Asynchronous failure location algorithm for fiber-optic networks

All current research on fiber-optic networks assume that the underlying fiber-optic network delivers the messages correctly to their intended destination. To satisfy the assumption of correct delivery of messages, we present an algorithm that locates possible stuck-at faults in the switching subsystems of the nodes of general asynchronous fiber-optic networks and provides the nodes of such a network with reliable paths for delivering messages sent between any two nodes. The algorithm has an O(n2E) message complexity and O(Elog2n+mnlog2n) bit storage complexity, where n, E, and m are the total number of nodes, the total number of edges, and the maximum degree of the network, respectively. 1: Introduction The rapid advent of fiber-optic communication technologies resulted in a significant increase in the speeds at which data may be transmitted. As a result, the user of fiber-optic high-bandwidth computer networks is introduced to new exciting applications such as multimedia programs where voice, data, and image can be sent simultaneously. No longer are users limited to transmission rates of a few million bits/second; with fiberoptic networks, users can send information at the rate of giga bits/second 141, [lo]. In this paper, we introduce a distributed algorithm to solve a new problem that is unique to fiber-optic networks. This is the problem of locating possible stuckat faults in the switching subsystems of the nodes of general asynchronous fiber-optic networks. Informally, a stuck-at switching subsystem always forwards the messages to a particular link regardless of the destination of the messages. This problem is extremely important because such faults could lead to erroneous routing of the messages and hence unreliable delivery of messages. All current research on fiber-optic networks assume that the underlying network delivers the messages correctly to their intended destination. For example, Cidon et al [6] introduced an algorithm of O(n) message complexity to solve the leader election problem on asynchronous fiberoptic networks, where n is the total number of nodes in the network. Abu-Amara and Gummadi [2] introduced an election algorithm that requires O(& log2D+m) time complexity and O(n) message complexity to run on synchronous fiber-optic networks, where D is the diameter of the network and m is the maximum degree of the network. Abu-Amara [l] developed a topology update algorithm of O(log2D) time complexity and O(n) message complexity. Cidon et a1 [51 developed a scheme for distributed control in fiber-optic networks. Recently, AbuAmara and Abu-Amara [3] introduced the first distributed algorithm that locates possible stuck-at faults in the switching subsystems of the nodes of svnchronous fiberoptic networks. The algorithm has O(m2+m D ) time complexity, where D is the new diameter of the network. To satisfy the assumption of correct delivery of messages, we present the first known algorithm that locates faulty switching subsystems in general asvnchronous fiber-optic networks and that guarantees the correct delivery of messages. In Section 5 , we present the algorithm. Before we present the algorithm, we discuss the model for fiber-optic networks in detail. 2: Fiber-optic model Our model follows the modified fiber-optic model proposed by Abu-Amara and Gummadi [2]. In this model, each node consists of a switching subsystem (SS) and a node control unit (NCU). Because all of the functions of the switching subsystem are implemented in hardware, there are no message queues in the switching subsystem. On the other hand, the node control unit is slow and requires the presence of message queues to buffer the messages forwarded by the switching subsystem, Each computer has a local clock. We assume that the clocks of the various computers are not necessarily synchronized. We further assume that each NCU(v) has a unique number ID(v) chosen from a totally ordered set. In our algorithm, we assume that the nodes do not initially know the IDS of the other nodes of the network. Therefore, the nodes do not initially know of any path that connects them to any other node. As the nodes see messages from other nodes, the nodes learn the IDS and paths in the network. This assumption is common in distributed algorithms [21 and [4]. We assume also that 69