We study a vacation-type queueing model, and a single-server multi-queue
polling model, with the special feature of retrials. Just before the server
arrives at a station there is some deterministic glue period. Customers (both
new arrivals and retrials) arriving at the station during this glue period will
be served during the visit of the server. Customers arriving in any other
period leave immediately and will retry after an exponentially distributed
time. Our main focus is on queue length analysis, both at embedded time points
(beginnings of glue periods, visit periods and switch- or vacation periods) and
at arbitrary time points.Comment: Keywords: vacation queue, polling model, retrials Submitted for
review to Performance evaluation journal, as an extended version of 'Vacation
and polling models with retrials', by Onno Boxma and Jacques Resin