Asymptotic Blocking Probabilities in Loss Networks with Subexponential Demands

TL;DR

This paper derives simple asymptotic formulas for blocking probabilities in loss networks with complex demand patterns, extending classical models and demonstrating accurate predictions even at small capacities.

Contribution

It introduces generalized asymptotic expressions for blocking probabilities using compound point processes, including resource reservation, improving analysis of complex loss networks.

Findings

Asymptotic formulas match simulations well for small capacities.

Extended models incorporate resource reservation.

Generalizes classical Erlang formulas for complex demands.

Abstract

The analysis of stochastic loss networks has long been of interest in computer and communications networks and is becoming important in the areas of service and information systems. In traditional settings, computing the well known Erlang formula for blocking probability in these systems becomes intractable for larger resource capacities. Using compound point processes to capture stochastic variability in the request process, we generalize existing models in this framework and derive simple asymptotic expressions for blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulas and simulation results even for relatively small resource capacities and relatively large values of blocking probabilities.