The problem of optimal scheduling in a system with parallel queues and a single server has
been extensively studied in queueing theory. However, such systems have mostly been analysed by
assuming homogeneous attributes of arrival and service processes, or Markov queueing models were
usually assumed in heterogeneous cases. The calculation of the optimal scheduling policy in such a
queueing system with switching costs and arbitrary inter-arrival and service time distributions is
not a trivial task. In this paper, we propose to combine simulation and neural network techniques
to solve this problem. The scheduling in this system is performed by means of a neural network
informing the controller at a service completion epoch on a queue index which has to be serviced
next. We adapt the simulated annealing algorithm to optimize the weights and the biases of the
multi-layer neural network initially trained on some arbitrary heuristic control policy with the aim to
minimize the average cost function which in turn can be calculated only via simulation. To verify the
quality of the obtained optimal solutions, the optimal scheduling policy was calculated by solving a
Markov decision problem formulated for the corresponding Markovian counterpart. The results of
numerical analysis show the effectiveness of this approach to find the optimal deterministic control
policy for the routing, scheduling or resource allocation in general queueing systems. Moreover, a
comparison of the results obtained for different distributions illustrates statistical insensitivity of the
optimal scheduling policy to the shape of inter-arrival and service time distributions for the same
first moments.