We study systems of parallel queues with finite buffers, a
single server with random connectivity to each queue,
and arriving job flows with random or class-dependent
accessibility to the queues. Only currently connected queues
may receive (preemptive) service at any given time, whereas
an arriving job can only join one of its accessible queues.
Using the coupling method, we study three key models,
progressively building from simpler to more complicated structures.
In the first model, there are only random server connectivities.
It is shown that allocating the server to the Connected queue
with the Fewest Empty Spaces (C-FES) stochastically minimizes
the number of lost jobs due to buffer overflows, under conditions
of independence and symmetry.
In the second model, we additionally consider random accessibility
of queues by arriving jobs. It is shown that allocating the
server to the C-FES and routing each arriving job to the currently
Accessible queue with the Most Empty Spaces (C-FES/A-MES) minimizes
the loss flow stochastically, under similar assumptions.
In the third model (addressing a target application), we consider
multiple classes of arriving job flows, each allowed
access to a deterministic subset of the queues. Under analogous
assumptions, it is again shown that the C-FES/A-MES policy
minimizes the loss flow stochastically.
The random connectivity/accessibility aspect enhances
significantly the structure and application scope of the classical
parallel queuing model. On the other hand, it introduces essential
additional dynamics and considerable complications. It is
interesting that a simple policy like FES/MES, known to be optimal
for the classical model, extends to the C-FES/A-MES in our case.