Modelling of Controlled Queueing Systems

J. Smieja and A. Swierniak (Poland)


Queuing systems, optimal control, bang-bang control.


This paper is concerned with a problem of controlling the queuing systems. Rather than deal with mean probabilities, which is the most often used approach to this problem, it concentrates on transient states and the description that allows to state the optimization problem. First a model of a queuing system with controlled service intensity is analyzed. Subsequently, a system with multiple service stations that can be switched in or off is introduced. Afterwards, another model is presented, in which control variable relates to maximum number of clients that can place their request in the queue. Finally, both models are combined. For each of the systems, the optimal control problem is formulated in L1 space and for the first one the gradient method for finding optimal control is presented.

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