Bus Operation Modeling Using Semi-Open Queuing Networks - Case of Makkah

Makkah bus project is part of Saudi Vision to establish an advanced public transportation network that meets the transportation needs of Makkah residents, visitors, and pilgrims. The public bus system has been tried in Makkah for the first time in Ramadan-1443 (2022) to serve people who would like to perform their Umrah and prayers in the holy mosque, Masjid Al-Haram. Although many KPIs (Key Performance Indicators) had been defined by the Makkah bus project, they were not measured during the Ramadan operation since the transit system was newly introduced and the operations started under heavy traffic conditions and high passenger demand. In addition, the measures for the system effectiveness and capacity had not been set yet. In this article, a Semi-Open Queuing Network model has been proposed to measure passenger serving capacity, system utilization, queue lengths and queue waiting times. For assessing the system performance, the network steady state probabilities have been derived for two scenarios: the first assumes that only one bus can load/unload at the bus stop whereas the second scenario assumes that multiple buses can load/unload simultaneously at the bus stop. The data have been collected from bus operation through ITS (Intelligent Transport Systems) and field observations. Based on real data, the system performance measures are estimated and reported. The results revealed that the system capacity is mostly affected by the dwell time and suggests that planners should first work to minimize the dwell time before increasing the number of buses.