@misc{BrandtBrandt1998, author = {Brandt, Andreas and Brandt, Manfred}, title = {On a Two-Queue Priority System with Impatience and its Application to a Call Center}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-3641}, number = {SC-98-21}, year = {1998}, abstract = {We consider a \$s\$-server system with two FCFS queues, where the arrival rates at the queues and the service rate may depend on the number \$n\$ of customers being in service or in the first queue, but the service rate is assumed to be constant for \$n>s\$. The customers in the first queue are impatient. If the offered waiting time exceeds a random maximal waiting time \$I\$, then the customer leaves the first queue after time \$I\$. If \$I\$ is less than a given deterministic time then he leaves the system else he transits to the end of the second queue. The customers in the first queue have priority. The service of a customer from the second queue will be started if the first queue is empty and more than a given number of servers become idle. For the model being a generalization of the \$M(n)/M(n)/s\!+\!GI\$ system balance conditions for the density of the stationary state process are derived yielding the stability conditions and the probabilities that precisely \$n\$ customers are in service or in the first queue. For obtaining performance measures for the second queue a system approximation basing on fitting impatience intensities is constructed. The results are applied to the performance analysis of a call center with an integrated voice-mail-server. For an important special case a stochastic decomposition is derived illuminating the connection to the dynamics of the \$M(n)/M(n)/s\!+\!GI\$ system.}, language = {en} }