Abstract
We analyze gated, exhaustive service of an infinite-server system with vacations. Customers enter a queue in a Poisson stream. The servers, working in parallel, serve customers in stages. A stage begins with all customers transferred from the queue to the servers (the gate opens). The servers then begin serving these customers, all simultaneously. The stage ends when their services are completed. Service is exhaustive because the servers must again examine the queue to see if any new customers arrived during the last stage. If there are any, a new stage begins. If there are none, the servers move on to other work. The time spent away from the queue is called vacation time. The queue may represent a node or station in a data transmission network and the servers may be communication channels.
We analyze the equilibrium behavior of the number of requests served during a stage for general service and vacation time distributions. This analysis leads to the solution of a Fredholm integral equation of the second kind. We find conditions under which the system is stable and compute bounds on performance metrics of interest. Approximate techniques are introduced and tested. Finally, an extension to polling systems is studied.