Availability Analysis of Repairable <Emphasis Type="Italic">N</Emphasis>-Server <Emphasis Type="Italic">n</Emphasis><Subscript><Emphasis Type="Italic">i</Emphasis></Subscript>-Replicated Systems

We develop an exact closed-form expression for the steady-state availability of a repairable, N-server system in which the ith server contains n _i identical, reconfigurable, breakdown-prone units. Our approach, which follows from the Markov chain balance equations and the recursive properties of Hessenberg matrix determinants, is simpler than previously proposed matrix geometric approaches, and can readily be adapted to the availability analysis of more complicated structures. We illustrate this by computing the steady-state availability of a mixed parallel-serial gracefully degrading replicated system.     

Clumping Data in 2-Way Tables: A User-Orientated Perspective

Following a critique of existing algorithms, an algorithm is presented which will re-organize a 2-way data table to bring like rows together, and like columns together. Extensions of the method are described, and justified, to accommodate distances measured in modular arithmetic, and with bipolar columns/rows, as in repertory grid analysis. One value of the algorithms is that the user can see relationships in the tables without the data in the cells themselves ever having been transformed. Thus, users will continue to feel they own their data.     

Refining the Diffusion Approximation for the <Emphasis Type="Italic">GI</Emphasis><Superscript><Emphasis Type="Italic">x</Emphasis></Superscript><Emphasis Type="Italic">/G/c</Emphasis> Queue

This paper deals with the GI ^x /G/c queueing system in a steady state. We refine a diffusion approximation method incorporating the constraint of traffic conservation for general queueing systems. An approximate expression for the distribution of the number of customers is obtained. Numerical results are presented to show that the refined model provides improved performance.