An Optimized Model for Service Rates’ Control in M/M/1 Queue Networks with Server Vacations
Evidence from literature had revealed that several studies on servers’ failures and customers’ behaviour in M/M/1 queue networks had been done. However, none of these studies had sufficiently established a relationship between optimality in servers’ usage and control of queue network resources. Consequently, this study proposes a fuzzy-based optimal control system of the threshold type such that all arrivals finding K customers in queue and service are rejected. The objective is to choose the service rate dynamically in order to minimize average cost. OMNeT++ was used as a simulation framework while dataset was generated randomly. The system was simulated with the system starting from an initial state k= 0, s = 0 and c = 0, employing the fuzzy control at each decision epoch. The evolution of k and s for the first 1500 time units indicates that an idle server is not turned on immediately after a customer arrives. This shows the hysteretic property of the system indicating the hystereticity of the optimal policy. Consequently, it is concluded that the proposed approach is efficient and promising
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