Recently, some research has been done to analyze the asymptotic behavior of queue length distribution in ATM(Asynchronous Transfer Mode) multiplexer, In this paper, we relate this asymptotic behavior with the asymptotic behavior of decreasing cell los...
Recently, some research has been done to analyze the asymptotic behavior of queue length distribution in ATM(Asynchronous Transfer Mode) multiplexer, In this paper, we relate this asymptotic behavior with the asymptotic behavior of decreasing cell loss probability when the buffer capacity is increased. We find with reasonable assumptions that the asymptotic rate of queue length distribution is the same as that of decreasing cell loss probability. Even under different priority control schemes and traffic classes, we find that this asymptotic rate of the individual cell loss probability of each traffic class does not change. As a consequence, we propose the upper bound of cell loss probability of each traffic class when a priority control scheme is employed. This bound is oornputationally feasible in a real-time. The numerical examples will be provided to validate this finding.