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Suppose there are four modalities 1, 2, 3, and 4, for moving goods between two particular destinations, with associated capacity $\mathscr{C}_i$ and cost $c_i$ for $i\in \{1,2,3,4\}$ and also that $c_1<c_2<c_3<c_4$. Suppose that there is demand to ship $N$ units of goods simultaneously and also that $\mathscr{C}_1 + \mathscr{C}_2 < N < \mathscr{C}_1+\mathscr{C}_2 +\mathscr{C}_3$.

It is convenient to assume that the system will behave as follows:

  • Services 1 and 2 will be at full utilization, service 3 at partial utilization, and service C at zero utilization.
  • If an additional unit of demand materializes, then service 3's utilization will increase by one unit.
  • If service 1 increases its capacity to $\mathscr{C}_1^\prime$ and there is no cost to switch services, then $\mathscr{C}_1^\prime-\mathscr{C}_1$ units of goods will defect from service 3 to service 1, assuming that service's three's utilization is at least $\mathscr{C}_1^\prime-\mathscr{C}_1$.

So my question is, what is the terminology for this kind of model system and associated behaviors. Do you say that such a system is "Pareto optimal", for example?

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