1 Introduction

How to manage a queuing system with one arrival and several service processes$\,$? Such a request for optimization requires to fix the criteria of satisfaction that are to be faced with. Service efficiency, customer effective efficiency and customer perceived fairness are usually among these criteria.

The customer's opinion differs from the manager's one, because of psychological reasons since decisions are to be taken in uncertain and imprecise environment, the "laws" of probability being only guessed. But this occurs also because both opinions are not based on the same averaging process. Customer averages -noted $\operatorname{E}_{c}\left(X\right)$- are processed on a "one man, one vote" basis, while managers are mostly using time averages -noted $\operatorname{E}_{t}\left(X\right)$- that are processed on a "one clock tick, one vote" basis[1].

Moreover, it appears that the focus is not on the same properties of the sojourn time $S$. Manager's answer depends mainly on exhaustivity and $\operatorname{E}_{}\left(S\right)$, while customer's answer depends mainly on fairness and $var\left(S\right)$.

This paper is organized as follows. Notations and assumptions will be given in Section 2, as well as the method used to obtain fuzzy intervals around the quantities of interest. In Section 3 and Section 4 the respective perceptions of managers and customers are compared using simulations of $Ga/Ga/n$ queuing systems. Thereafter, Section 5 will examine the behavior of these properties when global parameters are changed, the load and the shape of arrivals among them. The paper ends with a concluding Section.