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We consider a service system with an infinite number of exponential serverssharing a finite service capacity. The servers are ordered according to theirspeed, and arriving customers join the fastest idle server. A capacityallocation is an infinite sequence of service rates. We study the probabilisticproperties of this system by considering overflows from sub-systems with afinite number of servers. Several stability measures are suggested andanalysed. The tail of the series of service rates that minimizes the averageexpected delay (service time) is shown to be approximately geometricallydecreasing. We use this property in order to approximate the optimal allocationof service rates by constructing an appropriate dynamic program.

Delay-minimizing capacity allocation in an infinite server queueing system