Relationship between randomized F-policy and randomized N-policy in discrete-time queues

This paper investigates the interrelationship between the randomized F- policy and randomized N- policy in discrete-time queues with start-up time. The F-policy queuing system deals with the issue of controlling arrivals. The N-policy queueing system deals with the issue of controlling service, that is, when all the customers are served in the queue, the server is deactivated until N customers are accumulated in the queue. Using the recursive method, the steady-state probabilities are determined for both models. The relationships between the discrete-time Geo/Geo/1/K queues with (p, F)- and (q, N)-policies are established by a series of propositions. The benefit made by interrelationship is that the solution of one queue can be deduced from the other queue readily. Various performance measures and numerical results are carried out for illustration purposes. These queues are common in wireless communication systems, production systems, manufacturing systems.

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