Gated{type Polling Systems with Walking and Switch-in Times

We consider models of polling systems where switching times between channels are composed of two parts: walking times required to move from one channel (station) to another, and switch-in times that are incurred only when the server enters a station to render service. We analyze three Gated-type systems: (i) Cyclic polling with Gated regime, (ii) Cyclic polling with Globally-Gated regime, and (iii) Elevator-type polling with Globally-Gated regime. In all systems, the server visits station i if and only if the number of customers 1 2 (jobs) present there at the gating instant is greater than or equal to a given threshold K i 0. For all schemes we derive formulae for the multi-dimensional generating functions of the number of jobs in the various queues at polling instants, and derive bounds on mean waiting times, mean cycle times and mean number of jobs present in the system. For the Elevator scheme we further show that if switch-in times, as well as arrival rates, are equal among channels, then jobs' mean waiting times in all stations are equal.