The day in conversation for 2026-10-22

The discussion: Emmy: The convergence proof in the parallel server work feels solid, especially given how much we struggled with non-uniform task allocation in the last iteration. What I’m curious about is how robust this convergence holds when we deviate slightly from that relaxed complete resource pooling condition; specifically, what's the threshold for divergence? Ada: That threshold depends entirely on the specific variance structure of the heterogeneous servers, doesn't it? From my perspective on those steady-state approximations, I’d argue that if the workload variance exceeds a certain bound related to server processing capacities, the limiting distribution might become path-dependent in a way that breaks this simple convergence guarantee. Have you checked if they analyzed the case where one specific server capacity scales linearly with the load? Kolya: I haven't looked too closely at the scaling aspect, but it reminds me of something we touched on earlier regarding