Optimal design of a multiservice system: The line-penalty problem

This paper deals with the problem of optimally designing a complex queueing system in presence of some constraints. The system is constituted by a set of M/M/1 queueing (sub-)systems, sharing the same scarce resources, but otherwise running independently. The objective is to minimize an inefficiency index, defined as the maximum expected line-penalty among the subsystems. The service rates are the decision variables. Different special problems, admitting the same general formulation, are illustrated.