George W. Hart

Automatic alarm correlation for fault identification

In communication networks, a large number of alarms exist to signal any abnormal behavior of the network. As network faults typically result in a number of alarms, correlating these different alarms and identifying their source is a major problem in fault management. The alarm correlation problem is of major practical significance. Alarms that have not been correlated may not only lead to significant misdirected efforts, based on insufficient information, but may cause multiple corrective actions (possibly contradictory) as each alert is handled independently. The paper proposes a general framework to solve the alarm correlation problem. The authors introduce a new model for faults and alarms based on probabilistic finite state machines. They propose two algorithms. The first one acquires the fault models starting from possibly incomplete and incorrect date. The second one correlates alarms in the presence of multiple faults and noisy information. Both algorithms have polynomial time complexity, use an extension of the Viterbi algorithm to deal with the corrupted data, and can be implemented in hardware. As an example, they are applied to analyse faults using data generated by the ANS (Advanced Network and Services, Inc.)/NSF T3 network.

Blocking probabilities in multitraffic loss systems: insensitivity, asymptotic behavior, and approximations

It is known that, under any sharing policy, the state describing the number of calls established for each class of traffic in steady state has a product-form distribution when the connection time distribution has a rational Laplace transform. The product-form property further holds for arbitrary holding time distribution under coordinate convex sharing policies. For the complete sharing policy case, an aggregate state describing the number of occupied circuits is shown to maintain the product-form property under asymptotic behavior, when the capacity and traffic intensities go to infinity on a comparable scale. Two theorems relative to the asymptotic behavior of the blocking probabilities which provide some insight into the nature of the blocking phenomenon are given. An approximation which reduces the numerical complexity of evaluating the blocking probabilities for the different classes of service to the computation of a single Erlang formula and the determination of the root of a monotonous polynomial function is proposed. >

Two extensions of the Viterbi algorithm

The problem of minimum-cost correction of a corrupted set of data that has been generated by a known finite state machine (FSM) is examined. The Viterbi algorithm is modified to correct insertions and deletions as well as errors, still using a trellis diagram that has the same number of states as the FSM that generates the uncorrupted data. Two problems are examined. In the first problem the data is given in the traditional form of a string so the novel aspect is that insertions and deletions are now corrected. In the second problem, a unique string need not be given, but a regular language is given, and any string belonging to the regular language is a possible data string. Again, deletion addition, and changes of symbols are corrected. A direct generalization of the Viterbi decoding algorithm is thus proved to be an efficient technique for solving a much wider class of problems. >

Fault identification using a finite state machine model with unreliable partially observed data sequences

The problem of minimum cost identification of a finite state machine (FSM) using a trace of its event history is addressed. The motivation is fault identification in communication systems, although other applications are possible as well. The event history used for the identification is partially observed, i.e., it is known to be a member of a regular language. Any string which belongs in this regular language is a possible trace of the FSMs event history. Furthermore, the event history is assumed to be corrupted with deletions, additions, and changes of symbols. The FSM to be estimated is related to a known FSM by performing an unknown number of additions and changes of arcs. An identification algorithm based on a fast algorithm that can correct corrupted data strings generated by a known finite state machine is developed. Examples of the method are provided, including one based on the IEEE 802.2 logical link control protocol. >

Efficient management of time-evolving databases

Efficiently managing the history of a time-evolving system is one of the central problems in many database environments, like database systems that incorporate versioning, or object-oriented databases that implicitly or explicitly maintain the history of persistent objects. In this paper we propose algorithms that reconstruct past states of an evolving system for two general cases, i.e., when the systems state is represented by a set or by a hierarchy (a forest of trees). Sets are widely used as a canonical form of representing information in databases or program states. For more complex applications, like schema evolution in object-oriented databases, it becomes necessary to manage the history of data structures that have the form of forests or even graphs. The proposed algorithms use minimal space (proportional to the number of changes occurring in the evolution) and have the advantage of being on-line (in the amortized sense). Any past system state s(t) is reconstructed in time O. >

Correcting dependent errors in sequences generated by finite-state processes

A new channel model and channel inversion algorithm are presented for correcting symbol sequences that have been corrupted by an unknown combination of known fault mechanisms. The algorithm is similar to the Viterbi algorithm in that it is suitable for situations in which the uncorrupted data string is generated by a known finite-state process, but it is more versatile in that it can correct a much broader class of errors. Of particular importance is the fact that the algorithm corrects common context-sensitive errors, such as symbol changes, transpositions, mergers, splits, insertions, and deletions, which may be assigned different probabilities depending on the context of preceeding and subsequent symbols. As many communication channels can be modeled in this way, this algorithm is a significant extension over the Viterbi algorithm and previous decoding techniques. The notion of channel rules is introduced to provide a framework for the user to specify the channel operation. The algorithm is given in both an off-line form and a recursive form suitable for sequentially presented data streams. In most applications, the recursive form has computational complexity only a constant times that of the Viterbi algorithm. >

On the Design of Observers for Fault Detection in Communication Networks

This paper provides a framework for approaching the problem of fault detection in large Communication Networks. Communication process are modeled as Discrete Event Systems (D.E.S.), so any fault will appear as a change of a D.E.S. Here we concentrate on the simplest case of Discrete Event systems, namely Finite State Machines (FSM).

Reconfiguration algorithms for rearrangeable lightwave networks

The authors propose a minimally disruptive approach that transitions the network through a sequence of branch exchange operations, so that only two links are disrupted at any given time. It is shown that the problem of finding the shortest sequence, so as to minimize the duration of the reconfiguration phase, is equivalent to the problem of finding a decomposition of an auxiliary graph into the largest number of vertex-disjoint cycles. The authors then propose and compare three different polynomial-time greedy algorithms, on the basis of performance and time complexity. Noticing that the length of a sequence increases at most linearly with the size of the network, the authors derived the average rate of growth from simulation results.<<ETX>>

Topology identification for traffic and configuration management in dynamic networks

The authors address the problem of identifying the topology of a network from data collected at a designated node (possibly one of the network nodes). The data considered are descriptions of the local neighborhood about each node, which specify the identities of the node and of its neighbors. These data are neither required to be correct nor complete. The authors propose a model that describes and relates the network topology and the data. They define costs associated with this model, and reduce the identification problem to a combinational optimization problem with and an objective function based on these costs. A pseudo-polynomial-time algorithm is derived, which yields a local minimum of the objective function. The local minimum appears to be a reasonable solution, as shown by a range of examples.<<ETX>>

Memoryless nonlinear system identification with unknown model order

The problem of identifying a general memoryless input/output system from measurements of inputs and the corresponding outputs is considered. The measured output is sought to be represented as the linear combination of known functions of the input with some additive noise. The choice of model order to be used to fit the data is the main issue addressed, and a cost function involving the prediction error and the model order is derived. The cost function under certain approximations is shown to be similar to one obtained by H. Akaike (1969, 1970). If there is a real system generating the data, it is shown that the expected value of this cost function is always minimized at the true value of the order as long as the noise variance satisfies certain conditions. Asymptotic results for some cases are derived. An efficient algorithm is proposed for identifying the model order. Some simulation results using the proposed algorithm are also presented. >