The authors establish stochastic monotonicity of the event epoch sequences of generalized semi-Markov processes through the structure of the generalized semi-Markov schemes on which they are based. The present main condition states, roughly, that the occurrence of more events in the short run never leads to the activation of less events in the long run. They consider monotonicity with respect to two types of inputs: clock times (which translate to, e.g., service and interarrival times in queueing systems), and structural parameters (which translate to, e.g., buffer size, number of servers, and job population). For the second type of comparison, the authors replace a structural change with an equivalent change in clock times to reduce the comparison of one of the first type. When applied to queueing systems, the results yield new comparisons and also unify several existing results previously established using special properties of individual systems.
