  The Least Loaded (LL) routing algorithm has been in recent decades the
routing method of choice in circuit switched networks and therefore it provides
a benchmark against which new methods can be compared. This paper improves the
performance of the LL algorithm by additionally incorporating a machine
learning approach, using a conceptually simple supervised na\"ive Bayes (NB)
classifier. Based on a sequence of historical network snapshots, this predicts
the potential future circuit blocking probability between each node pair. These
snapshots are taken for each service request arriving to the network and record
the number of busy capacity units on each link at that instant. The candidate
route for serving a current service request is based on both the link loads and
the potential future blocking probability of the entire network in case this
route is indeed used. The performance of this proposed approach is studied via
simulations and compared with both the conventional LL algorithm and the
Shortest Path (SP) based approach. Results indicate that the proposed
supervised na\"ive Bayes classifier-assisted LL routing algorithm significantly
reduces blocking probability of service connection requests and outperforms
both the conventional LL and SP routing algorithms. To enable the learning
process based on a large number of network snapshots, we also develop a
parallel computing framework to implement parallel learning and performance
evaluation. Also, a network control system supporting na\"ive Bayes
classifier-assisted LL routing algorithm is addressed.
