Effective bandwidths at multi-class queues
Queueing Systems: Theory and Applications
IEEE/ACM Transactions on Networking (TON)
A histogram-based model for video traffic behavior in an ATM multiplexer
IEEE/ACM Transactions on Networking (TON)
Modeling video sources for real-time scheduling
Multimedia Systems
IEEE Journal on Selected Areas in Communications
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For an ATM multiplexer we develop a recursive asymptotic expansion method for approximating the queue length distribution and investigate the radius of convergence of the queue asymptotic expansion series. The analysis focuses on "small" to "moderate" buffer sizes under the conditions of strictly stable multiple time scale arrivals. For a class of examples we analytically determine the radius of convergence using methods of linear operator theory. We also give general sufficient conditions under which the radius converges to zero; this shows roughly what situations have to be avoided for the proposed method to work well. We combine the asymptotic expansion method with the EB approximation, and give an approximation procedure for the buffer probabilities for all buffer ranges. The procedure is tested on extensive numerical examples. We suggest this procedure for efficient admission control in ATM networks.