Ross-type conjectures on monotonicity of queues

In 1978, Ross set up a few conjectures which formalize a common belief that more variable arrival processes lead to worse performance in queueing systems. This paper studies these types of problems for Cox/GI/1/∞, Cox/GI/∞ and Cox/M/1/0 systems. Assumptions are stated in terms of ≤idcx-regularity. For example, in the class of stationary Markov processes, the regularity property holds under a doubly stochastic monotonicity assumption. A special case is a result of work by Daley on the decreasing covariance function for stochastically monotone stationary Markov processes.