Analysis of a batch service multi-server polling system with dynamic service control

This paper considers a multi-server polling system with batch service of an unlimited size, i.e., the so called 'Israeli queue' with multi-server, where the service rate of each server switches between a low and a high value depending on the number of groups standing in front of the servers upon its service completion. By means of matrix geometric method and LU-type RG factorization of the infinitesimal generator in irreducible QBD process, the explicit closed-form of rate matrix $R$ and the steady state distribution of the queue length are respectively derived. In terms of the results, some stationary performance measures are obtained. In addition, some numerical examples are presented.