A distributed algorithm for deadlock detection and resolution

A Distributed Algorithm for Deadlock Detection and Resolution

Don P.Mitchell ?

Michael J.Merritt ?

AT&T Bell Laboratories

ABSTRACT

This paper presents two distributed algorithms for detecting and resolving dead-locks. By insuring that only one of the deadlock processes will detect it, the problem of

resolving the deadlock is simpli?ed.That process could simply abort itself.In one ver-

sion of the algorithm, an arbitrary process detects deadlock; and in a second version, the

process with the lowest priority detects deadlock.

1. Introduction

A system of processes is deadlocked when a cycle forms in its wait-for graph.One method of deal-ing with this problem is to allow deadlocks to form but to detect them quickly and abort a process to break the cycle. If the system is local to a single site, a central resource-management process can accomplish this. All other processes request resources from the manager which maintains a representation of the wait-for graph and watches for cycle formation.

There are two problems with this approach.First, the whole system is vulnerable to the failure of the management process; and second, message passing to and from the manager is expensive.If the system is distributed over many sites, these two problems are much more severe. Although message passing is becoming cheaper,the issue of fault tolerance will certainly remain.

A number of distributed algorithms for deadlock detection have been published, and they seem to fall into two categories. Those in the ?rst category pass information about process demands in an attempt to maintain relevant parts of the global wait-for graph on each site[MENASCE79, GLIGOR80, OBERMARCK82].

The second category of algorithms was inspired by work on parallel graph algorithms[DIJKSTRA80, CHANG82].In this category simpler messages are passed from process to process[CHANDY82, BRACHA83].

The global wait-for graph is not explicitly built up; however, a cycle in the graph will ultimately cause mes-sages to return to their initiators thus alerting them to the existence of deadlock.

The algorithms presented in this paper fall into this second category.An important advantage of these algorithms over earlier work is that only one process in a cycle will detect the deadlock, simplifying the problem of resolving the deadlock.A second advantage rests in their simplicity.Indeed, one author implemented the ?rst algorithm in a local database system in under an hour.They are just as simple to analyse. Even in the face of lost messages and process failures, the correctness proofs are trivial.

2. The System Model

The system can be described by the wait-for graph,a directed graph in which each node represents a pro-cess, and an edge indicates that one process is waiting on a resource held exclusively by another.Assuming each process waits on one resource at a time, the maximum outdegree of the wait-for graph will be one. The direction of the edges are from the waiting process to the process holding the desired resource.

Each node is given two labels. The?rst (indicated by an index in the lower half of the node) is a pri-vate label that is unique to the node thought not necessarily constant.The second label (indicated by an ?Address: AT&T Bell Laboratories, 600 Mountain Ave., Murray Hill, NJ 07974.

index in the upper half of the node) is public.It represents a number that can be read by other processes, and the same value may appear in other nodes.

The edges and labels de?ne the state of the system at any moment.

3. Simple Deadlock Detection

Block

u

STATE BEFORE outdegree=0

v

Activate Transmit

Detect

Figure1

Figure 1 shows the four types of nondeterministic state transitions that de?ne this algorithm.The function "inc(x,y)", means a value larger than both x and y that is unique to that https://www.doczj.com/doc/224341200.html,bel values which neither are a precondition for a transition nor change as a result of a transition have been left blank.Each process begins with its private label equal to its public label.

The private label of each node is always unique to that node, and non-decreasing over time. These two properties can be easily realized by keeping the low-order bits of the label constant and unique while increasing the high-order bits when desired.

The Block step occurs when a process begins to wait on some resource held by another,creating an edge in the wait-for graph.One of the crucial features of this algorithm is the label change that occurs then. Both the public and private labels of the waiting process increase to a value greater than their previous val-ues and greater than the public label of the process being waited on.The private and public labels of the node are changed to the same new value.

The Activate step means that an edge disappeared because a process got a resource, or timed out and gave up waiting, or failed. This step also occurs if the owner of a resource changes.When the waiting pro-cess notices that, it must Activate and then Block again if it is to continue waiting for that resource.

The Tr a nsmit step occurs when the waiting process reads the public label of the process it is waiting on and discovers that it is larger than its own. In that case, the waiting process replaces its own public label with the one it just read.One effect of this is that larger labels tend to migrate (in the opposite direction) along the edges of the wait-for graph.

The Detect step means that a process sees its own public label come back and knows that it is part of a cycle. A cycle of N processes will be detected after N?1Transmit steps.Only one process in a cycle will detect deadlock which simpli?es the problem of resolution.The process could simply abort (or at least, release its resources) to break the deadlock, or it could initiate some other deadlock resolution scheme.

4. A Proof of Correctness

Lemma 1:

As in the ?gure above,if there is an edge between two nodes and u>w then u=v.

Proof:

The de?nition of the Block step guarantees that this will be true when an edge ?rst forms.The only way the label u will change during the lifetime of that edge is if a Transmit step is executed, and that will not happen as long as u>w,and w is nondecreasing over time.

Lemma 2:

At the instant a cycle forms, the public labels of the nodes in it do not all have the same value.

Proof:

When the cycle forms, the last edge (like all edges) is created by a node executing the Block step.That node will have a new public label different from any other public label because the inc function generates unique values.

Lemma 3:

The maximum public label value in a cycle is equal to the private label of one and only one node in the cycle.

Proof:

By Lemma 2 when a cycle forms, all the public labels cannot have the maximum value. At least one node with maximum public label value must precede a node with a different, lower public label.Thus by Lemma 1, the private label of the preceding node must equal the maximum label value. Since no Block operations can be performed by nodes in a cycle, this will remain true throughout its lifetime.Private labels are unique, so only one node can obey this condition.

Theorem 1:

If a cycle of N nodes forms and persists long enough, exactly one node in it will execute the Detect step of the algorithm.This will happen after N?1consecutive Transmit steps.

Proof:

If a cycle forms and does not break on its own,N?1Transmit steps will carry the largest public label value all the way around the cycle. By Lemma 3, this means one and only one node will eventually execute the Detect step.

5. Aborting Low-Priority Transactions

The algorithm just presented suffers from a signi?cant drawback if the detecting process aborts to break deadlock.Since older processes tend to have larger label numbers, they are more likely to become the detecting process in a cycle. A designer may wish to assign a unique priority,p i,to each process i,on the basis of age, number of locks held, or other criteria, and select the process with the lowest priority in the cycle to be aborted.This is exactly the function provided by the following algorithm.

Block u

p

STATE BEFORE

outdegree =0

STATE AFTER Activate

Transmit

(

u

>q )

Detect Figure 2

This algorithm is an extension of the last algorithm; unique public and private priority numbers have been added.In the ?gure above,public labels and priority numbers appear as the top left and right values in a node, and the private labels and priority numbers are the bottom left and right values, respectively.Ini-tially,each process posts its unique private label and priority number.Nodes with equal public labels post the lower priority number (the Transmit step) and a node aborts when it sees its own private priority number together in a node with its own public label (the Detect step).

This algorithm aborts the lowest-priority process in any cycle that doesn’t break on its own. Since the process with the highest public label may be waiting for a lock held by the lowest-priority process, the low-priority number may not start propagating around the cycle until after the public label has gone full-cir-cle. Thus,this algorithm can take up to twice as long to detect deadlock as the ?rst algorithm.

Theorem 2:

If a cycle of N nodes forms and persists long enough, the lowest priority process in the cycle will execute the Detect step after at least N ?1and at most 2N ?2consecutive Transmit steps.

The proof of this theorem is similar to that of Theorem 1.

6. Discussion

In these algorithms, only one deadlocked process detects deadlock.This clears up the problem of deciding which process should initiate deadlock resolution.The detecting process could simply abort to break deadlock.In the ?rst algorithm, an arbitrary process detects deadlock; and in the second, the process with lowest priority in the cycle will detect.

These algorithms do not use synchronized message passing.When one process posts a value in its public label, there is no guarantee that another process (executing the Transmit step) will read it before it is replaced by a new value. It is assumed that successive reads of a label will yield successive values; never out of order.

Process failures (in which all resources held are released) will not cause deadlocks to persist, but they may lead to false deadlock detection.This happens when the cycle has already been broken (by a time-out

or failure) when the deadlock is detected.Indeed, an actual cycle may never hav e existed in any single sys-tem state.If this is a problem in some applications, the deadlock-detecting process could initiate some type of cycle checking.Passing another set of messages around the cycle could at least guarantee that a real cycle existed at some point in time.

This paper assumes a system in which no central management of resources exists, but in which resources can be locked. Such a system has many advantages, but is open to livelock conditions.

The ?rst algorithm has been implemented in an experimental database system and has performed well.

References

[BRACHA83] Bracha,Gabriel, Sam Toueg, "A Distributed Algorithm For Generalized Deadlock Detection," TR 83-558, June 1983, Department of Computer Science, Cornell Uni-

versity.

[CHANDY82] Chandy,K.M., J. Misra, "A Distributed Algorithm for Detecting Resource Dead-locks in Distributed Systems," ACM SIGACT-SIGOPS Symposium on Principles of

Distributed Computing, August 1982, Ottawa,Canada.

[CHANG82] Change,Ernest J. H., "Echo Algorithms: Depth Parallel Operations on General Graphs,"IEEE Transactions on Software Engineering,V ol. SE-8, No. 4, July 1982.

[DIJKSTRA80] Dijkstra,Edsger W., C. S. Scholten, "Termination Detection for Diffusing Computa-tions,"Information Processing Letters,V ol. 11, No. 1, August 1980.

[GLIGOR80] Gligor,Virgil and Susan H. Shattuck, "On Deadlock Detection in Distributed Sys-tems,"IEEE Transactions on Software Engineering,V ol. SE-6, No. 5, September

1980.

[MENASCE79] Menasce,Daniel and Richard Muntz, "Locking and Deadlock Detection in Dis-tributed Data Bases,"IEEE Transactions on Software Engineering,V ol. SE-5, No. 3,

May 1979.

[OBERMARCK82] Obermarck,Ron, "Distributed Deadlock Detection Algorithm,"ACM Transactions on Database Systems,V ol. 7, No. 2, June 1982.

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高中英语_An exciting job教学设计学情分析教材分析课后反思

人教版选修Unit 5 The power of nature阅读课教学设计 Learning aims Knowledge aims: Master the useful words and expressions related to the text. Ability aims: Learn about some disasters that are caused by natural forces, how people feel in dangerous situations. Emotion aims: Learn the ways in which humans protect themselves from natural disasters. Step1 Leading-in 1.Where would you like to spend your holiday? 2.What about a volcano? 3.What about doing such dangerous work as part of your job ? https://www.doczj.com/doc/224341200.html, every part of a volcano. Ash cloud/volcanic ash/ Crater/ Lava /Magma chamber 【设计意图】通过图片激发学生兴趣，引出本单元的话题，要求学生通过讨论, 了解火山基本信息，引出火山文化背景，为后面的阅读做铺垫。利用头脑风暴法收集学生对课文内容的预测并板书下来。文内容进行预测，培养学生预测阅读内容的能力。同时通过预测激起进一步探究 Step2. Skimming What’s the main topic of the article?

新目标英语七年级下课文原文unit1-6

Unit1 SectionA 1a Canada, France ,Japan ,the United States ,Australia, Singapore ,the United Kingdom,China 1b Boy1:Where is you pen pal from,Mike? Boy2:He's from Canada. Boy1:Really?My pen pal's from Australia.How about you,Lily?Where's your pen pal from? Girl1:She's from Japan.Where is Tony's pen pal from? Gril2:I think she's from Singapore. 2b 2c Conversation1 A: Where's you pen pal from, John? B: He's from Japan, A:Oh,really?Where does he live? B: Tokyo. Conversation2 A: Where's your pen pal from, Jodie? B: She's from France. A: Oh, she lives in Pairs. Conversation3 A: Andrew, where's your pen pal from? B: She's from France. A: Uh-huh. Where does she live? B: Oh, She lives in Paris.