  Two independent Poisson streams of jobs flow into a single-server service
system having a limited common buffer that can hold at most one job. If a
type-i job (i=1,2) finds the server busy, it is blocked and routed to a
separate type-i retrial (orbit) queue that attempts to re-dispatch its jobs at
its specific Poisson rate. This creates a system with three dependent queues.
Such a queueing system serves as a model for two competing job streams in a
carrier sensing multiple access system. We study the queueing system using
multi-dimensional probability generating functions, and derive its necessary
and sufficient stability conditions while solving a boundary value problem.
Various performance measures are calculated and numerical results are
presented.
