Authors: Ulf Wiger (ulf@wiger.net), Thomas Arts (thomas@quviq.com).
Scalable deadlock-resolving locking system
A scalable, deadlock-resolving resource locker
This application is based on an algorithm designed by Ulf Wiger 1993, and later model-checked (and refined) by Thomas Arts.
Compared to the implementation verified by Thomas Arts, 'locks' has included a hierarchical lock structure and has both read and write locks. It is also distributed, supporting multi-node locks and quorum ('majority').
The algorithm is based on computing potential indirect dependencies and informing dependent transactions in a 'fill-in-the-blanks' manner.
Eventually, one transaction will have enough information to detect a deadlock, even though no central dependency graph or dependency probes are used. Resolution happens with a (at least close to) minimal number of messages, making the algorithm unusually scalable. Since it uses deadlock detection instead of deadlock prevention, there are no phantom deadlocks.
Note: Unlock has not (yet) been implemented. Once the transaction ends, all locks held by it are released automatically.
Deadlocks can be resolved by one agent surrendering a lock to another agent. The surrendering agent will be put last in the lock queue.
Note that this is a bad idea if the surrendering agent's client has already acted on the lock. Optionally, the agent can abort whenever it would otherwise have had to surrender a lock. This might be preferrable in some cases, and will still only happen if there is an actual deadlock. It is usually possible to design a system so that deadlocks will not occur during normal operation.
The agent that is told to surrender will do so unless the client has asked
for the transaction to be aborted AND the lock being surrendered has been
reported as held to the client. That is, the abort_on_deadlock option
when starting an agent may still allow some surrenders to take place - only
not on locks that the client already thinks it has. See the locks_leader
for an example of an application where abort_on_deadlock=false is the
desired mode of operation.
Call application:start(locks) on each node that needs to participate in
locking.
The lock identifiers used by 'locks' are non-empty lists of key elements.
The lock table is viewed as a tree, and e.g. [a] implicitly locks [a,1],
[a,2], etc. Locks can be read (shared) or write (exclusive). Shared locks
are automatically upgraded to exclusive locks if requested (and if possible).
Using 'locks' in a database system, one might use a lock naming scheme like
[DbInstance, Table, Lock], where [DbInstance] would be equivalent to a
schema lock, [DbInstance, Table] a table lock, etc.
There is only one lock table per Erlang node, so use prefixed keys, or a unique top-level key.
While it is possible to use the locks_server API directly to lock single
objects, distributed locking and deadlock detection is done by locks_agent.
The official API to use is locks.
Agents are started e.g. using locks_agent:begin_transaction(...), and are
separate state machines (processes). The locks_server informs agents via
#locks_info{} messages (containing not only the ID of the agent that holds
a lock, but also of any agents waiting for one), and each agent keeps track
of a dependency graph. Agents inform each other ('younger' agents inform
'older' agents) of indirect dependencies, using an algorithm that guarantees
that one involved agent will eventually have enough data to detect any deadlock.
If a deadlock is detected, the 'oldest' agent must yield its lock. This is
either done as a 'surrender', where the agent yields the lock and is placed
last in the lock's wait queue, or by aborting. Which behavior is used is
controlled by the option {abort_on_deadlock, bool()}, given at the beginning
of the transaction.
Using the function locks:lock(Agent, LockID, Mode, Nodes, Req), a lock
can be acquired on several nodes at once.
Agent :: pid().
LockID :: [any()].
Mode :: read | write.
Nodes :: [node()].
Req :: all | any | majority.
The agent monitors the lock servers on each node. If it determines that too few lock servers are available to fulfill the lock requirement, it will abort.
The following text describes the implementation verified by Thomas Arts during 1999-2000. It contains several explanations of the algorithm, identifying a number of alternative design choices as unsafe. There are also some hints regarding optimization potential.
A few comparisons with the current implementation:
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When Arts talks about 'the object' and 'the client', these correspond to the object_server (which handles all locks on the node) and the agent respectively.
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The implementation also served read and write requests on the object. This has been removed, and it is up to the client to ensure that it does not operate on a resource requiring a lock, without first acquiring the lock.
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Canceling a lock request is not yet implemented.
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Lock update messages do not contain the requesting agent. Instead, a separate message from the locks_server acknowledges a surrender request, and the agent will ignore any lock updates for that lock, which precede the 'surrendered' message.
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The verification did not deal with 'hierarchical' locks (e.g. table and object locks). The current implementation treats all locks as part of a hierarchy, and introduces the notion of an 'indirect' lock. Indirect locks are only of concern to the locks_server; the agents only need to know that they are waiting for another agent that holds the lock - whether the lock is held directly or indirectly is of no concern. To wit, if an agent A takes a lock on [a, b], and it is granted, it will indirectly lock [a]. If another agent B tries to lock [a, b, c] while A holds [a, b], the locks_server will infer that A also indirectly locks [a, b, c]. This indirect lock is created as-needed (if no one tries to lock [a, b, c], no indirect lock needs to be created - indeed must not, as the domain of potential children is unbounded.
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Multi-node locks are not considered below. The current implementation treats each lock on each node as an individual lock. For example, locking [a] on nodes [N1, N2] will result in two lock requests, {[a], N1} and {[a], N2}. The agent keeps track of which locks belonged to the same request, viz. we may consider the lock granted only when we have a lock on [a] on all, or a majority, of the requested nodes. If some of the requested nodes are not available, the lock may still be considered held if a majority of them can be claimed. The exact semantics are specified when requesting the lock. Note also that this introduces the risk of deadlock within a single lock: If agent A and B both try to claim [a] on [N1, N2], and A gets the lock on N1, while B gets the lock on N2, this will be a deadlock. However, if the lock is still considered pending by the agent which needs to surrender, the client will not notice this, and the conflict will be resolved automatically.
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Even with the above differences, the dependency analysis and deadlock- related decision-making is the same as in Arts's version - only modified to accomodate the slightly different data representation.
Basically the algorithm consists of two entities, viz. one for the object and one for the client. These entities are best seen as interfaces that arrange for the client to get access to an object, and ensure that the object is only accessed by clients which are allowed to do so.
The algorithm implementing the object interface should provide read and write functionality, but also guarantee that such read or write is guaranteed to be done by a client that has the right to do so (i.e. holds the lock).
The algorithm implementing the client interface keeps track of the objects that need to be locked for a read and/or write operation. The client interface is actively asking the objects for read/write permission (a lock) and waits for the results supplied by the objects. The information is gathered, combined with consecutive information provided by the objects and competing clients and action is taken upon the received information. The client interface can either conclude that it has obtained read/write access to all required objects, or, by absence of all information, wait for more information and/or send information to competing clients.
In the following we describe the algorithms for both entities in more detail and motivate the different design decisions. The design seems optimal within the setting we have in mind, however, other settings are plausible candidates for practical applications as well. Therefore, we first describe the setting we work in and sketch alternative design possibilities for situations that we think are of additional practical interest.
We assume computers to run in a distributed environment, connected with a communication network of which the speed is slow compared to the computation speed of the individual computers in the net.
Clients and objects have a unique reference and a total order exists among these references. The uniqueness of the reference is guaranteed. However, the set of possible references is finite.
No strong assumption is therefore made about the relationship between creating a client or object and the assigned reference. As a heuristic we assume a client that is created later in time has a larger reference than the earlier created clients (w.r.t. the order on references). This heuristic is, though, violated now and then and therefore we do not consider it a rule.
We assume enough memory available to store all information about the relationship between locks and objects of interest to us. Moreover, we assume the existence of a sequence of numbers as long as we need to attach version numbers to messages, such that within the lifetime of an object, we do not run out of numbers.
The algorithm implementing the interface to the object stores requests from clients for access to certain locks. The requests are stored in a waiting queue in order of arrival. The first element of the queue is considered to have granted access to the object. Upon arrival of a request from a client, it is put at the end of the queue and all clients in the queue are notified about the new situation of the queue.
Clients are also allowed to cancel their request, in which case they are just removed from the queue. Again, all clients remaining in the queue are notified. A cancel request always arrives when a client processes is somehow killed or unreachable.
The client that holds the lock on the object, i.e., is the first in the waiting queue may request to surrender, i.e., it is no longer the first in the queue. Upon a surrender request, the requesting client is placed last in the queue and all clients are again notified about the new order in the queue.
Placing a surrendering client at the end of the queue is the only safe general way of implementing a surrender action. It is not safe to just swap with the client directly behind it. Moreover, the object cannot oversee what other place would be safe to surrender to. In some cases the client, however, could obtain so much information that it would be able to compute a safe place in the queue to surrender to.
Nevertheless, having the client ask to surrender to a certain place is in general unsafe.
Every notification to the clients of the updated state of the queue is supplied with a version number. The version number is increased after every change in the queue. Moreover, the notifications are also carrying the identity of the client that induced the notification to be sent, i.e. the client that requested access, canceled or surrendered. Both are necessary items for the client in order to have a safe execution.
The algorithm also implements a read and write operation on the object, where the read and write are only allowed whenever the requesting client holds the lock for the object (i.e., is first in the queue).
In case the references assigned to clients reflect their creation, viz. the reference gets bigger the later a client is created (e.g. absolute time as reference), the above object can be optimized by having the tail of the waiting queue (i.e. all elements except for the first one) sorted with respect to the total order on the references. However, this is unsafe in case of a finite set of references. One can work around this unsafe situation in case the set of references is big enough and timeout primitives are used to deal with starvation.
This alternative implementation method is not optimally efficient in general, but may be more efficient in cases were negotiation about objects is relatively fast compared with the time it takes to run out of references. Clients that do not get served in time, should however restart their requests, which may take severe overhead for some individual clients, whereas the other clients are served much faster.
The interface for the client gets activated whenever a client needs some objects to perform an operation on. Access to the objects is requested by the client interface and after all objects have been locked, the client is notified that the operation may take place. After performing the operation, the client interface is addressed by the client and the interface releases the locks on all the objects it has acquired for the client.
The communication between client interface and object interface is already described in the object part. A lock can be requested, surrendered or a request can be canceled.
The client interface is constantly updated when the queue of an object that it has requested changes. This information is stored by the client interface, and as such, the client interface detects easily when all objects are assigned to it.
The queue information that the object provides has a version number and the identity of a client attached to it. The client keeps track of this version information and whenever information is received with a version number smaller than a version number of earlier received information, this information is ignored. It is unsafe to disregard the version information, since because of delays in the network, information could arrive in the wrong order and the client could cause a deadlock by acting wrongly on the old information.
The attached client information in the deadlock is used by the client as an acknowledgment on a surrender request. Whenever the client sends a surrender request, it should ignore all information coming from the surrendered object, until it carries its own client identity. The latter is necessary to ensure a safe operation in case the client surrenders and outdated information arrives stating that the client just received access again.
Whenever the information about the queues of the objects is such that not (yet) all the objects are assigned, the client interface computes the so-called wait-for graph; the graph expressing which client waits for which other client to get access to an object.
If this graph contains a cycle, then a deadlock situation exists. The client interface checks for cycles in the graph and if such a cycle exists, it computes which of the clients in this cycle that holds the lock for an object has the largest reference (since there exists a total order of the references, this is uniquely defined). If the client interface does not represent this largest reference itself, it waits for more object information to come.
If, however, the client interface represents this largest reference, it sends a surrender message to the object it holds that caused the deadlock situation. Note that it is important to select this particular client among the ones that indeed hold a lock.
In order to be able to surrender only one object, one needs to store the relation between the object and the clients waiting for that particular object. It should be clear which object is waited for in the deadlock situation, since the client that surrenders may very well hold other objects, which are not involved in a deadlock situation.
In case of only little memory available, one might choose for not storing all information but surrender all objects the client holds. This is a safe strategy, but inefficient.
Instead of having the client with largest reference surrendering, one could also demand the smallest client to surrender. In our setting, the largest is more optimal, since the reference contains information about the time the client asked for the object. The smaller the reference, the longer the client is waiting for the object.
In special circumstances a client interface could compute that surrendering to the end of the queue is not the most efficient. However, such a computation needs extra information from the application that the algorithm is used for. For example, if it is known that every client is at most claiming three objects at a time, this information could very well be used to compute more optimal surrendering positions.
When a client interface does not encounter a cycle in the graph, it reports the graph information to other clients. Note that all clients only have part of the information of the "global" wait-for graph. By spreading the information to other clients, one ensures in the end that at least one client obtains the "global" wait-for graph as its local graph. Here one has several possibilities in spreading the information around.
The efficiency and optimality of the strategy of which client is sending this information to which other client(s) depends on the way the objects and clients relate (how many clients are demanding the same object, how many objects are demanded by the clients, etc.).
The most naive way of spreading the information is that a client sends its wait-for graph to all clients that occur in this graph. Optimally a client only sends part of the graph to another client, if that client does not have that information and is not getting it from another client.
The latter can partly be achieved by clients only sending information to clients that have a smaller reference, or alternatively, only to those that have a bigger reference.
Another strategy which reduces the number of messages sent, and therefore is efficient when computation is much cheaper than sending (as in our setting) is that clients only send to clients that it is waiting for and only send the information of the clients that wait for it.
Analogous to this, the client could send the clients that wait for it, the information of the clients it is waiting for.
Any of the above spreading strategies can even be improved by computing which information the client one wants to send something to should already have, such that no superfluous information is sent if avoidable.
The wait-for graph is easily implemented by using standard data structures and computing cycles in such a graph is a well known operation for which several algorithms exist in literature.
Specific for the client interface algorithm is that nodes in the graph contain both client identity, the object that the client is locking,and whether the client has obtained the lock to this object. An arc is drawn from one node to another if the client in this triple is waiting for the client in the other node. Note here that not all clients need be presented in the graph, but only those that hold a lock. However, the relation that expresses a client waiting for another client takes all known clients into account.
Whenever a cycle is detected, from the nodes on this cycle the client with largest reference surrenders the object it locks.
| locks |
| locks_agent |
| locks_leader |
| locks_server |
| locks_ttb |