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Optimal control of service in tandem queues

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3 Author(s)
Z. Rosberg ; Technion Israel Institute of Technology, Haifa, Israel ; P. Varaiya ; J. Walrand

Customers arrive in a Poisson stream into a network consisting of two M/M/1 service stations in tandem. The service rate u \in [0, a] at station 1 is to be selected as a function of the state ( x_{1}, x_{2} ) where xiis the number of customers at station i so as to minimize the expected total discounted or average cost corresponding to the instantaneous cost c_{1}x_{1} + c_{2}x_{2} . The optimal policy is of the form u=a or u=0 according as x_{1} < S(x_{2}) or x_{1} \geq S(X_{2}) and S is a switching function. For the case of discounted cost, the optimal process can be nonergodic, but it is ergodic for the case of average cost.

Published in:

IEEE Transactions on Automatic Control  (Volume:27 ,  Issue: 3 )