This work studied the effect of the router buffer sizing on the overall throughput of computer and internet networks. We are motivated by the fact that in high speed routers, the buffer size is crucial; in other words too large or too tiny buffer size always poses some constraints. We therefore present a FuzzyBased Buffer Management (FBBM) scheme that performs buffer allocation and packet dropping for wired and wireless networks that accommodates the demands of both the present and the future generation networks. In this scheme, buffers are allocated to requesting application by using buffer allocation factor while packets are dropped for an application by using packets dropping factor. A buffer allocation factor for requesting application was computed adaptively based on three fuzzy parameters of an application, namely, priority, rate of flow and packet size. The scheme has been extensively simulated to test the performance in terms of buffer utilization, handoff / new calls acceptance and dropping probability. The results show that fuzzy based buffer allocation and packet dropping scheme performs better than conventional scheme that employs static buffer allocation and random early detection dropping strategy. The use of other adaptive machine learning techniques are recommended to be incorporated into the fuzzy logic based system. Particularly some neural network principles can be used for selecting the proper adjustment of the fuzzy logic system parameters. Fuzzy Logic and neural networks have been successfully combined in many other applications. It can play an important role in the induction of rules and membership function parameters from observations.