6533b7d7fe1ef96bd126868f

RESEARCH PRODUCT

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

Antonio Di CrescenzoAmelia G. NobileVirginia GiornoBalasubramanian Krishna Kumar

subject

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)

description

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 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.

yearjournalcountryeditionlanguage
2018-05-11Mathematics; Volume 6; Issue 5; Pages: 81
10.3390/math6050081https://dx.doi.org/10.3390/math6050081