PERFORMANCE BOUNDS AND PATHWISE STABILITY FOR GENERALIZED VACATION AND POLLING SYSTEMS

We consider a generalized Vacation or polling system, modeled as an in put-output process operating over successive ''cycles,'' in which the service mechanism can be in an ''up'' mode (processing) or ''down'' mo de (e.g., vacation, walking). Our primary motivation is polling system s, in which there are several queues and the server moves cyclically b etween them providing some service in each. Our basic assumption is th at the amount of work that leaves the system in a ''cycle'' is no less than the amount present at the beginning of the cycle. This includes the standard gated and exhaustive policies for polling systems in whic h a cycle begins whenever the server arrives at some prespecified queu e. The input and output processes satisfy model-dependent conditions: pathwise bounds on the average rate and the burstiness (Cruz bounds); existence of long-nm average rates; a pathwise generalized Law of the Iterated Logarithm; or exponentially or polynomially bounded tail prob abilities of burstiness. In each model we show that these properties a re inherited by performance measures such as the workload and output p rocesses, and that the system is stable (in a model-dependent sense) i f the input rate is smaller than the up-mode processing rate.