On Parallel Queuing with Random Server Connectivity and Routing Constraints

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 ~CFES! 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-FES0 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-FES0A-MES policy minimizes the loss flow stochastically+ Probability in the Engineering and Informational Sciences, 16, 2002, 185–203+ Printed in the U+S+A+