Designing production and service systems using queuing theory: principles and application to an airport passenger security screening system

Queues of people, products and machines frequently occur in many production and service systems, resulting in significant inefficiencies. This paper discusses the significant impact on these problems of the queuing theory introduced by Erlang and Kendall. A methodology based on the M/M/m queuing model (including a validation phase through a goodness-of-fit test) is proposed. This methodology makes parametric analyses of system performance according to the different possible ranges of input parameters. It helps solve several typical problems found in production systems (e.g., resource design, traffic and logistics analysis) and services (e.g., optimal design and management). There is a good tradeoff between the robustness of the results, coherence with real industrial systems and mathematical complexity. A real-world application involving the design optimisation of a passenger security screening system in an international airport is presented. In particular, the optimal number of security gates in the design is discussed.