Performance Analysis of a Two-Stage Tandem Queue With Heterogeneous Parallel Servers Under Random Selection

Abstract

Tandem queueing systems provide a fundamental framework for modeling multi-tier service architectures widely encountered in cloud computing, edge computing, and communication networks. In such systems, the interaction between service stages and the allocation of workloads across heterogeneous servers play a critical role in determining overall system performance. This paper investigates a two-stage tandem loss system motivated by modern service infrastructures. The first stage consists of a single server with buffering, representing an entry or preprocessing unit, while the second stage comprises $c$ heterogeneous parallel servers corresponding to distributed service nodes. A random server selection policy is employed to capture decentralized and low-complexity routing mechanisms used in large-scale systems. To enable tractable analysis, a set-based state representation is introduced, leading to closed-form expressions for steady-state probabilities. Based on this formulation, explicit performance measures, including system occupancy and loss probabilities, are derived. Furthermore, two benchmark configurations—homogeneous servers and a single aggregated server—are developed to construct analytical upper and lower bounds for the loss probability, establishing a clear performance ordering among system configurations. An asymptotic analysis shows that, as the number of servers increases, the inter-loss times exhibit an increasingly close approach to exponential behavior, consistent with the Poisson limit established for the loss process. These theoretical findings are validated through extensive Monte Carlo simulations and Kolmogorov–Smirnov goodness-of-fit tests. The simulation results show an overall decreasing tendency in the KS statistic as the number of heterogeneous parallel servers increases, supporting the asymptotic behavior established by the analysis. The results provide practical insights into the performance evaluation of heterogeneous multi-server systems and offer useful approximations for the design and analysis of cloud and edge computing infrastructures.