  We consider a service system with an infinite number of exponential servers
sharing a finite service capacity. The servers are ordered according to their
speed, and arriving customers join the fastest idle server. A capacity
allocation is an infinite sequence of service rates. We study the probabilistic
properties of this system by considering overflows from sub-systems with a
finite number of servers. Several stability measures are suggested and
analysed. The tail of the series of service rates that minimizes the average
expected delay (service time) is shown to be approximately geometrically
decreasing. We use this property in order to approximate the optimal allocation
of service rates by constructing an appropriate dynamic program.
