Server control in a two-node Markovian queueing network with a limited total number of servers is considered. Two problems have been studied; the first problem is to find a quasi-steady-state control policy for a periodic review of server allocation. This policy can be regarded as a feedback control policy to adapt the network parameter changes by changing the number of servers at each node.

The second problem (main problem of this research) is that of on-line server control. Two policies for this control are proposed. The first policy allocates the servers to each node according to the network state and is preemptive. Markovian models have been used for analysis. We found that the performance of the network (mean number or mean time in the network) using this policy can be improved significantly (reductions up to about 50%) and this performance is affected by the ratio of the service rates. The form of the best policy is defined. The second policy allocates the server(s) to each node according to a rule based on the ratio between queue lengths and is non-preemptive. Simulation is used to study the performance in a few cases. We found that the performance is improved by similar amounts.