Analysis by queuing model of multi-threshold mechanism in ATM switches

In this paper, we present a queuing model for a congestion control mechanism in ATM (asynchronous transfer mode) switches for ABR (available bit rate) services. ABR services are designed to support applications that are loss sensitive but tolerant to delay. ABR sources dynamically adjust their transmission rates in response to congestion feedback from the network, and according to a congestion control algorithm which is implemented in ATM switches such as EFCI (explicit forward congestion indicator) and ER (explicit rate) algorithms. Our mechanism, named "multi-threshold mechanism", has a behaviour similar to the one of the EFCI algorithm but it allows switches to adjust dynamically their input rates as well as their output rates according to different thresholds of their buffer size. The multi-threshold mechanism is modelled in this paper by a queue M/M/1 where input and output rates are controlled. Steady state probabilities as well as mean waiting time and queue average length are given.