The paper deals with a finite-source queueing system serving one class of
customers and consisting of heterogeneous servers with unequal service intensities and of one common queue. The main model has a non-preemptive service
when the customer can not change the server during its service time. The
optimal allocation problem is formulated as a Markov-decision one. We show
numerically that the optimal policy which minimizes the long-run average number of customers in the system has a threshold structure. We derive the matrix
expressions for the mean performance measures and compare the main model
with alternative simplified queuing systems which are analysed for the arbitrary
number of servers. We observe that the preemptive heterogeneous model operating under a threshold policy is a good approximation for the main model
by calculating the mean number of customers in the system. Moreover,using
the preemptive and non-preemptive queueing models with the faster server first
policy the lower and upper bounds are calculated for this mean value