Applying queuing theory to the design and optimization of production/service systems

Queues of people, products, and machines frequently occur in many production systems (goods manufacturing and service supply) and result in significant inefficiencies. For example, machines waiting to be repaired may result in lost production, vehicles forced to wait before being unloaded may delay subsequent shipments, and people made to wait for a service (i.e. bank, hospital, supermarket) may become frustrated which could result in lost future business. This paper discusses the tremendous positive impact of queuing theory (introduced by Erlang and Kendall) on the problems typically found in production systems (e.g. optimal design, resource rationalization, traffic and logistics analysis). The fundamental models in this theory are discussed and then applied to the design and optimization of production systems. Finally, a real world application of M/M/n queuing theory is presented involving design optimization of a passenger security screening system in an international airport.