Solution

Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 31 / 4 / e / Solution

{title2=$\bar J_B(x)=J(x)\ (0\leq x\leq B),\quad\bar J_B(x)=\infty\text{ otherwise}$}

For the local convex action defining the <linear workload rate for a local convex action>, continuity and the <contraction principle for large deviations> give workload <rate functions>. The pointwise bound $\bar q_B\leq q$ makes $\bar J_B(x)\geq\inf_{y\geq x}J(y)=J(x)$ on nonnegative workloads. Constant-rate burst paths produce the reverse bound for x at most B. Values outside the buffer interval are impossible. This statement concerns the rate at the workload value, rather than equality of exact finite-buffer and infinite-buffer stationary distributions.

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 Incoming links: Finite-buffer workload rate truncation