Queuing Theory Application to Service Delivery Optimisation in Nigeria Customs Service Ports

Port clearance delays at Nigerian seaports impose an estimated 300 billion naira annually in direct demurrage charges and indirect supply chain costs on importers and the national economy. This study applies queuing theory analysis to evaluate service delivery bottlenecks at the Nigeria Customs Service examination and valuation bays within Apapa Port, Lagos, South West Nigeria. An M/G/s queuing model is formulated to reflect the general service time distribution observed empirically, as clearance durations vary significantly by cargo type and HS code complexity. Arrival rate and service time data are collected through direct observation and customs platform transaction records over an eight-week period. Server utilisation rates across four examination bay clusters are estimated and compared against efficiency thresholds. Results indicate that two bay clusters operate at utilisation rates exceeding 94 percent, generating average clearance waiting times of 6.2 days against the ECOWAS benchmark of 48 hours. Simulation experiments using Arena Simulation Software model the impact of adding examination officers and digitalising the valuation process on system-wide throughput. Combined digitalisation and two additional server configuration reduces average waiting time to 31 hours and reduces system-wide queue length by 71 percent. The study recommends phased implementation of digital pre-clearance and examination officer expansion as priority reforms. Keywords: queuing theory, port clearance, Nigeria Customs Service, service optimisation, M/G/s model.