Abstract EquiX is a search language for XML that combines the power of querying with the simplicity of searching. Requirements for such languages are discussed, and it is shown that EquiX meets the necessary criteria. Both a graph‐based abstract syntax and a formal concrete syntax are presented for EquiX queries. In addition, the semantics is defined and an evaluation algorithm is presented. The evaluation algorithm is polynomial under combined complexity. EquiX combines pattern matching, quantification, and logical expressions to query both the data and meta‐data of XML documents. The result of a query in EquiX is a set of XML documents. A DTD describing the result documents is derived automatically from the query.

A stochastic model of buffering in a data communication system is considered, with source and sink transmission parameters depending on the number of active sources. For models in this control setting the authors analyze an effective numerical method for evaluating the equilibrium distribution of buffer content. The theoretical basis of the method is established first. Then, it is shown that the method has the same complexity, in terms of the total number of sources, as known analytical methods for the model with constant parameters. Asymptotics for tail probabilities at high buffer levels and under heavy load are also derived, and the complexity of their computation is compared with that of evaluating explicit formulas. In comparison to earlier results this approach reduces the complexity of computing the probability of overflow and its asymptotic estimates. The speed-up stems from the application of interpolation schemes.>

A controlled Markov model of the slotted ALOHA system in which the control parameter is the retransmission probability and a set of controls is the interval [0, 1] is considered. Numerical results are presented which show that the policy which maximizes the system's expected packet flow per time slot is not optimal. It is shown that, although it is not optimal, this policy can be considerably better than the optimal two-action control-limit policy.

This work is devoted to the analysis of page replacement algorithms under assumptions on the stochastic nature of the sequence of memory accesses. A detailed discussion of the authors' results, some of which were published in Russian, and their relations to other papers is given. The object of study of this paper is two families of page replacement algorithms (PRA's) which contain certain algorithms of practical and theoretical interest. Analytical results are derived using the assumption that the references to the pages are independent identically distributed (iid) random variables. The algorithms of the first family are intervening between FIFO and LRU and the algorithms of the second family estimate the most frequently referenced pages considerably better than LRU. Explicit expressions of the page fault probabilities are obtained for these families and least upper bounds of performance are established which are independent of the page request probabilities. It is shown that for the second family the fault probabilities are less than twice the optimal one.