This thesis applies recent advances in the field of robust optimization to the optimal control of multiclass queueing networks. We develop models that take into account the uncertainty of interarrival and service time in multiclass queueing network problems without assuming a specific probability distribution, while remaining highly tractable and providing insight into the corresponding optimal...

In this paper we propose a new statistical model for multi-scale traffic, and present an exact queueing analysis for the model. The model is based on the central moments and the marginal distributions of the cumulative traffic loads in different time scales. Only the first two moments are needed to characterize the traffic process, which greatly simplifies the representation and estimation. The...

In the queueing theory we usually ignore the fact that utility server is often a technical device and its breakdown can occur. Common analytic models (see for example in [1] or [2]) assume that the server works reliably without failures causing its deficit. If failures of the server occur often and we would use an analytic model of reliable queueing system for modeling studied system, reached o...

The traac equations are a set of linear equations, which are the basis for the exact analysis of product form queueing networks, and the approximate analysis of non-product form queueing networks. Conditions characterising the structure of the network that guarantees the existence of a solution for the traac equations are therefore of great importance. This note provides a necessary and suucien...

This paper studies a queueing system with a Markov arrival process and cyclic service times. When customers are distinguished by the types of their service times, the queueing processes experienced by different types of customers are different. First, a computational approach is developed to find the distributions of the queue length and waiting time of each type of customer. The results are us...

Abstract In this paper we show how to go beyond the study of the topological properties of the Internet, by measuring its dynamical state using special active probing techniques and the methods of network tomography. We demonstrate this approach by measuring the key state parameters of Internet paths, the characteristics of queueing delay, in a part of the European Internet. In the paper we des...

In this paper, we explore the use of static risk measures from the mathematical finance literature to assess the performance of some standard nonstationary queueing systems. To do this we study two important queueing models, namely the infinite server queue and the multi-server queue with abandonment. We derive exact expressions for the value of many standard risk measures for the M t / M / ∞ ,...

We consider a class of inhomogeneous Markovian queueing models with batch arrivals and group services. Bounds on the truncation errors in weak ergodic case are obtained. Two concrete queueing models are studied as examples.

A connection between permutations that avoid 4231 and a certain queueing discipline is established. It is proved that a more restrictive queueing discipline corresponds to avoiding both 4231 and 42513, and enumeration results for such permutations are given.

In this paper we identify important characteristics of a fading/shadowing fading channel and present the work of measurement-based channel modeling for packet-level network queueing analysis. Our integration of wireless channel modeling and data queueing analysis at the packet-level provides a unique approach to study the eeect of various channel dynamics on high layer network performance, whic...