Queue structure control in a single-server system with variable service rate (Q1385772)

A truncated permutation method for sequential design of alternatives reduces the problem of optimal queue structure for \(n\) messages at a node \((n>1)\) to a problem of scheduling theory. The latter in turn reduces to the equivalent problem of finding an optimal permutation \(\pi^* \in\Pi= \{\pi\}= \{(i_1,i_2, \dots, i_k, \dots, i_n)\}\), whose element \(i_k\) is the message occupying the \(k\)-th place in the queue, and the form of \(\pi^*\) represents the queue structure at the node. We consider a more general case, when the function used to generate \(\pi^*\) allows for the server parameters as well as for the parameters of all the messages following \(i_k\). As in many known cases, the rule for the construction of the permutation \(\pi^*\) optimizing the performance criterion is easily recast in an algorithm form, and the ordering procedure itself is iterative.