On preservation of classes of life distributions under reliability operations: Some complementary results

A counterexample of general character is constructed showing that the NWUE class is not preserved under mixing. Some general classes of life distributions are introduced and their behavior under mixing and convolution is studied. These classes have a theoretical character but coincide in many cases with well-known classes. It is proved that the DMRL class is not preserved under convolution.     

A queueing system with vacations after N services

This article is devoted to the study of an M/G/1 queue with a particular vacation discipline. The server is due to take a vacation as soon as it has served exactly N customers since the end of the previous vacation. N may be either a constant or a random variable. If the system becomes empty before the server has served N customers, then it stays idle until the next customer arrival. Such a vacation discipline arises, for example, in production systems and in order picking in warehouses. We determine the joint transform of the length of a visit period and the number of customers in the system at the end of that period. We also derive the generating function of the number of customers at a random instant, and the Laplace–Stieltjes transform of the delay of a customer. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 646–658, 2015