Optimizing Ladder Truck and Car Lift Occupancy in Fire and Rescue Departments Using Queuing Theory

Abstract

The article presents the results of research conducted using the theory of queuing in order to optimize the number of special equipment in the fire and rescue units of the Ministry of Emergency Situations and to improve the overall efficiency of its utilization. The study emphasizes that the presence of hazards, the number of which has been constantly increasing in recent years, has inevitably led to a rise in accidents, explosions, fires, catastrophes, and other emergencies of natural, man-made, and environmental origin. This trend has placed growing demands on fire and rescue units, highlighting the need for scientifically based methods of resource planning and optimization. Within the framework of the research, the mathematical apparatus of queuing theory was applied to evaluate the workload of fire and rescue units, to identify patterns in emergency call arrivals, and to determine the optimal number of special equipment units required under varying conditions. Statistical analysis confirmed that the flow of emergency calls can be described by a Poisson distribution, while service times and fire extinguishing durations follow exponential distributions. These probabilistic models provided the necessary foundation for optimization, ensuring rational allocation of equipment and minimizing delays in response. Particular attention was paid to the challenges posed by rapid urban development. Large industrial facilities, critical infrastructure, and especially the sharp increase in the number of high-rise buildings create new fire safety risks. Ensuring effective fire protection in such environments is a pressing issue today. The results of the study contribute to the development of scientifically grounded strategies for resource optimization, offering practical recommendations for improving the reliability and efficiency of fire and rescue operations in modern urban settings.