Delay analysis of continuous bit rate traffic over an ATM network

A packet multiplexer is modeled for continuous bit rate (CBR) traffic in an asynchronous transfer mode (ATM) network as an nD/D/1 queue. The efficiencies of various algorithms for finding the delay distribution are compared. In particular, a new algorithm is proposed whose time complexity is O(n²), where n is the number of voice sources being multiplexed. The use of the central limit theorem can reduce the time complexity to O(n) for large n . An asymptotic formula is found whose time complexity is independent of n and it works well (for practical purposes) over a wide range of parameter values. The authors examine and comment on the use of the M/D/1 results as an approximation. In addition to comparing the performances of these algorithms, they show that the buffer requirements for such a queue are significantly less than the theoretical maximum (even when the requirement on the call disruption probability is very low). This result has important implications in the design of buffer size. The buffer requirement is relatively insensitive to the design criterion (call disruption probability)