## Dynamic routing in large-scale service systems with heterogeneous servers.(English)Zbl 1094.60058

A single Poisson stream of stochastically identical customers is fed into a large scale service system of pools with heterogeneous exponential servers. Letting the arrival intensity go to infinity and taking the overall service capacity as the demand size plus a safety capacity proportional to the square root of the demand yields the so called Halfin-Whitt regime. Under this asymptotics it is shown that for large systems the policy that sends customers to the fastest servers first is nearly optimal. (This is different from the finite system situation where threshold policies are optimal.) It turns out that in the limit a state space collapse occurs. Using this, asymptotic performance measures based on diffusion approximations are computed. Especially it is shown that in the limiting regime under consideration both the quality of service (delay probability) and the system efficiency achieve high performance.

### MSC:

 60K25 Queueing theory (aspects of probability theory) 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems 90B22 Queues and service in operations research
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