A finite capacity resequencing model with Markovian arrivals

In this paper, we consider a two-server finite capacity queuing model in which messages should leave the system in the order in which they entered the system. Messages arrive according to a Markovian arrival process and any message finding the buffer full is considered lost. Out-of-sequence messages are stored in a (finite) buffer and may lead to blocking when a processed message cannot be placed in the buffer. The steady state analysis of the model is performed by exploiting the structure of the coefficient matrices. The departure process is characterized and two interesting optimization problems along with illustrative numerical examples are discussed.