On optimality of the FCFS discipline in multiserver queueing systems and networks (Q2773624)

A queueing system with \(m\) servers is considered. It is assumed that the service discipline in the system does not allow time sharing and service interruption. It is also assumed that the discipline is admissible, i.e., it exhibits the ``future independence'' property. The main topic of the article is optimization of the service discipline in the class of admissible disciplines. Let \(d_n\) be the actual waiting time (or the sojourn time) of the \(n\)th customer in the system. Then the FCFS discipline is optimal in the following sense: For every \(n\in\mathbb N\), the service discipline FCFS is not worse than any admissible discipline \(T\), i.e., NEWLINE\[NEWLINE h(d^{\text{FCFS}}_1,\dots,d^{\text{FCFS}}_n) \leq_{\text{st}} h(d^T_1,\dots,d^T_n) NEWLINE\]NEWLINE for every Schur-convex function \(h\:\mathbb R^n\to\mathbb R\).