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

In this paper we consider a single Asynchronous Transfer Mode (ATM) transmission link, to which Constant Bit Rote (CBR) or Variable Bit Rate (VBR) and Available Bit Rate (ABR) or UnspeciJied Bit Rate (UBR) calls arrive according to independent Poisson processes. CBR/VBR calls (characterized by their equivalent bandwidth) are blocked and leave the system if the availablelink capacity is less than the required at the time of arrival. ABR/UBR calls , however, accept partial blocking [3], 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 longer time spent in the system, as detailed in [3]. 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 (greedy sources). Additionally, if this minimal accepted bandwidth is unavailable at the time of arrival ABRIUBR calls are allowed to wait in a finite queue. This system is modelled by a Morkov Process and the blocking probabilities, the moments and the distribution of the ABR/UBR waiting and service time are derived.