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Applications of Control Theory to Computer Systems Optimization
Full text linkComputer systems complexity is growing rapidly, thus making the efficient
use of their resources an increasingly challenging task. In many cases the
optimization of the management in such systems has been developed with
ad-hoc techniques and heuristics.
In this thesis, a more general and flexible approach is explored to resource
management, based on the powerful framework of stochastic optimal control.
This approach requires a careful modeling of the system of interest as a
dynamical system with appropriate cost functions and stochastic descriptions
of the inputs that are imposed by the external environment. Then, the
question of an optimal management policy that minimizes the expected cost
becomes mathematically well posed and can be systematically investigated.
Two cases studies illustrating the approach are developed, as summarized
below.
In Chapters 1–5, the classical replacement problem for memory hierarchies
is cast within the framework of optimal control theory. Memory references
are assumed to comply with the Least Recently Used Stack Model
(LRUSM); arbitrary stack-distance distributions are considered.
An optimal policy is derived to minimize the miss rate for an infinite trace
(a control over an infinite horizon). We call it a K-L policy where K(C)
and L(C) are parameters, whose value is a function of the buffer (cache)
size C, determined by the stack-distance distribution. Then, the concept of
Least Profit Rate (LPR) policy is introduced and it is shown that, for the
LRUSM model, LPR is an optimal policy over an infinite horizon which, in
steady state, coincides with the K-L policy. The LPR satisfies the inclusion
property whereby the content of a given buffer is also contained in all larger
buffers. This property is known to enable the efficient computation of the
number of misses for a given address trace, simultaneously for all buffer sizes.
Furthermore, the LPR formulation leads to a linear time computation of the
values K(C) and L(C) for all relevant values of C, improving on the cubic
bound that naturally arises within the K-L derivation. Furthermore, the
properties of LPR are exploited to derive an efficient algorithm to optimally
partition a buffer concurrently accessed by multiple processes. Finally, the
miss rate of LPR is compared with that of OPT, the well-known optimal
off-line policy, to investigate the difference between an exact and a statistical
knowledge of the future of the trace.
Obtaining a closed form characterization of the optimal replacement policy
over a finite horizon has proved to be rather more difficult than over the
infinite horizon. The problem has been solved for monotone stack-distance
distributions. Separate arguments establish the optimality of the Least
Recently Used (LRU) policy for all nonincreasing distributions and of the Most
Recently Used (MRU) policy for all nondecreasing distributions. Interestingly,
LRU and MRU are special cases of LPR, within the LRUSM model,
for nonincreasing and non decreasing distributions, respectively. The results
have been obtained by introducing a significant variant of the standard Bellman’s
equation, potentially useful for other control problems.
In Chapters 6–7 it is studied the problem of processors allocation for the
Galois System, a tool for automatically parallelizing, by means of speculative
execution, algorithms that present data amorphous parallelism. The Galois
System is modeled using graph-theoretic concepts and the optimization goal
is identified in trying to maximize the parallelism, while keeping a constant
conflict ratio. This is linked to a function for which we analytically derive
some properties that are then used to design an algorithm that controls the
number of processors in a quick and stable way. For this purpose an extension
to the well known Turán’s theorem is developed.La complessità dei sistemi informatici sta crescendo rapidamente, rendendo
l’uso efficiente delle loro risorse un compito sempre piú proibitivo. In molti
casi la gestione ottimizzata di questi sistemi è stata sviluppata con tecniche
ad-hoc ed euristiche.
In questa tesi viene esplorato un approccio piú generale e flessibile alla
gestione delle risorse, fondato sul potente quadro teorico del controllo ottimo
stocastico. Questo approccio richiede un’attenta modellizzazione del sistema
di interesse come sistema dinamico, con appropriate funzioni di costo e descrizioni
stocastiche degli ingressi imposti dall’ambiente esterno. A questo punto
la ricerca di una politica di gestione ottima che minimizzi il costo aspettato è
matematicamente ben posta e può essere risolta sistematicamente. Vengono
sviluppati due casi di studio, come riassunto di seguito.
Nei Capitoli 1–5 il classico problema di sostituzione (replacement) per le
gerarchie di memoria viene formulato nel quadro della teoria del controllo
ottimo. Si assume che i riferimenti di memoria rispettino il Least Recently
Used Stack Model (LRUSM) e vengono considerate distribuzioni arbitrarie
sullo stack.
Una politica ottima per minimizzare il tasso di miss (accessi fuori dal
buffer) per una traccia di lunghezza infinita viene derivata e chiamata K-L,
dove K(C) ed L(C) sono parametri il cui valore è un funzione, determinata
dalla distribuzione di accessi allo stack, della taglia C del buffer. In seguito
viene introdotto il concetto di politica a tasso di profitto minimo (Least Profit
Rate – LPR) e si dimostra che, nell’LRUSM, LPR è una politica ottima
su orizzonte infinito che, allo stato stazionario, coincide con la politica K-L.
LPR soddisfa la proprietà di inclusione: i contenuti di buffer di dimensione
minore sono inclusi in quelli maggiori. Questa proprietà consente di calcolare
efficientemente il numero di miss per una data traccia in contemporanea per
tutte le taglie del buffer. Inoltre le proprietà della LPR vengono sfruttate
per derivare un efficiente algoritmo di partizionamento per buffer condivisi
concorrentemente fra piú processi. Infine il tasso di miss di LPR viene confrontato
con quello di OPT, la nota politica ottima off-line, per indagare la
differenza fra una conoscenza esatta e una statistica del futuro della traccia.
Ottenere una forma chiusa per la politica di sostituzione su orizzonte
finito si è dimostrato un problema ben piú difficile che su orizzonte infinito,
ed è stato risolto nel caso di distribuzioni di accesso monotone. Argomenti
diversi dimostrano rispettivamente l’ottimalità della politica Least Recently
Used (LRU) per distribuzioni non crescenti e quella di Most Recently Used
(MRU) per distribuzioni non decrescenti. I risultati sono stati ottenuti grazie
all’introduzione di una significativa variante dell’usuale equazione di Bellman,
potenzialmente utile in altri problemi di controllo.
Nei Capitolo 6–7 viene studiato il problema dell’allocazione dei processori
nel sistema Galois, uno strumento per la parallelizzazione automatica,
per mezzo di esecuzione ottimistica (speculative execution), di algoritmi che
presentino un cosiddetto parallelismo amorfo sui dati (data amorphous parallelism).
Il sistema Galois viene modellizzato tramite concetti di teoria dei
grafi e l’obiettivo dell’ottimizzazione è identificato nella massimizzazione del
parallelismo col vincolo di mantenere basso il tasso di conflitti. Questo viene
collegato ad una funzione, per cui vengono analiticamente derivate alcune
proprietà che sono poi usate nella progettazione di un algoritmo capace di
controllare il numero di processori in maniera stabile e veloce. A tal fine
viene sviluppata un’estensione del noto teorema di Turán
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Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
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