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If N is a queueing network and c_s is the mean service time at
server s of N, define NCF (respectively, NEF) to be the queueing
network N where the service time at server s is a constant c_s
(respectively, an independent exponentially distributed random
variable with mean c_s) and the packets are served in a
first-come-first-served order.

Recently, Harchol-Balter and Wolfe introduced the problem of
determining the class S of queueing networks N for which NCF
has smaller average delay than NEF. This problem has applications
to bounding delays in packet-routing networks.

In this paper we consider the same problem, only restricted to the
case of light traffic. We define SL to be the set of queueing
networks N for which NCF has smaller average delay than NEF in the
case of light traffic. We discover a sufficient criterion to
determine whether a network N belongs to SL, where this criterion is
extremely simple and easy to check. Using this criterion we are able
to show that many networks belong to SL that were previously not known
to belong to S. The significance of this result is that it
suggests that many more networks are contained in S than has already
been shown.