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a b s t r a c tThis paper considers a Geo/Geo/1 discrete-time queue with preemptive priority. Both the arrival and service processes are Bernoulli processes. There are two kinds of customers: low-priority and high-priority customers. The high-priority customers have a preemptive priority over low-priority customers. If the total number of customers is equal or more than the threshold (k), the arrival of low-priority customers will be ignored. Hence the system buffer size is finite only for the low-priority customers. A recursive numerical procedure is developed to find the steady-state probabilities. With the aid of recursive equations, we transform the infinite steady-state departure-epoch equations set to a set of (k + 1) Â (k + 2)/2 linear equations set based on the embedded Markov Chain technique. Then, this reduced linear equations set is used to compute the steady-state departureepoch probabilities. The important performance measures of the system are calculated. Finally, the applicability of the solution procedure is shown by a numerical example and the sensitivity of the performance measures to the changes in system parameters is analyzed.

To exploit the full potential of parallelism of light in optical processing systems it is of paramount importance to have optical components which can efficiently generate arrays of >100 × 100 beams and/or images. In this paper we report on fabrication of very large binary phase grating beam splitters, better known as Dammann gratings. These space-invariant fan-out elements are the essential components when solving alloptical digital logic based 2-D and 3-D problems. Using very advanced computational techniques such as simulated annealing and downhill greedy algorithm, we have been successful in calculating the structure of fan-out elements as large as 200 × 200. The calculated structures have been plotted using electron-beam lithographic techniques with resolution of 0.1 μm. These computer-generated amplitude holograms, to our knowledge, are the largest fan-out elements fabricated to date. These amplitude masks have been copied in a range of materials including thin films of metals, dielectrics, photoresists, and bleached silver halide holographic plates to create phase elements. This results in an increase in the 2-D diffraction efficiency of the elements from 15% to >65%.