 
Summary: The Annals of Applied Probability
2008, Vol. 18, No. 4, 15481568
DOI: 10.1214/07AAP497
© Institute of Mathematical Statistics, 2008
CENTRAL LIMIT THEOREM FOR A MANYSERVER QUEUE
WITH RANDOM SERVICE RATES
BY RAMI ATAR
TechnionIsrael Institute of Technology
Given a random variable N with values in N, and N i.i.d. positive random
variables {k}, we consider a queue with renewal arrivals and N exponential
servers, where server k serves at rate k, under two work conserving routing
schemes. In the first, the service rates {k} need not be known to the router,
and each customer to arrive at a time when some servers are idle is routed to
the server that has been idle for the longest time (or otherwise it is queued).
In the second, the service rates are known to the router, and a customer that
arrives to find idle servers is routed to the one whose service rate is greatest.
In the manyserver heavy traffic regime of Halfin and Whitt, the process that
represents the number of customers in the system is shown to converge to a
onedimensional diffusion with a random drift coefficient, where the law of
the drift depends on the routing scheme. A related result is also provided for
