A Limit Theorem for Functionals of Jumps of Birth and Death Processes under Heavy Traffic Condition

Abstract

For a class of birth and death processes under a heavy traffic condition, the asymptotic behavior of functionals of their jumps is investigated. It is shown that, under suitable normalization, the functionals converge in law to a process that is the sum of a Brownian motion and a constant times the local time of a reflecting Brownian motion at zero. Some applications to queueing processes are presented.