In this paper, we develop simple models to study the performance of BitTorrent, a second generation peerto -peer (P2P) application. We first present a simple fluid model and study the scalability, performance and e#ciency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its e#ect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet.

We derive formulas approximating the asymptotic variance of four estimators for the steadystate blocking probability in a multi-server loss system, exploiting diffusion process limits. These formulas can be used to predict simulation run lengths required to obtain desired statistical precision before the simulation has been run, which can aid in the design of simulation experiments. They also indicate that one estimator can be much better than another, depending on the loading. An indirect estimator based on estimating the mean occupancy is significantly more (less) efficient than a direct estimator for heavy (light) loads. A major concern is the way computational effort scales with system size. For all the estimators, the asymptotic variance tends to be inversely proportional to the system size, so that the computational effort (regarded as proportional to the product of the asymptotic variance and the arrival rate) does not grow as system size increases. Indeed, holding the blocking probability fixed, the computational effort with a good estimator decreases to 0 as the system size increases. The asymptotic variance formulas also reveal the impact of the arrival-process and service-time variability on the statistical precision. We validate these formulas by comparing them to exact numerical

Abstract: In order to obtain Markov heavy-traffic approximations for infinite-server queues with general non-exponential service-time distributions and general arrival processes, possibly with time-varying arrival rates, we establish heavy-traffic limits for two-parameter stochastic processes. We

We study the G/GI/∞ queue from two different perspectives in the same heavy-traffic regime. First, we represent the dynamics of the system using a measure-valued process that keeps track of the age of each customer in the system. Using the continuous-mapping approach together with the martingale functional central limit theorem, we obtain fluid and diffusion limits for this process in a space of distribution-valued processes. Next, we study a measurevalued process that keeps track of the residual service time of each customer in the system. In this case, using the functional central limit theorem and the random time change theorem together with the continuous-mapping approach, we again obtain fluid and diffusion limits in our space of distribution-valued processes. In both cases, we find that our diffusion limits may be characterized as distribution-valued Ornstein-Uhlenbeck processes. Further, these diffusion limits can be analyzed using standard results from the theory of Markov processes.

Martingale proofs of many-server heavy-traffic limits for Markovian queues

In this paper, we develop simple models to study the performance of BitTorrent, a second generation peer-to-peer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its effect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet.

In this paper, we develop simple models to study the performance of BitTorrent, a second generation peer-to-peer (P2P) application. We first present a simple fluid model and study the scalability, performance and efficiency of such a file-sharing mechanism. We then consider the built-in incentive mechanism of BitTorrent and study its effect on network performance. We also provide numerical results based on both simulations and real traces obtained from the Internet.

Excursion-based universal approximations for the Erlang-A queue in steady-state

This thesis was a product of many years of work that has been influenced by many who have been a part of my academic life during my undergraduate studies at Bilkent University, and then during my graduate studies at Colorado State University-Pueblo and at Georgia Tech. I am grateful to all those teachers who have helped me to gain skills I now possess. Dr. Jim Dai deserves the most credit for making this quest a success. He provided me not only with academic advisement and guidance in my research and classes but has also been a true mentor, friend and inspiration. He has played an important role in my personal and academic development for the last four years. He is always going to be the reference point as to what I should achieve as an academician and an advisor. I am grateful for the opportunity to work with him and for all the time he devoted towards my development. Each meeting with him was a great joy and source of excitement. Dr. Amy Ward has also served as a co-advisor for almost a year. I would like to thank her for guiding me while exploring new research directions. It was a pleasure to have her as a co–advisor. I would like to thank Dr. Ron Billings, Dr. Anton Kleywegt, and Dr. Mor Armony for