A tandem queue with a movable server: An eigenvalue approach

In this paper, we analyze a two station tandem queue with Poisson arrivals and exponential service times. All arrivals occur at the first line, and, after receiving service at the first station, they proceed to the second line. There is only a finite buffer between the stations, and, as soon as the buffer is full, any job completed by the first server is lost. To reduce customer loss, the first server can move to the second station and help the second server, thereby increasing its service rate. Once the work at station two is complete, the job leaves the system. The problem will be solved by using eigenvalues which can be obtained in explicit form. It is shown that this method is substantially faster than matrix analytic methods.