Probabilistic Retry and Threshold Multirate Loss Models for Impatient Calls

Abstract

In this paper, a link of fixed capacity is considered that services calls from different service-classes. Calls arrive in the link according to a Poisson process, have an initial (peak) bandwidth requirement while their service time is exponentially distributed. We model this system as a multirate loss system and analyze two different multirate loss models. In the first model, named probabilistic retry loss model, if there is no available link bandwidth, a new call is blocked but retries with a lower bandwidth requirement and increased service time. To allow for the fact that a blocked call may be impatient, we assume that it retries with a probability. In the second model, named probabilistic threshold loss model, a call may reduce its bandwidth requirement (before blocking occurs) based on the occupied link bandwidth. To determine call blocking probabilities in both multirate loss models, we show that approximate but recursive formulas do exist that provide quite satisfactory results compared to simulation.

Keywords

• call blocking
• retry
• threshold
• loss
• Poisson
• recursive