A Partially-Blocking Queueing System with CBR/VBR and ABR/UBR Arrival Streams

In this paper we consider an ATM transmission link, to which CBR or VBR and ABR or UBR calls arrive according to independent Poisson processes. CBR/VBR calls (characterized by their equivalent bandwidth) are blocked and leave the system if the available link capacity is less than required at the time of arrival. ABR/UBR calls, however, accept partial blocking, meaning that they may enter service even if the available capacity is less than the specified required peak bandwidth, but greater than the so called minimal accepted bandwidth. Partially blocked ABR/UBR calls instead experience longer service time, since smaller given bandwidth entails proportionally longer time spent in the system, as first suggested in 3] and analyzed in details herein. Throughout the life time of an ABR/UBR connection, its bandwidth consumption fluctuates in accordance with the current load on the link but always at the highest possible value up to their peak bandwidth (greedy sources). Additionally, if this minimal accepted bandwidth is unavailable at the time of arrival, ABR/UBR calls are allowed to wait in a finite queue. This system is modeled by a Continuous Time Markov Chain (CTMC) and the CBR/VBR and ABR/UBR blocking probabilities and the mean ABR/UBR waiting- and service times are derived.