Transform Methods for Heavy-Traffic Analysis

Abstract

The drift method was recently developed to study queueing systems in steady-state. It was successfully used to obtain bounds on the moments of the scaled queue lengths, that are asymptotically tight in heavy-traffic, in a wide variety of systems including generalized switches, input-queued switches, bandwidth sharing networks, etc. In this paper we develop the use of transform techniques for heavy-traffic analysis, with a special focus on the use of moment generating functions. This approach simplifies the proofs of the drift method, and provides a new perspective on the drift method. We present a general framework and then use the MGF method to obtain the stationary distribution of queue lengths in heavy-traffic in queueing systems that satisfy the Complete Resource Pooling condition. In particular, we study load balancing systems and generalized switches under general settings.

References in corpus (2)

• Validity of heavy traffic steady-state approximations in generalized Jackson Networks
• Diffusion models and steady-state approximations for exponentially ergodic Markovian queues

Cited by in corpus (4)

• Load balancing system under Join the Shortest Queue: Many-Server-Heavy-Traffic Asymptotics
• Throughput and Delay Optimality of Power-of-d Choices in Inhomogeneous Load Balancing Systems
• Finite-Time Behavior of Erlang-C Model: Mixing Time, Mean Queue Length and Tail Bounds
• Steady-State Convergence of the Continuous-Time Routing System with General Distributions in Heavy Traffic