Highly Concurrent and Fault-Tolerant h-out of-k Mutual Exclusion Using Cohorts Coteries for Distributed Systems

Distributed Systems A distributed system consists of interconnected, autonomous nodes which communicate with each other by passing messages.

CS vs Mutual Exclusion A node in the system may need to enter the critical section (CS) occasionally to access a shared resource, such as a shared file or a shared table, etc. How to control the nodes so that the shared resource is accessed by at most one node at a time is called the mutual exclusion problem.

K-Mutual Exclusion If there are k, k  1, identical copies of shared resources, such as a k-user software license, then there can be at most k nodes accessing the resources at a time. This raises the k-mutual exclusion problem.

h-out of k-mutual exclusion On some occasions, a node may require to access h (1  h  k) copies out of the k shared resources at a time; for example, a node may need h disks from a pool of k disks to proceed. How to control the nodes to acquire the desired number of resources with the total number of resources accessed concurrently not exceeding k is called the h-out of k-mutual exclusion problem or the h-out of-k resource allocation problem [10].

Related Work There are four distributed h-out of-k mutual exclusion algorithms proposed in the literature [2, 5, 9. 10]. The first algorithm using request broadcast is proposed by Raynal in [10], and three algorithms using k-arbiters, (h, k)-arbiters, and k-coteries are later proposed in [2], [9], and [5], respectively.

Jiang’s Algorithm Among the four algorithms, only Jiang’s algorithm using k-coteries is fault-tolerant. It can tolerate node and/or network link failures even when the failures lead to network partitioning. Furthermore, it is shown in [5] to have lower message cost than others.

Basic Idea of Jiang’s Alg. The basic idea of the algorithm is simple: a node should select h mutually disjoint sets and collect permissions from all the nodes of the h sets to enter CS for accessing h resources. To render the algorithm fault-tolerant, a node is demanded to repeatedly reselect h mutually disjoint sets for gathering incremental permissions when a node fails to gather enough permissions to enter CS after a time-out period.

Drawbacks of Jiang’s Alg. First, it does not specify explicitly how a node can efficiently select and reselect h mutually disjoint sets. Second, when there is contention, a low- priority node always yields its gathered permissions to high-priority nodes, which causes higher message overhead and may prohibit nodes from entering CS concurrently.

Overview of the Proposed Alg. In this paper, we proposed another h-out of-k mutual exclusion algorithm using a specific k- coterie  cohorts coterie to eliminate the drawbacks of Jiang’s algorithm. Constant message cost in the best case A candidate to achieve the highest availability, the probability that a node can gather enough permissions to enter CS in an error-prone environment, among all the algorithms using k- coteries.

k-Coterie

Cohorts Structure

Quorum under Coh(k, m)

An Example

Domination

ND k-coteries Since an available quorum implies an available entry to CS, we should always concentrate on ND (nondominated) k- coteries that no other k-coterie can dominate. The algorithm using ND k-coteries, for example the proposed algorithm, is a candidate to achieve the highest availability.

The quorum construction procedure

Probe(C i, g)

Case 1 for Probe(C i, g) to return

Case 2 for Probe(C i, g) to return

Case 3 for Probe(C i, g) to return

Pre-release

Maekawa’s Alg. (1983) uses six types of messages: REQUEST LOCKED FAILED RELEASE INQUIRE RELINQUISH

Differences of Ours and Maekawa’s 1.Our mechanism does not use FAILED message. 2.Our mechanism uses an extra PRE- RELEASE message. 3.Our mechanism sends INQUIRE message conditionally (instead of insistently) only when there is possibility of deadlock.

Conflict resolution mechanism #1

Conflict resolution mechanism #2

Conflict resolution mechanism #3

Conflict resolution mechanism #4

Conflict resolution mechanism #5 On receiving a RELINQUISH message form w (w must be the locker), node v swaps w with u, sets u as the locker, and sends a LOCKED message to u, where u is the node at the front of R-QUEUE.

Conflict resolution mechanism #6

Conflict resolution mechanism #7

Conflict resolution mechanism #8

Comparisions

Conclusion The proposed algorithm becomes a k-mutual exclusion algorithm for k>h=1, and becomes a mutual exclusion algorithm for k=h=1. It is resilient to node and/or link failures and has constant message cost in the best case. Furthermore, it is a candidate to achieve the highest availability among all the algorithms using k-coteries since the cohorts coterie is ND. It has the k-concurrency property to allow more nodes in CS concurrently. However, it’s mutual exclusion delay may be long since it probe nodes cohorts by cohorts instead of probing all nodes in a quorum at once.