Analysis Of M/G/1Vacation Oueue With Server’s Immediately Setup-Time After Ending Vacation

Abstract Applying the total probability decomposition technique and Laplace transform, this paper studies the M/G/1vacation queue with server’s immediately setup-time after ending vacation. The transient queue-length distribution and the steady queue-length distribution are discussed at any time t under both single vacation system and multistage vacation, and then the expressions of the Laplace transform of the transient queue-length distribution and the recursion expression of the steady queue-length distribution are obtained. Meanwhile, it is demonstrated that the stochastic decomposition of the steady has queue length and waiting time in the vacation queueing systems. Moreover, by the numerical example, we discuss the sensitivity of the expected additional queue length and the expected additional waiting time towards of system parameters in the single vacation queueing system.