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We introduce and investigate a probabilistic model of a coherent system which consists of m elements and is intended for fulfilment of homogeneous tasks. On the first stage, one task out of the total number n of tasks enters each element of the system. The result of work of an element is either a fulfilment of the task or a failure of the element. In the case of the failure of an element, it is excluded from the system, and the task which is not fulfilled returns to the queue of those waiting for fulfilment. On the second stage, m1 tasks are sent to the system, where m1 is the number of elements of the system remained operable after the first stage, and so on. In the paper, a detailed analysis of the suggested model is realised in the case where each element of the system fulfils tasks with the same probability independently of the rest of the elements. [ABSTRACT FROM AUTHOR]

We consider the probability P( A) of the event A that while n messages each consisting of N blocks are encoded by a Hamming-type code all errors are corrected. It is assumed that the ith message has mi( ω1) errors, ω1 ∈ Ω1, where mi are independent identically distributed random variables defined on the probability space (Ω1, 1, P1). The probability P( A) is determined in the framework of the generalised allocation scheme introduced by V. F. Kolchin. It is shown that in the case where n, N → ∞ in such a manner that α = n/ N → α0 < ∞ the probabilities P( A) converge to one and the same limit for almost all ω1 ∈ Ω1, and the value of this limit is found. [ABSTRACT FROM AUTHOR]