Approximate Analysis of a Hierarchical Queuing Network

A hierarchical queuing network is a layered network of queues in which all arrivals receive initial service from a primary server, and some customers receive additional service jointly from a primary and a secondary server. This paper considers the simplest such network, involving two levels and a single secondary server who functions as a consultant to several primary servers and always works in conjunction with the primary server who refers the customer to him. An approximate analysis of this hierarchical queuing network is carried out for three operating disciplines governing the consultation process. The analytical results compare favorably with the results of computer simulations and are therefore used to explore several important issues in the design of such networks. Hierarchical queues are common in public-service systems, including new medical-care systems known as “telemedicine.”