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.

multiclass loss system, overflow routing, maximum packing, stochastic order, preorder, coupling"
Queueing theory (msc 60K25), Inequalities; stochastic orderings (msc 60E15), Performance evaluation; queueing; scheduling (msc 68M20), Network models, stochastic (msc 90B15), Queues and service (msc 90B22)
Logistics (theme 3), Energy (theme 4)
CWI. Probability, Networks and Algorithms [PNA]

Jonckheere, M, & Leskela, L.S. (2007). Stochastic bounds for two-layer loss systems. CWI. Probability, Networks and Algorithms [PNA]. CWI.