Performance modelling of a multirate loss system with batched Poisson arrivals under a probabilistic threshold policy

Abstract

The authors consider a link accommodating batched Poisson arriving calls of different service classes. A batch of generally distributed number of calls arrive to the link at exponentially distributed time‐points. Each call is treated separately from the rest, and its acceptance is decided, according to the available link bandwidth (partial batch blocking discipline). For congestion control, if the number of in‐service calls of a service class exceeds a threshold (dedicated to the service class), a new call of the same service class is accepted with a probability, dependent on the system state (probabilistic threshold policy). The link is analysed as a multirate loss system, via a reversible Markov chain. The latter leads to a product form solution (PFS) for the steady‐state distribution. Based on the PFS, the authors propose models for the accurate determination of time and call congestion probabilities and link utilisation. Comparison against other existing models under the complete sharing or the bandwidth reservation policy reveals the necessity and consistency of the proposed models.

Keywords

• multirate loss system
• batched Poisson arrivals
• probabilistic threshold policy
• congestion control
• product form solution
• reversible Markov chain