Computation of steady-state probabilities for resource-sharing call-center queueing systems

Two routing rules for a queueing system of two stations are considered as alternative models for modeling a call-center network. These routing rules allow customers to switch queues under certain server and other resource availability conditions, either external to the system upon arrival to the network, or internal to the system after arrival to a primary call center. Under the assumption of Poisson arrivals and exponentially distributed service times, these systems are analyzed using matrix-geometric techniques, yielding a non-trivial set of ergodicity conditions and the steady-state joint probability distribution for the number of customers at each station. An extensive numerical analysis is conducted, yielding some physical insight into these systems and related generalizations.