Abstract
This study investigates a random -policy Geo/G/1 queue with startup and closedown times. is newly determined every time a new cycle begins. When random customers are accumulated, the server is immediately turned on but is temporarily unavailable to the waiting customers. It needs a startup time before starting providing service. After all customers in the system are served exhaustively, the server is shut down by a closedown time. Using the generating function and supplementary variable technique, analytic solutions of system size, lengths of state periods, and sojourn time are derived.
Highlights
This study investigates a random N-policy Geo/G/1 queue with startup and closedown times
This paper deals with a random N-policy Geo/G/1 queueing system in which the random variable N, the startup time, and the closedown time obey the general distributions, respectively
A closedown period begins at the end of a busy period and ends at the completion of closedown time
Summary
This paper deals with a random N-policy Geo/G/1 queueing system in which the random variable N, the startup time, and the closedown time obey the general distributions, respectively. The server needs the startup time before starting each of his service periods. Bisdikian 12 applied the decomposition property to derived queue size for a random N-policy M/G/1 queue in which N is a random variable He investigated the analytic solutions of waiting time for both the FIFO and LIFO service disciplines. Ke derived the distribution of various system characteristics for two different kinds of NT policy M/G/1 queueing system with breakdown, startup and closedown time. Moreno extended a modified N-policy issue, where the first N customers of each consecutive service period are served together and the rest of customers are served singly She gave detailed derivations of system characteristics for a discrete time Geo/G/1 queue and developed a cost function to search the optimal operating N-policy at a minimum cost.
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