Stochastic Games For A Multiclass E₂/E₂/1 Queueing System With Model Fuzziness

We consider a I-dimensional stochastic control game with model fuzziness that exactly emerges from a multiclass E2/E2/1 queueing control model under heavy-traffic condition with model fuzziness.Specifically speaking,it is assumed that the decision maker(DM)do not totally know the rates of arrivals to the queueing network and the rates of service.We show that the stochastic control game can be approximated by a multidimensional Brownian control model(BCP)that is driven by a Brownian motion.The BCP is formulated as a game with two players:a minimizer that has an equivalent role to the DM in the queueing model and a maximizer who acts to set up the fuzziness of the model.Finally,we also show that a state space collapse property holds,that is,the multidimensional BCP can be reduced to a one-dimensional BCP with fuzziness that is equivalent to I-dimensional BCP in a certain sense.