This paper presents a method for modeling the operation of the frame synchronization algorithms of the several levels of a synchronous time division multiplex hierarchy as a Markov chain. A method, discussed elsewhere by one of the authors, is used to drastically reduce the number of states in the Markov chain and make a numerical calculation of the mean first passage times possible. The mean reframing times as a function of appropriate parameters are determined for three examples, with one approaching the complexity of a practical system. A determination of the same quantities by methods unrelated to the proposed approach gives results which are in excellent agreement.

This study is concerned with the problem of monitoring the performance of communication links, as indicated by bit error rate, with the objective of detecting as rapidly as possible failures or extreme degradation caused by any source. The monitoring method is based on the use of an artificial threshold for the decision variable and the generation of a measurable "pseudoerror." The study relates pseudoerror probability to true-error probability for two models-one using an analytical-numerical approach and the other using a Monte Carlo simulation. Variation of the parameters in the models adequately approximates the first-order effects of many types of link failure. The results indicate that a monitor indication based on pseudoerror is feasible and has many desirable properties.