Monotonicity of cost functions in a general class of queueing networks

摘要

Monotonicity of cost functions in queuing networks with blocking is established by means of induction-based comparisons. For an arbitrary configuration of queueing stations with general interarrival times and geometrically distributed service times, it is shown that increasing the initial population increased the expected cost (including blocking penalties for jobs that are rejected) incurred over a finite horizon. The criticality of the constraint imposed on the service times is demonstrated by two counterexamples.