Many-Server Queueing Systems with Heterogeneous Strategic Servers in Heavy Traffic

Strategic Servers with Individual Preferences in Heavy Traffic Agents in service systems are known to strategically adjust their service speeds to maximize idle time. “Many-Server Queueing Systems with Heterogeneous Strategic Servers in Heavy Traffic” by Büke, dos Reis, and Platonov is the first work to rigorously examine strategic heterogeneous servers in queueing systems. The authors address this technically challenging problem using a novel asymptotic framework that provides valuable insights into equilibrium behavior. The analysis goes beyond existing literature by incorporating a remarkably general class of utility functions and routing policies, allowing for variation in agents’ marginal utility of idleness. One of the key results shows that the celebrated square-root staffing rule retains its optimality—even in the presence of strategic behavior—when agents are sufficiently averse to low levels of idleness.