Markovian Queueing Models with Scheduled Arrival Patterns: The Optimal Model for Public Transportation

Zana Najm Abdullah  Nasrallah; Khalid Rahamtalla  Khedir; Mohammedelameen  Eissa

Zana Najm Abdullah Nasrallah Department of Statistics, Kirkuk University, Kirkuk, Iraq
Khalid Rahamtalla Khedir Sudan University of Science & Technology, College of Science, Department of Statistics. Po Box 407 Khartoum, Sudan
Mohammedelameen Eissa Sudan University of Science & Technology, College of Science, Department of Statistics. Po Box 407 Khartoum, Sudan

Keywords: Markovian queuing model, Scheduled arrivals, Public transportation, Congestion optimization, Urban transit efficiency

Abstract

This study introduces a Markovian queuing model with scheduled arrival patterns to improve the evaluation and optimization of public transportation systems. While traditional models often overlook the variability in passenger demand throughout the day, this research addresses this gap by incorporating scheduled arrival dynamics that better reflect real-world scenarios at bus stops and train stations. The model employs Markovian equations and simulation methods to analyze the impact of arrival schedules on passenger flow and capacity management. Results demonstrate that the model effectively predicts congestion levels, optimizes service intervals, and improves overall system responsiveness. These findings offer actionable insights for transit planners and policymakers to enhance scheduling strategies, resource allocation, and passenger satisfaction, particularly during peak hours. This work provides a valuable framework for improving urban transit efficiency and reliability.

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