Asymptotic study of some bulk service systems with a large number of equivalently replaceable channels

A bulk service system of $N$ channels is studied. Each channel receives its own entries; if it is busy the entries are transferred to other, free channels where the servicing is either slower or performed by several channels simultaneously. If no free channels are available at a given time, then the entry is lost. For Poisson input fluxes and a exponential servicing time, asymptotic expressions for stationary probabilities of failure are found as $N \to\infty$.