Stability of a Three-Station Fluid Network

This paper studies the stability of a three-station fluid network. We prove that the global stability region of our three-station network is not monotone in the service times and so, we may move a service time vector out of the global stability region by reducing the service time for a class. We introduce the monotone global stability region and show that a linear program (LP) related to a piecewise linear Lyapunov function characterizes this largest monotone subset of the global stability region for our three-station network. The linear program proposed by Bertsimas, Gamarnik and Tsitsiklis [1] does not characterize either the global stability region or even the monotone global stability region of our three-station network. We also show that the global stability region of our three-station network is not the intersection of its stability regions under the static buffer priority disciplines and that the LP related to the linear Lyapunov function proposed by Chen and Zhang [11] does not..

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..

Some generalizations of bucket brigade assembly lines

To my parent