Proportional fairness and its relationship with multi-class queueing networks

We consider multi-class single-server queueing networks that have a product form stationary distribution. A new limit result proves a sequence of such networks converges weakly to a stochastic flow level model. The stochastic flow level model found is insensitive. A large deviation principle for the stationary distribution of these multi-class queueing networks is also found. Its rate function has a dual form that coincides with proportional fairness. We then give the first rigorous proof that the stationary throughput of a multi-class single-server queueing network converges to a proportionally fair allocation. This work combines classical queueing networks with more recent work on stochastic flow level models and proportional fairness. One could view these seemingly different models as the same system described at different levels of granularity: a microscopic, queueing level description; a macroscopic, flow level description and a teleological, optimization description.Comment: Published in at http://dx.doi.org/10.1214/09-AAP612 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Performansi Algoritma SFQ untuk Aplikasi VoIP pada LAN

Traffic control merupakan salah satu fitur dari sistem operasi Linux yang dapat digunakan untuk melakukan pengaturan paket data. Algoritma Stochastic Fairness Queueing merupakan salah satu algoritma penjadwalan paket classless pada traffic control. Algortima ini mengelompokkan aliran data yang masuk menggunakan fungsi hash kemudian mengeluarkan output antrian secara round robin sehingga mengurangi waktu tunggu antrian paket .Dengan pengaruh penggunaan algoritma Stochastic Fairness Queueing yang diterapkan pada aplikasi VoIP ini diharapkan dapat memberikan nilai QoS yang baik untuk masing-masing aplikasi. Pada penelitian ini dilakukan implementasi jaringan local area network dengan menggunakan PC Router berbasis Ubuntu untuk menerapkan traffic control dan menitikberatkan analisis perbandingan performansi QoS yang meliputi parameter delay, jiter, dan throughput antara algoritma stochastic fairnees queueing dan algoritma first in first out.Hasil analisis implementasi yang dilakukan menunjukkan bahwa pemakaian algoritma stochastic fairness queueing untuk aplikasi voice lebih baik dari algoritma first in first out. Hal ini terlihat dari hasil analisis menunjukkan bahwa penereapan algoritma stochastic fairness queueing menyebabkan penurunan delay sebesar 5 % dan penurunan jitter sebesar 13.24%

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

Analisis Performansi algoritma SFQ untuk aplikasi VoIP,HTTP,FTP

Traffic Control merupakan salah satu fitur dari sistem operasi Linux yang dapat digunakan untuk melakukan pengaturan paket data. Algoritma Stochastic Fairness Queueing merupakan salah satu algoritma penjadwalan paket classless pada traffic control. Algortima ini mengelompokkan aliran data yang masuk menggunakan fungsi hash kemudian mengeluarkan output antrian secara round robin sehingga mengurangi waktu tunggu antrian paket .Dengan pengaruh penggunaan algoritma Stochastic Fairness Queueing yang diterapkan pada aplikasi VoIP, file transfer, dan web ini diharapkan dapat memberikan nilai QoS yang baik untuk masing-masing aplikasi.Pada tugas akhir ini dilakukan implementasi jaringan local area network dengan menggunakan PC Router berbasis Ubuntu untuk menerapkan Traffic Control dan menitikberatkan analisis perbandingan performansi QoS yang meliputi parameter delay, jiter, throughput, dan packet loss antara algoritma stochastic fairnees queueing dan algoritma first in first out.Hasil analisis implementasi yang dilakukan pada masing-masing scenario menunjukkan bahwa pemakaian algoritma stochastic fairness queueing untuk aplikasi voice dan download dengan file transfer protocol lebih baik dari algoritma first in first out. Hal ini terlihat dari hasil analisis menunjukkan bahwa penereapan algoritma stochastic fairness queueing menyebabkan penurunan delay sebesar 5 % untuk paket voice dan penurunan jitter sebesar 13.24% untuk komunikasi voice dan 7,7% untuk aplikasi download dengan protocol FTP, kenaikan throughput sebesar 8.75% untuk komunikasi voice dan 7,15% untuk aplikasi download dengan protocol FTP

Insensitive, maximum stable allocations converge to proportional fairness

We describe a queueing model where service is allocated as a function of queue sizes. We consider allocations policies that are insensitive to service requirements and have a maximal stability region. We take a limit where the queueing model become congested. We study how service is allocated under this limit. We demonstrates that the only possible limit allocation is one that maximizes a proportionally fair optimization problem.Comment: 9 page

Concave Switching in Single and Multihop Networks

Switched queueing networks model wireless networks, input queued switches and numerous other networked communications systems. For single-hop networks, we consider a {($\alpha,g$)-switch policy} which combines the MaxWeight policies with bandwidth sharing networks -- a further well studied model of Internet congestion. We prove the maximum stability property for this class of randomized policies. Thus these policies have the same first order behavior as the MaxWeight policies. However, for multihop networks some of these generalized polices address a number of critical weakness of the MaxWeight/BackPressure policies. For multihop networks with fixed routing, we consider the Proportional Scheduler (or (1,log)-policy). In this setting, the BackPressure policy is maximum stable, but must maintain a queue for every route-destination, which typically grows rapidly with a network's size. However, this proportionally fair policy only needs to maintain a queue for each outgoing link, which is typically bounded in number. As is common with Internet routing, by maintaining per-link queueing each node only needs to know the next hop for each packet and not its entire route. Further, in contrast to BackPressure, the Proportional Scheduler does not compare downstream queue lengths to determine weights, only local link information is required. This leads to greater potential for decomposed implementations of the policy. Through a reduction argument and an entropy argument, we demonstrate that, whilst maintaining substantially less queueing overhead, the Proportional Scheduler achieves maximum throughput stability.Comment: 28 page

Stability of multi-dimensional birth-and-death processes with state-dependent 0-homogeneous jumps

We study the positive recurrence of multi-dimensional birth-and-death processes describing the evolution of a large class of stochastic systems, a typical example being the randomly varying number of flow-level transfers in a telecommunication wire-line or wireless network. We first provide a generic method to construct a Lyapunov function when the drift can be extended to a smooth function on $\mathbb R^N$, using an associated deterministic dynamical system. This approach gives an elementary proof of ergodicity without needing to establish the convergence of the scaled version of the process towards a fluid limit and then proving that the stability of the fluid limit implies the stability of the process. We also provide a counterpart result proving instability conditions. We then show how discontinuous drifts change the nature of the stability conditions and we provide generic sufficient stability conditions having a simple geometric interpretation. These conditions turn out to be necessary (outside a negligible set of the parameter space) for piece-wise constant drifts in dimension 2.Comment: 18 pages, 4 figure