Asynchronous stochastic approximation and adaptation in a competitive system (Q2769663)

The paper deals with an economic application in which two classes of customers (C1, C2) and two resources of ``services'' (e.g. mainframe computer (MF) and an (infinite) bank of personal computers (PC)) exist. In particular, it is assumed that the customers from the first class are free to select from the both types of services MF and PC, the customers from the second class must use the MF only. The service time for the class of the customers C1 on PC is known, the service rate on MF depends on the numbers of the customers; a character of random elements is specified. Moreover, it is assumed that the customers select the service to minimize the service cost, however, the cost can be represented by the service time and it is is assumed to depend on the decisions of all future arrivals to the time of departure. Consequently, a competitive factor exists in the problem. In the paper it is mentioned the fact that an origin of the model can be in communications problems. The paper follows a model introduced by \textit{E. Altman} and \textit{N. Schimkin} [Oper. Res. 46, 776--784 (1998; Zbl 0987.90020)]. NEWLINENEWLINENEWLINEEvidently, the aim of the paper is to introduce a learning system to determine a ``good'' strategy for the class of the customers C1. To construct the algorithm a stochastic asynchronous approximation approach is employed. The suggested algorithm assymptotically corresponds to the symmetric Nash equilibrium strategy. Of course, the definition of the symmetric Nash equilibrium strategy is recalled in the paper.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].