On Whitt's conjecture for queues in which service times and interarrival times depend linearly and randomly upon waiting times |
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Authors: | Hanqin Zhang |
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Affiliation: | (1) Academia Sinica, Institute of Applied Mathematics, and Asian-Pacific Operations Research Center, 100080 Beijing, PR China |
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Abstract: | We consider a modification of the standardG/G/1 queueing system with infinite waiting space and the first-in-first-out discipline in which the service times and interarrival times depend linearly and randomly on the waiting times. In this model the waiting times satisfy a modified version of the classical Lindley recursion. When the waiting-time distributions converge to a proper limit, Whitt [10] proposed a normal approximation for this steady-state limit. In this paper we prove a limit theorem for the steady-state limit of the system. Thus, our result provides a solid foundation for Whitt's normal approximation of the steady-state distribution of the system.Supported in part by a grant from the National Natural Science Foundation of China. |
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Keywords: | State-dependent service and interarrival times Lindley equation recursive stochastic equations stability normal approximations |
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