A Polling Model with Smart Customers (original) (raw)

We consider a single-server, cyclic polling system with switch-over times. A distinguishing feature of the model is that the rates of the Poisson arrival processes at the various queues depend on the server location. We refer to this as 'smart customers', as an example of this is the situation where arriving customers choose which queue they join, based on the current position of the server. For this system, we derive the waiting time distribution for each customer type, by applying a generalized version of the distributional form of Little’s law to the joint queue length distribution at departure epochs. We also provide an alternative, more efficient way to determine the mean queue lengths and mean waiting times, using Mean Value Analysis for polling systems. Under certain conditions, a Pseudo-Conservation Law for the total amount of work in the system holds. Typical features of the model under consideration are demonstrated in several numerical examples, for instance the optimal queue for customers to join.