The theory of controllable queueing systems is used in many applications, including control of admission, servicing, routing and scheduling of jobs in queues and networks of queues. As a theoretical base it uses the theory of Markov, semi-Markov, and semi-regenerative decision processes. For real construction of optimal policies it is usually used some numerical methods that is based on Howard's iteration algorithm or on mathematical programming tools. But because of the high dimensionality of the problem an investigation of some qualitative properties of optimal policies, such as their monotonity, is also interesting.

The special problem of optimal jobs allocation to heterogeneous servers also arises in many applications including recequensing of queues. The problem of optimal jobs allocation to two heterogeneous servers with respect to the long ran average mean number of jobs in the system minimization was considered in [1], where it was shown that in this case an optimal policy has a threshold property and consists in using the fastest server if necessary. For the multi-server system these properties of optimal policies were generalized in [2].

For such a system engaged by additional cost structure those type of results are unavailable. In the talk some results of numerical analysis of such a system with and without additional cost structure will be given. This gives also the possibility to investigate the qualitative properties of optimal policies and their behavior when parameters are varied. For some numerical examples we calculate appropriate threshold levels for different values of system parameters.

References

1. W. Lin, P.R. Kumar. Optimal control of a queueing system with two heterogeneous servers. IEEE Trans. on Autom. Control, 29 (1984), pp. 696-703.
2. V.V. Rykov. Monotone Control of Queueing Systems with Heterogeneous Servers. QUESTA, 37 (2001), 391-403.