# On the Comparison of Waiting Times in Tandem Queues

Using a definition of partial ordering of distribution functions, it is proven
that for a tandem queueing system with many stations in series, where each
station can have either one server with an arbitrary service distribution or a
number of constant servers in parallel, the expected total waiting in system of
every customer decreases as the interarrival and service distributions become
smaller with respect to that ordering. Some stronger conclusions are also given
under stronger order relations. Using these results, bounds for the expected
total waiting time in system are then readily obtained for wide classes of
tandem queues.