Backpressure-based adaptive routing algorithms where each packet is routed along a possibly different path have been extensively studied in the literature. However, such algorithms typically result in poor delay performance and involve high implementation complexity. In this paper, we develop a new adaptive routing algorithm built upon the widely-studied back-pressure algorithm. We decouple the routing and scheduling components of the algorithm by designing a probabilistic routing table which is used to route packets to per-destination queues. The scheduling decisions in the case of wireless networks are made using counters called shadow queues. The results are also extended to the case of networks which employ simple forms of network coding. In that case, our algorithm provides a low-complexity solution to optimally exploit the routing-coding tradeoff.

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In this paper, we develop a probabilistic methodology for failure diagnosis in finite state machines based on a sequence of unreliable observations. Given prior knowledge of the input probability distribution but without actual knowledge of the applied input sequence, the core problem we consider is to choose from a pool of known, deterministic finite state machines (FSMs) the one that most likely matches the given sequence of observations. The problem becomes challenging because of sensor failures which may corrupt the observed sequence by inserting, deleting, and transposing symbols with certain probabilities (that are assumed known). We propose an efficient recursive algorithm for obtaining the most likely underlying FSM, given the possibly erroneous observed sequence. The proposed algorithm essentially allows us to perform online maximum likelihood failure diagnosis and is applicable to more general settings where one is required to choose the most likely underlying hidden Markov model (HMM) based on a sequence of observations that may get corrupted with known probabilities. The algorithm generalizes existing recursive algorithms for likelihood calculation in HMMs by allowing loops in the associated trellis diagram. We illustrate the proposed methodology using an example of diagnosis in the context of communication protocols.Index Terms-Deletions, discrete event systems (DESs), failure diagnosis, finite state machines (FSMs), insertions, maximum likelihood model classification, probabilistic automata, transpositions.

In this paper we develop a probabilistic methodology for calculating the likelihood that an observed, possibly corrupted event sequence was generated by two (or more) candidate finite state machines (FSMs) (one of which could represent the normal mode of operation and the other(s) could represent the failed model(s)). Our objective is to perform failure diagnosis by deciding which FSM is most likely to have generated the observed event sequence. The underlying problem relates to the evaluation problem in Hidden Markov Models (HMMs) which calculates the probability that an observed sequence is generated by a given Markov model. However, the additional challenge in our setup is the fact that errors may corrupt the observed sequence, potentially causing loops in the resulting trellis diagram. These errors include, in their most basic form, event insertions and deletions and could arise under a variety of conditions (e.g., due to sensor failures or due to problems encountered in the links connecting the system sensors with the diagnoser). Given the possibly erroneous observed sequence, we propose an algorithm for obtaining the most likely underlying FSM.

We consider small generalized switches with less than or equal to four links, and study scheduling policies designed to minimize the total number of packets in the system. By focusing on very small switches, we are able to derive optimal or heavy-traffic optimal policies whose performance can then be compared to previously conjectured optimal policies. In particular, it has been conjectured that the max-weight policy with weight q α is optimal in heavy-traffic when α → 0. Our results show that this conjecture is not true.