A Queueing System Subject to Breakdown and Having Non-Stationary Poisson Arrivals.

摘要

This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as an M/Ek/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. Thus, both the arrival and service distributions are nonstationary. The durations of the operating and failed periods are exponential with mean 1/c-alpha and Erlang with mean 1/c-beta, respectively. Generating functions are used to derive the steady-state quantities L and W, both of which are decreasing and convex functions of c. The paper includes an analysis of several special and extreme cases and an application to a production-storage system. (Author)