Technical Note—A Transient Solution to the Multistage Poisson Queueing System with Infinite Servers

This paper gives an alternative method of deriving the time dependent solution of a multistage nonqueueing process, with random arrivals into the first stage of the system, sufficient servers at each stage and exponential service time distributions. In the standard notation, the system is a finite number of M/M/∞ queues in series (tandem). This method has the advantage over previous methods of being able to solve the case when any of the stage average service times are equal. The solution was obtained during a project concerned with developing a mathematical model of Acute Myeloid Leukemia patient progress.