QUEUE PROBLEMS WITH HETEROGENEOUS ARRIVAL AND SERVICE PROCESSES

Abstract

Queuing problems in modern systems are increasingly complex due to the emergence of high variability in customer arrival patterns and service capacity. This study examines the phenomenon of queues with heterogeneous arrival and service processes, where the assumptions of Poisson distribution and standard exponential service times are no longer sufficient to describe the system reality. Using a stochastic modeling approach, this study analyzes how heterogeneity in customer characteristics and differences in server performance affect system performance metrics such as average waiting time and queue length. The methodology used involves discrete-time and continuous-time Markov chain analysis to model workload fluctuations. The results show that ignoring heterogeneity factors often leads to inaccurate capacity estimates, which lead to operational inefficiencies. This study recommends dynamic resource allocation strategies and adaptive prioritization policies to mitigate the negative impacts of system variability.