Batch service systems with heterogeneous servers

van Ommeren, Jan-Kees [Stochastic Operations Research, University of Twente, The Netherlands] Baer, Niek [Stochastic Operations Research, University of Twente, The Netherlands] Mishra, Nishant [UCL] Roy, Debjit [Indian Institute of Management Ahmedabad,, India]

Bulk-service multi-server queues with heterogeneous server capacity and thresholds are commonly seen in several situations such as passenger transport or package delivery services. In this paper, we develop a novel decomposition-based solution approach for such queues using arguments from renewal theory. We then obtain the distribution of the waiting time measure for multi-type server systems. We also obtain other useful performance measures such as utilization, expected throughput time, and expected queue lengths.