240 research outputs found
Store-Forward and its implications for Proportional Scheduling
The Proportional Scheduler was recently proposed as a scheduling algorithm
for multi-hop switch networks. For these networks, the BackPressure scheduler
is the classical benchmark. For networks with fixed routing, the Proportional
Scheduler is maximum stable, myopic and, furthermore, will alleviate certain
scaling issued found in BackPressure for large networks. Nonetheless, the
equilibrium and delay properties of the Proportional Scheduler has not been
fully characterized.
In this article, we postulate on the equilibrium behaviour of the
Proportional Scheduler though the analysis of an analogous rule called the
Store-Forward allocation. It has been shown that Store-Forward has
asymptotically allocates according to the Proportional Scheduler. Further, for
Store-Forward networks, numerous equilibrium quantities are explicitly
calculable. For FIFO networks under Store-Forward, we calculate the policies
stationary distribution and end-to-end route delay. We discuss network
topologies when the stationary distribution is product-form, a phenomenon which
we call \emph{product form resource pooling}. We extend this product form
notion to independent set scheduling on perfect graphs, where we show that
non-neighbouring queues are statistically independent. Finally, we analyse the
large deviations behaviour of the equilibrium distribution of Store-Forward
networks in order to construct Lyapunov functions for FIFO switch networks
Load Balancing in the Non-Degenerate Slowdown Regime
We analyse Join-the-Shortest-Queue in a contemporary scaling regime known as
the Non-Degenerate Slowdown regime. Join-the-Shortest-Queue (JSQ) is a
classical load balancing policy for queueing systems with multiple parallel
servers. Parallel server queueing systems are regularly analysed and
dimensioned by diffusion approximations achieved in the Halfin-Whitt scaling
regime. However, when jobs must be dispatched to a server upon arrival, we
advocate the Non-Degenerate Slowdown regime (NDS) to compare different
load-balancing rules.
In this paper we identify novel diffusion approximation and timescale
separation that provides insights into the performance of JSQ. We calculate the
price of irrevocably dispatching jobs to servers and prove this to within 15%
(in the NDS regime) of the rules that may manoeuvre jobs between servers. We
also compare ours results for the JSQ policy with the NDS approximations of
many modern load balancing policies such as Idle-Queue-First and
Power-of--choices policies which act as low information proxies for the JSQ
policy. Our analysis leads us to construct new rules that have identical
performance to JSQ but require less communication overhead than
power-of-2-choices.Comment: Revised journal submission versio
An integrated packet/flow model for TCP performance analysis
Processor sharing (PS) models for TCP behavior nicely capture the bandwidth sharing and statistical multiplexing effect of TCP flows on the flow level. However, these ‘rough’ models do not provide insight into the impact of packet-level parameters (such as round trip time and buffer size) on, e.g., throughput and flow transfer times. This paper proposes an integrated packet/flow-level model: it exploits the advantages of PS approach on the flow level and, at the same time, it incorporates the most significant packet-level effects
Queueing networks: solutions and applications
During the pasttwo decades queueing network models have proven to be a versatile tool for computer system and computer communication system performance evaluation. This chapter provides a survey of th field with a particular emphasis on applications. We start with a brief historical retrospective which also servesto introduce the majr issues and application areas. Formal results for product form queuenig networks are reviewed with particular emphasis on the implications for computer systems modeling. Computation algorithms, sensitivity analysis and optimization techniques are among the topics covered. Many of the important applicationsof queueing networks are not amenableto exact analysis and an (often confusing) array of approximation methods have been developed over the years. A taxonomy of approximation methods is given and used as the basis for for surveing the major approximation methods that have been studied. The application of queueing network to a number of areas is surveyed, including computer system cpacity planning, packet switching networks, parallel processing, database systems and availability modeling.Durante as últimas duas décadas modelos de redes de filas provaram ser uma ferramenta versátil para avaliação de desempenho de sistemas de computação e sistemas de comunicação. Este capítulo faz um apanhado geral da área, com ênfase em aplicações. Começamos com uma breve retrospectiva histórica que serve também para introduzir os pontos mais importantes e as áreas de aplicação. Resultados formais para redes de filas em forma de produto são revisados com ênfase na modelagem de sistemas de computação. Algoritmos de computação, análise de sensibilidade e técnicas de otimização estão entre os tópicos revistos. Muitas dentre importantes aplicações de redes de filas não são tratáveis por análise exata e uma série (frequentemente confusa) de métodos de aproximação tem sido desenvolvida. Uma taxonomia de métodos de aproximação é dada e usada como base para revisão dos mais importantes métodos de aproximação propostos. Uma revisão das aplicações de redes de filas em um número de áreas é feita, incluindo planejamento de capacidade de sistemas de computação, redes de comunicação por chaveamento de pacotes, processamento paralelo, sistemas de bancos de dados e modelagem de confiabilidade
Scheduling for a Processor Sharing System with Linear Slowdown
We consider the problem of scheduling arrivals to a congestion system with a
finite number of users having identical deterministic demand sizes. The
congestion is of the processor sharing type in the sense that all users in the
system at any given time are served simultaneously. However, in contrast to
classical processor sharing congestion models, the processing slowdown is
proportional to the number of users in the system at any time. That is, the
rate of service experienced by all users is linearly decreasing with the number
of users. For each user there is an ideal departure time (due date). A
centralized scheduling goal is then to select arrival times so as to minimize
the total penalty due to deviations from ideal times weighted with sojourn
times. Each deviation is assumed quadratic, or more generally convex. But due
to the dynamics of the system, the scheduling objective function is non-convex.
Specifically, the system objective function is a non-smooth piecewise convex
function. Nevertheless, we are able to leverage the structure of the problem to
derive an algorithm that finds the global optimum in a (large but) finite
number of steps, each involving the solution of a constrained convex program.
Further, we put forward several heuristics. The first is the traversal of
neighbouring constrained convex programming problems, that is guaranteed to
reach a local minimum of the centralized problem. This is a form of a "local
search", where we use the problem structure in a novel manner. The second is a
one-coordinate "global search", used in coordinate pivot iteration. We then
merge these two heuristics into a unified "local-global" heuristic, and
numerically illustrate the effectiveness of this heuristic
- …