Loss ratio approximations in buffered systems with regulated inputs

The estimation of the expected traffic loss ratio (workload loss ratio, WLR) is a key issue in provisioning Quality of Service in packet based communication networks. The stationary (long run) loss ratio in queuing analysis is usually estimated through other assessable quantities, typically based on the approximates of the buffer overflow probability. These approaches have the drawback, that the relation between loss ratio and buffer overflow probability is often hardly quantifiable and it can in principle be arbitrary. In this paper we present novel upper approximations for workload loss ratio derived from the original definition of stationary loss ratio. These direct bounds are applicable for general service curve network elements with regulated flows acting as inputs. The performance of these bounds is systematically analyzed and compared to prior indirect (based on buffer saturation probability) loss ratio bound and its newly developed improvements. The extensive numerical investigations also exemplify that in most cases our novel direct bounds can lead to significant save in buffer requirements when guaranteeing a prescribed QoS level in terms of loss ratio.