Minimization of Expected Response Time under Stationary Information System in Distributed Service Networks

Abstract

In today's rapidly evolving technological landscape, distributed service networks play a pivotal role in enabling efficient operations across a range of industries, including cloud computing, telecommunications, and logistics. As the complexity and scale of these networks increase, optimizing service performance—particularly in terms of minimizing response time—has become a critical objective. This paper addresses the challenge of reducing the expected response time within a distributed service network operating under a stationary information environment. We present a robust mathematical framework that captures the essential characteristics of such networks, including the arrival rates of service requests, the capacity constraints of service nodes, and inherent communication delays across the system. The model is grounded in operations research principles and integrates tools from queueing theory and probabilistic modelling to realistically reflect the network's dynamic behaviour. To achieve optimal performance, an optimization-based methodology is proposed for determining both the allocation of resources and the routing of requests. The approach focuses on balancing the system load and effectively distributing service demand among available nodes to minimize bottlenecks and latency. By formulating the problem as a mathematical optimization task, we identify strategies that enhance system responsiveness under various operational scenarios. The theoretical insights are complemented by a comprehensive set of simulation experiments that test the model's performance across different network configurations and workloads. The simulation results demonstrate the reliability and efficiency of the proposed approach, validating its potential for real-world application. These findings offer valuable decision-making support for network designers and system administrators tasked with managing large-scale distributed infrastructures. Overall, this study makes a significant contribution to the optimization of distributed service networks by introducing a systematic method for minimizing response time. The integration of theoretical modeling with empirical validation ensures that the proposed framework is both rigorous and practical. This research advances the field by providing scalable, data-driven strategies that can be tailored to diverse network settings, ultimately promoting more responsive and resource-efficient service delivery.