A Comparative Study of Fuzzy Versus \ Fixed " Thresholds

High performance cell-based communications networks including ATM have been conceived to carry asynchronous traac sources and support a continuum of transport rates ranging from low bit-rate to high bit-rate traac. When a number of bursty traac sources add cells, the network is inevitably subject to congestion. Traditional approaches to congestion management include admission control algorithms, smoothing functions, and the use of nite-sized buuers with queue management techniques. Most queue management schemes, reported in the literature, utilize \\xed" thresholds, i.e. either binary or a limited number of predetermined values based on the cell priorities, to determine when to permit or refuse entry of cells into the buuer. The aim is to achieve a desired tradeoo between the number of cells carried through the network, propagation delays of the cells, and the number of discarded cells. While binary thresholds are excessively restrictive, the rationale underlying the use of a large number of priorities appears to be ad hoc, unnatural, and unclear. This paper introduces, perhaps for the rst time, the notion of cell-blocking, wherein a fuzzy thresholding function, based on Zadeh's fuzzy set theory, is utilized to deliberately refuse entry to a fraction of incoming cells from other switches. The blocked cells must be rerouted by the sending switch to other switches and, in the process, they may incur delays. The fraction of blocked cells is a continuous function of the current buuer occupancy level unlike the abrupt, discrete thresholds in the traditional approaches. The fuzzy cell-blocking scheme is simulated on a computer and the simulation results for a given, realistic traac stimulus, characterized by Poisson arrivals and exponentially distributed departures, are contrasted against those from the traditional approach. A comparative analysis reveals that fuzzy queue management adapts superbly to sharp changes in cell arrival rates and maximum burstiness of bursty traac sources, yielding lower cell discard rates, high throughput of cells through the network, and lower cell-blocking rates. 2