A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

A Time-Non-Homogeneous Double-Ended Queue with Failures and Repairs and Its Continuous Approximation

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We consider a time-non-homogeneous double-ended queue subject to catastrophes and repairs.The catastrophes occur according to a non-homogeneous Poisson process and lead the system into a state orange zinger tomato of failure.Instantaneously, the system is put under repair, such that repair time is governed by a time-varying intensity function.We analyze the transient and the asymptotic behavior of the queueing system.Moreover, we derive a heavy-traffic approximation that allows approximating the state of the systems by a time-non-homogeneous Wiener swisse high strength magnesium powder berry process subject to jumps to a spurious state (due to catastrophes) and random returns to the zero state (due to repairs).

Special attention is devoted to the case of periodic catastrophe and repair intensity functions.The first-passage-time problem through constant levels is also treated both for the queueing model and the approximating diffusion process.Finally, the goodness of the diffusive approximating procedure is discussed.