We consider the covariance structure of an interrupted Markov modulated Poisson process. In this process, periods of on-time and off-time alternate; the on-time interval has a phase-type distribution and the off-time interval has a general one. The off-time period represents the time during which no customers arrive. The on-time period on the other hand, represents the time during which customers do arrive. Here, the arrival rate depends on the phase condition of the on-time interval distribution. We derive the Laplace-Stieltjes transform for the inter-arrival time distribution. Using the results, we study the correlation structures of succeeding inter-arrival times. When the on-time length distribution is hyperexponential, the covariance of succeeding inter-arrival lengths is positive, whereas becomes negative for Erlangian on-time lengths.

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Hildreth's algorithm is a classical iterative. method for solving strictly convex quadratic programming problems, which uses the rows of constraint matrix just. one at a time. This algorithm is particularly suited to large and sparse problems, because it acts upon the given problem data directly and the coefficient matrix is never modified in the course of the iteration. The original Hildreth's algorithm is mathematically equivalent to Causs-Seidel method applied to the dual of the given quadratic programming problem. In this paper, we propose an SOR modification of Hildreth's algorithm for solving interval constrained quadratic programming problems. We prove global convergence of the algorithm and show that, the rate of convergence is linear. Computational results are also presented to demonstrate the effectiveness of the algorithm.

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A detection law (the conditional detection rate. ) which corresponds to the model of Washburn's lateral range curve is presented in this paper. The detection law dealt, with here is a general one which includes the inverse cube law and the definite range law. The lateral range curve and the sweep width of this law are derived explicitly. Two met,hods for estimating the parameters of the law are presented and a set of actual data, is analyzed. Applying the model, we investigate the forestalling detection problem in a search-and-search situation. Taking account, of the forestalling detection by the target, the generalized formulas of the lateral range curve and the sweep width are derived.

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Selection from among n objects by relative rank with no recall - the "secretary problem" -in the asymptotic case when n → ∞ was considered, assuming that k, the cost ratio, is a finite constant. The essential part is what we shall call Phase 1, where the number of observations i remains to be O(√<n>). Then the expected number of observations is of course O(√<n>). The expected value of the attained absolute rank is also O(√<n>). It is interesting to not,e that, with the optimal rule, the expected cost of observations comes out to be equal to the expected rank.

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