 3/2/2021 pi acquires units of Rh COP 4610 pi Rh State Sk 80

State Transition for Release • In Sj, pi is allowed to release units of Rh, iff there is (Rh, pi) in the graph, and there is no request edge from pi. • Sj Sk, where the RRG for Sk is derived from Sj by incrementing wh. pi Rh State Sj 3/2/2021 pi releases 2 units of Rh COP 4610 pi Rh State Sk 81

Example 3/2/2021 p 0 p 0 p 0 p 1 p 1 p 1 COP 4610 82

Deadlock Detection • May have a CRG that is not completely reducible, but it is not a deadlock state • For each process: – Find at least one sequence which leaves each process unblocked. • There may be different sequences for different processes -- not necessarily an efficient approach 3/2/2021 COP 4610 83

Deadlock Detection • May have a CRG that is not completely reducible, but it is not a deadlock state • Only need to find sequences, which leave each process unblocked. p 0 3/2/2021 p 1 COP 4610 84

Deadlock Detection • May have a CRG that is not completely reducible, but it is not a deadlock state • Only need to find a set of sequences, which leaves each process unblocked. 3/2/2021 COP 4610 85

General Resource Graphs • Have consumable and reusable resources • Apply consumable reductions to consumables, and reusable reductions to reusables • See Figure 10. 29 3/2/2021 COP 4610 86

GRG Example (Fig 10. 29) p 3 p 2 R 0 R 2 R 1 p 0 p 1 Reusable Consumable Not in Fig 10. 29 3/2/2021 COP 4610 87

GRG Example (Fig 10. 29) p 3 p 2 Reduce by p 3 R 0 R 2 R 1 p 0 p 1 Reusable Consumable 3/2/2021 COP 4610 88

GRG Example (Fig 10. 29) p 3 p 2 R 1 R 0 p 0 R 2 p 1 Reduce by p 0 Reusable Consumable 3/2/2021 COP 4610 89

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. 3/2/2021 COP 4610 90

Recovery from Deadlock: Process Termination • Abort all deadlocked processes. – Roll back to a previous checkpoint • Abort one process at a time until the deadlock cycle is eliminated. • 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. – Resources process needs to complete. – How many processes will need to be terminated. – Is process interactive or batch? 3/2/2021 COP 4610 91

Recovery from Deadlock: Resource Preemption • Selecting a victim – minimize cost. • Rollback – return to some safe state, restart process from that state. • Starvation – same process may always be picked as victim, include number of rollback in cost factor. 3/2/2021 COP 4610 92

Combined Approach to Deadlock Handling • Combine three basic approaches – prevention – avoidance – detection • Allowing the use of the optimal approach for each of resources in the system. • Partition resources into hierarchically ordered classes. • Use most appropriate technique for handling deadlocks within each class. 3/2/2021 COP 4610 93

Summary • Deadlock is a situation where a set of blocked processes are waiting for each other • Three ways to deal with deadlocks – Deadlock prevention – Deadlock avoidance – Deadlock recovery 3/2/2021 COP 4610 94