Scheduling a Two Station Multiclass Queueing Network in Heavy Traffic
Scheduling a Two Station Multiclass Queueing Network in Heavy Traffic
Lawrence M Wein
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7) di- rectly. Proposition 2. 1. Every feasible policy {Y, 9) for the limiting control problem yields a corresponding feasible policy {Z, U, 0) for the workload formulation and every feasible policy [Z, U, 6) yields a corresponding feasible policy {¥, 6). It was shown in Wein [17] that if the control process Y is non-anticipating with respect to the Brownian motion A' in the limiting control problem, then the control process U is non-anticipating with respect to the Brownian motion B in the wor...kload formulation. It was also shown that the solution to the workload formulation remains unchanged whether 9 is non-anticipating with respect to X or with respect to B. 4. Solution to the Workload Formulation The solution {U, Z, 9) to the workload formulation (3. 3)-(3. 8) of the limiting control problem was derived in Wein [17]. This is a self-contained section that summarizes the solution. The parameters pi, Mtk and vi appearing in this section are all defined in terms of the primitive problem data by definitions (2.
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