A Note on the Effectiveness of a Pool

A measure of ineffectiveness I of a pool of independent service facilities is defined and it isshown to be rather insensitive to changes in the service-time distribution for queues with aPoisson input, assuming equal mean service rates of the servers. This result reduces considerationto the simple case of exponentially distributed service times and in this case (i) I can be computedusing well-known formulae and (ii) it is possible to construct a simple upper bound for I.