Nicholas Bambos, George Michailidis
2002 Probability in the engineering and informational sciences (Print)  
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
more » ... t 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-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+ 185 The random connectivity0accessibility 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 FES0MES, known to be optimal for the classical model, extends to the C-FES0A-MES in our case+
doi:10.1017/s0269964802162048 fatcat:eahexy24n5ay7f227s2fukrqjm