We study a multiclass Markovian queueing network with switchover across a set of many-server stations. New arrivals to each station follow a nonstationary Poisson process. Each job waiting in queue may, after some exponentially distributed patience time, switch over to another station or leave the network following a probabilistic and state-dependent mechanism. We analyze the performance of such networks under the many-server heavy-traffic limiting regimes, including the critically loaded quality-and-efficiency-driven (QED) regime, and the overloaded efficiency-driven (ED) regime. We also study the limits corresponding to mixing the underloaded quality-driven (QD) regime with the QED and ED regimes. We establish fluid and diffusion limits of the queue-length processes in all regimes. The fluid limits are characterized by ordinary differential equations. The diffusion limits are characterized by stochastic differential equations, with a piecewise-linear drift term and a constant (QED) or time-varying (ED) covariance matrix. We investigate the load balancing effect of switchover in the mixed regimes, demonstrating the migration of workload from overloaded stations to underloaded stations and quantifying the load balancing impact of switchover probabilities.

Classical results for exchangeable systems of random variables are extended to multiclass systems satisfying a natural partial exchangeability assumption. It is proved that the conditional law of a finite multiclass system, given the value of the vector of the empirical measures of its classes, corresponds to independent uniform orderings of the samples within {each} class, and that a family of such systems converges in law {if and only if} the corresponding empirical measure vectors converge in law. As a corollary, convergence within {each} class to an infinite independent and identically distributed system implies asymptotic independence between {different} classes. A result implying the Hewitt-Savage 0-1 law is also extended.