Bilateral phase-type distributions

In this article we define a class of distributions called bilateral phase type (BPH), and study its closure and computational properties. The class of BPH distributions is closed under convolution, negative convolution, and mixtures. The one-sided version of BPH, called generalized phase type (GPH), is also defined. The class of GPH distributions is strictly larger than the class of phase-type distributions introduced by Neuts, and is closed under convolution, negative convolution with nonnegativity condition, mixtures, and formation of coherent systems. We give computational schemes to compute the resulting distributions from the above operations and extend them to analyze queueing processes. In particular, we present efficient algorithms to compute the steady-state and transient waiting times in GPH/GPH/1 queues and a simple algorithm to compute the steady-state waiting time in M/GPH/1 queues.     

U.S. Troops and Foreign Economic Growth

By way of an evolutionary game model we show that mediation in international conflicts might be harmful to the conflicting parties. In fact, under anarchy both parties can be better off than under an international regime if mediation reduces the parties’ reactive capacities (i.e. their abilites to respond to an aggression). This result is applied to issues currently discussed in the literature on international relations such as the role of the United Nations as a mediator of international conflicts.