Multiclass queueing systems in heavy traffic: an asymptotic approach based on distributional and conservation laws

We propose a new approach to analyze multiclass queueing systems in heavy traffic based on what we consider as fundamental laws in queueing systems, namely distributional and conservation laws. Methodologically, we extend the distributional laws from single class queueing systems to multiple classes and combine them with conservation laws to find the heavy traffic behavior of the following systems: a)EGI/G/1 queue under FIFO, b) EGI/G/1 queue with priorities, c) Polling systems with general arrival distributions. Compared with traditional heavy traffic analysis via Brownian processes, our approach gives more insight to the asymptotics used, solves systems that traditional heavy traffic theory has not fully addressed, and more importantly leads to closed form answers, which compared to simulation are very accurate even for moderate traffic

An axiomatic approach to queueing systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, 1995.Includes bibliographical references (leaves 177-181).by Georgia Mourtzinou.Ph.D

Transient laws of non-stationary queueing systems and their applications

In this paper we consider the general class of non-stationary queueing models and identify structural relationships between the number of customers in the system and the delay at time t, denoted by L(t) andS(t), respectively. In particular, we first establish a transient Little’s law at the same level of generality as the classical stationary version of Little’s law. We then obtain transient distributional laws for overtake free non-stationary systems. These laws relate the distributions of L(t) andS(t) and constitute a complete set of equations that describes the dynamics of overtake free non-stationary queueing systems. We further extend these laws to multiclass systems as well. Finally, to demonstrate the power of the transient laws we apply them to a variety queueing systems: Infinite and single server systems with non-stationary Poisson arrivals and general non-stationary services, multiclass single server systems with general non-stationary arrivals and services, and multiserver systems with renewal arrivals and deterministic services, operating in the transient domain. For all specific systems we relate the performance measures using the established set of laws and obtain a complete description of the system in the sense that we have a sufficient number of integral equations and unknowns. We then solve the set of integral equations using asymptotic expansions and exact numerical techniques. We also report computational results from our methods