On the core of cooperative queueing games

We consider a class of cooperative games for managing several canonical queueing systems. When cooperating parties invest optimally in common capacity or choose the optimal amount of demand to serve, cooperation leads to ``single-attribute{''} games whose characteristic function is embedded in a one-dimensional function. We show that when and only when the latter function is elastic will all embedded games have a non-empty core, and the core contains a population monotonic allocation. We present sufficient conditions for this property to be satisfied. Our analysis reveals that in most Erlang B and Erlang C queueing systems, the games under our consideration have a non-empty core, but there are exceptions, which we illustrate through a counterexample. (C) 2011 Elsevier B.V. All rights reserved.