Interrelationship between controlling arrival and service in queueing systems

In this paper, the interrelationship between the F-Policy problem and the truncated N-Policy problem is considered. The F-Policy problem deals with the issue of controlling arrivals to a queueing system. The N-Policy problem involves a queueing system in which the server leaves the system (for alternative jobs) when it becomes empty and returns when the queue builds up to a predetermined level. The steady state probability distribution and expressions for the measures of effectiveness for these two systems are obtained. The complementarity relationships between these two queueing systems are established. These relationships provide insight into these queueing problems and facilitate the solution to any one of the problems given the solution to the other. Through a series of propositions, other relationships between these queueing systems are also established.