Queueing systems with a single server in which customers wait to be served at
a finite number of distinct locations (buffers/queues) are called discrete
polling systems. Polling systems in which arrivals of users occur anywhere in a
continuum are called continuous polling systems. Often one encounters a
combination of the two systems: the users can either arrive in a continuum or
wait in a finite set (i.e. wait at a finite number of queues). We call these
systems mixed polling systems. Also, in some applications, customers are
rerouted to a new location (for another service) after their service is
completed. In this work, we study mixed polling systems with rerouting. We
obtain their steady state performance by discretization using the known pseudo
conservation laws of discrete polling systems. Their stationary expected
workload is obtained as a limit of the stationary expected workload of a
discrete system. The main tools for our analysis are: a) the fixed point
analysis of infinite dimensional operators and; b) the convergence of Riemann
sums to an integral.
We analyze two applications using our results on mixed polling systems and
discuss the optimal system design. We consider a local area network, in which a
moving ferry facilitates communication (data transfer) using a wireless link.
We also consider a distributed waste collection system and derive the optimal
collection point. In both examples, the service requests can arrive anywhere in
a subset of the two dimensional plane. Namely, some users arrive in a
continuous set while others wait for their service in a finite set. The only
polling systems that can model these applications are mixed systems with
rerouting as introduced in this manuscript.Comment: to appear in Performance Evaluatio
