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

2018

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 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 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 cas…

time-non-homogeneous jump-diffusion processesComputer scienceGeneral Mathematicsdouble-ended queues01 natural sciencestransition densitiesdouble-ended queues; time-non-homogeneous birth-death processes; catastrophes; repairs; transient probabilities; periodic intensity functions; time-non-homogeneous jump-diffusion processes; transition densities; first-passage-time010104 statistics & probabilitysymbols.namesakeZero state responseWiener processrepairsComputer Science (miscellaneous)Applied mathematicstime-non-homogeneous birth-death processes0101 mathematicsSpurious relationshipEngineering (miscellaneous)Queuefirst-passage-timeQueueing theorytransient probabilitieslcsh:Mathematics010102 general mathematicslcsh:QA1-939catastrophesperiodic intensity functionssymbolsDouble-ended queueFirst-hitting-time modelConstant (mathematics)Mathematics; Volume 6; Issue 5; Pages: 81
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