Customer-Server Population Dynamics in Heavy Traffic

We study a many-server queueing model with server vacations, where the population size dynamics of servers and customers are coupled: may leave for vacation only when no await, capacity available to is directly affected by number on vacation. focus scaling regimes in which queue fluctuate at matching time scales so that their limiting coupled. Specifically, we argue interesting coupled occur (a) Halfin–Whitt regime, (b) nondegenerate slowdown (c) intermediate near whereas asymptotically decouple other heavy-traffic regimes. characterize dynamics, different each regime. consider relevant respective performance measures (b)—namely, probability wait slowdown. Although closed-form formulas these have been derived models do not accommodate it difficult obtain setting vacations. Instead, propose approximate depend steady-state mean previously without test accuracy numerically.