Asymptotic Blocking Probabilities in Loss Networks with Subexponential 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 probabilities 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 the blocking probabilities. In addition, we extend our model to incorporate reserving resources in advance. Although asymptotic, our experiments show an excellent match between derived formulae and simulation results even for relatively small resource capacities and relatively large values of the blocking probabilities.