Stochastic bounds for two-layer loss systems

TL;DR

This paper develops stochastic bounds for a two-layer multiclass loss system with overflow routing, providing practical performance bounds through comparison and coupling techniques.

Contribution

It introduces new stochastic comparison methods to derive bounds for complex two-layer loss systems with overflow routing.

Findings

Derived upper and lower performance bounds

Established comparison techniques for system parameters

Applicable to multiclass loss systems with layered servers

Abstract

This paper studies multiclass loss systems with two layers of servers, where each server at the first layer is dedicated to a certain customer class, while the servers at the second layer can handle all customer classes. The routing of customers follows an overflow scheme, where arriving customers are preferentially directed to the first layer. Stochastic comparison and coupling techniques are developed for studying how the system is affected by packing of customers, altered service rates, and altered server configurations. This analysis leads to easily computable upper and lower bounds for the performance of the system.