We study the problem of optimal customer admission to multiserver queues. These queues are assumed to live in an extraneous environment which changes in a semi-Markovian way. Arrivals, service mechanism and random reward/cost structure may all depend on these surroundings. Included as special cases are SM/M/c queues, in particular G/M/c queues, in a random environment. By a direct inductive approach we establish optimality of a generalized control-limit rule depending on the actual environment. Particular emphasis is laid on different applications that show the versatility of the proposed setup.

The surprising fact that global statistical properties computed on a genomewide scale may reveal species information has first been observed in studies of dinucleotide frequencies. Here we will look at the same phenomenon with a totally different statistical approach. We show that patterns in the short-range statistical correlations in DNA sequences serve as evolutionary fingerprints of eukaryotes. All chromosomes of a species display the same characteristic pattern, markedly different from those of other species. The chromosomes of a species are sorted onto the same branch of a phylogenetic tree due to this correlation pattern. The average correlation between nucleotides at a distance k is quantified in two independent ways: (i) by estimating it from a higher-order Markov process and (ii) by computing the mutual information function at a distance k. We show how the quality of phylogenetic reconstruction depends on the range of correlation strengths and on the length of the underlying sequence segment. This concept of the correlation pattern as a phylogenetic signature of eukaryote species combines two rather distant domains of research, namely phylogenetic analysis based on molecular observation and the study of the correlation structure of DNA sequences.

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Attempts to identify a species on the basis of its DNA sequence on purely statistical grounds have been formulated for more than a decade. The most prominent of such genome signatures relies on neighborhood correlations (i.e., dinucleotide frequencies) and, consequently, attributes species identification to mechanisms operating on the dinucleotide level (e.g., neighbor-dependent mutations). For the examples of Mus musculus and Rattus norvegicus we analyze short- and intermediate-range statistical correlations in DNA sequences. These correlation profiles are computed for all chromosomes of the two species. We find that with increasing range of correlations the capacity to distinguish between the species on the basis of this correlation profile is getting better and requires ever shorter sequence segments for obtaining a full species separation. This finding suggests that distinctive traits within the sequence are situated beyond the level of few nucleotides. The large-scale statistical patterning of DNA sequences on which such genome signatures are based is thus substantially determined by mobile elements (e.g., transposons and retrotransposons). The study and interspecies comparison of such correlation profiles can, therefore, reveal features of retrotransposition, segmental duplications, and other processes of genome evolution.