The application of queueing theory in a study of the Wellington Airport check-in system

Abstract

Two multiserver queueing models of the Wellington Airport Check-In System were analysed in this study; the two models suggested are the M/Ek/C(∞,FIFO) and the M/LOGNORMAL/C(∞,FIFO) systems. Since there is at present no analytical solution to the latter model and an 'extremely difficult to derive' solution to the former, the approach in this study was by way of simulation and approximation techniques. The results from the simulations indicated that the approximation formulae suggested by Maaloe (5) would provide fairly accurate and quick answers to steady states M/Ek/C systems at high utilization factor ρ(i.e. ρ = λ/μc → 1 where λ is the mean arrival rate, μ the mean service rate) with small C values. The approximation formula suggested by Lee (36), and which had been used before by Airline O.R. teams (5, 24) doing similar studies, was found to give results which underestimate slightly the actual waiting times of customers at lower utilization factors but improves as the latter approaches one. For the determination of the expected arrival rates at the check-in counters, a simple model was built to predict the expected half-hourly arrival rates of passengers throughout the day. This model, which is based upon Aircraft schedule-departure by type and time; expected passenger loads; arrival pattern(s) of passengers before flight departures; average group size of passenger arrivals; percentage of city check-ins, was found to give reasonably accurate predictions. With the availability of information about the expected arrival rates of passengers at the counters throughout the day, we should now be able to man the counters according to whatever level of service we desire.