The following problem is solved: when are we obliged to walk upstairs in a building supplied with two lifts (or elevators), if repairs to the lifts are quickly carried out? Sufficient conditions are given on the distributions of operating- and down-times under which the times when both lifts are inoperative are asymptotically distributed as a Poisson process.
"A Problem of Two Lifts." Ann. Probab. 5 (4) 550 - 559, August, 1977. https://doi.org/10.1214/aop/1176995760