Here the validity of a no-derivative Complex Method for the optiinization of constrained nonlinear } prograrnming (NLP) problerns is discussed. This method, starting with N (N2n+1, where n is the dimension of the pioblem) feasible points, determines the optimum by a typical deseent method, Though this method is capable of determining a nearly optimal feasible solution, its convergence in the general case is not guaranteed, However, this method has good convergence properties for unconstrained problems; hence transfbrmation of the constrained NLP problem to a seTies of smooth unconstrained problerns by the use of a pena3ty function and the application of the cornplex method to these functions is proposed for the determination of the optirn.um, A number of problerns are solved by the complex method as well as by the use of a penalty function and the complex method, and the results are compared.
This paper deals with the diffusion approximatien technique for solving piulti-server queueing problems with balking having Erlangian inter-arrival time and Erlangian service time distributions. Probability efjoining of a ' new customer to the system is assumed to vary as e'rv where T is a positive parametef and pt is the queue length. The ap'proximation technique is based on the theery of diffusion, considering only means and variances ofarriyai and 'departure processes, Approximate formultis for P (n), probability of finding n customers in the system, and L, mean number of customers in the system, at steady state, are given. Finally, compaiisons of approximate and exact or si:nulated values of mean number L of customers in the system are made for some EllEk!s (ee) systems with balking to show the effectiveness of the approximation technique and graphs of approximate values of L for several systems are drawn which can be used in practice.
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