Joint stationary distribution of the number of customers in the system and reordering buffer in the multiserver reordering queue

The paper considers a continuous-time multiserver queueing system with buffer on infinite capacity and reordering. The Poisson flow of customers arrives at the system. Service times of customers at each server are exponentially distributed with the same parameter. Each customer obtains a sequential number upon arrival. The order of customers upon arrival should be preserved upon departure from the system. Customers whose service finished but which violated the order are kept in the reordering buffer of infinite capacity. A joint stationary distribution of the number of customers in the buffer, servers, and reordering buffer is obtained in terms of a computational algorithm and a generating function. A numerical example is provided.