Queueing models for buffers with dial-up servers

A dial-up server is not permanently connected to a buffer but once requested, becomes available after some initial delay. Deciding when to dial up for a server involves a trade-off between minimizing the waiting time (e.g., dialing up at low occupancy) and reducing the dial-up cost (dialing up only when the backlog is large). In this paper we consider a model consisting of two buffers that send messages to each other on a common, bidirectional dial-up link. Either buffer, upon having a number of messages larger than a predetermined threshold, initiates a dial-up. The first channel so established serves both queues and is released when both buffers are empty. We discuss extensions of the model to the more general case in which the two buffers are connected by a permanent link and dial up for additional service only when occupancy exceeds a threshold. Another special case of this general model, that of a single buffer with permanent and dial-up (overflow) servers, is also analyzed. For both models, we compute the buffer-occupancy generating functions and ascertain system operating costs. © 1989.