Application Stochastic Approximation Procedure in the Presence of Delayed Groups of Clients

In the presence of delayed groups of delayed customers, the Robbins-Monro stochastic approximation technique is modified to be functional. To get an accurate explanation of the suggested treatment, two loss systems are added. Each client is reliable after fixed time intervals with the process of the following client according to the result of the previous one, where a client s serving time is considered to be a discrete random variable. Where the analysis of their results is obtained, taking into account that it was considered a special case is that the maximum time of delay is the unit. The analysis shows that the efficiencies of the procedure can be improved by controlling on some parameters such as maximize number of servers or minimize groups capacity, and the best result can be obtained when we take both in consideration. Efficiency depends on the clients overall service time and the groups number of clients. The most significant consequence is that the efficiencies of the process are enhanced by increasing the allocation of operating time and client service times. In general, in many fields, such as medicine, computer science, business, and applied sciences, our proposal can be used for other stochastic approximation processes to increase efficiency