Upper Bounds for Single Server Queues with Doubly Stochastic Poisson Arrivals

Consider the following type of single server queues. Arrivals are according to a Doubly Stochastic Poisson process with a stationary, ergodic random intensity {λ(t)}. Service times are independent, identically distributed, also independent from arrivals. It is proven that the mean stationary work-load is not greater than E[ω(λ(0))], where ω(a) denotes the mean stationary work-load in the M/GI/1 queue with arrival intensity a and the same service process. Similar results are given for the mean stationary queue size and the mean stationary delay.