A Note on the Effectiveness of a Pool

Abstract

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