Consistency of infinitesimal perturbation analysis estimators with rates

We study a class of infinitesimal perturbation analysis (IPA) algorithms for queueing systems with load-dependent service and/or arrival rates. Such IPA algorithms were originally motivated by applications to large queueing systems in conjunction with aggregation algorithms. We prove strong consistency of these estimators through a type of birth and death queue. This work was supported in part by the NSF under Grants Nos. ECS85-15449 and CDR-8803012, by ONR under Contracts Nos. N00014-89-J-0075 and N00014-90-K-1093, and by the US Army under Contract No. DAAL-03-83-K-0171. This paper was written while the author was with the Division of Applied Sciences at Harvard University.