The linear matroid parity problem

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1985.MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING.Bibliography: leaves 94-96.by John H. Vande Vate.Ph.D

Stability and Instability of a Two-Station Queueing Network

This paper proves that the stability region of a 2-station, 5-class reentrant queueing network, operating under a non-preemptive static bu#er priority service policy, depends on the distributions of the interarrival and service times. In particular, our result shows that conditions on the mean interarrival and service times are not enough to determine the stability of a queueing network, under a particular policy. We prove that when all distributions are exponential, the network is unstable in the sense that, with probability one, the total number of jobs in the network goes to infinity with time. We show that the same network with all interarrival and service times being deterministic is stable. When all distributions are uniform with a given range, our simulation studies show that the stability of the network depends on the width of the uniform distribution. Finally, we show that the same network, with deterministic interarrival and service times, is unstable when the it is operated under the preemptive version of the static bu#er priority service policy. Thus, our examples also demonstrate that the stability region depends on the preemption mechanism used

Minimizing Deflection And Bending Moment In A Beam With End Supports

We give heuristics to sequence blocks on a beam, like books on a bookshelf, to minimize simultaneously the maximum deflection and the maximum bending moment of the beam. For a beam with simple supports at the ends, one heuristic places the blocks so that the maximum deflection is no more than 16/9 # 3 1.027 times the theoretical minimum and the maximum bending moment is within 4 times the minimum. Another heuristic allows maximum deflection up to 2.054 times the theoretical minimum but restricts the maximum bending moment to within 2 times the minimum. Similar results hold for beams with fixed supports at the ends

Heuristics for Balancing Turbine Fans

We develop heuristics for a problem that models the static balancing of turbine fans: Load point masses at regularly spaced positions on the periphery of a circle so that the residual unbalance about the center --- which corresponds to the axis of rotation of the fan --- is as small as possible. We prove that our heuristics provide the same worst-case guarantee in terms of residual unbalance as does total enumeration. Furthermore, computational tests show that our heuristics are orders of magnitude faster and not far from optimum on average. The balancing of rotating elements in modern machinery is critical, and is done in some cases by sophisticated balancing machines. The presence of unbalance in a rotating machine results in vibrations and excess stresses on the bearings, both of which shorten its useful life. Static unbalance, the primary source of unbalance in narrow, disc-shaped rotors such as turbine fans, occurs when the center of gravity of the fan does not coincide with the a..