491 research outputs found
Recommended from our members
A Robust Queueing Network Analyzer Based on Indices of Dispersion
In post-industrial economies, modern service systems are dramatically changing the daily lives of many people. Such systems are often complicated by uncertainty: service providers usually cannot predict when a customer will arrive and how long the service will be. Fortunately, useful guidance can often be provided by exploiting stochastic models such as queueing networks. In iterating the design of service systems, decision makers usually favor analytical analysis of the models over simulation methods, due to the prohibitive computation time required to obtain optimal solutions for service operation problems involving multidimensional stochastic networks. However, queueing networks that can be solved analytically require strong assumptions that are rarely satisfied, whereas realistic models that exhibit complicated dependence structure are prohibitively hard to analyze exactly.
In this thesis, we continue the effort to develop useful analytical performance approximations for the single-class open queueing network with Markovian routing, unlimited waiting space and the first-come first-served service discipline. We focus on open queueing networks where the external arrival processes are not Poisson and the service times are not exponential.
We develop a new non-parametric robust queueing algorithm for the performance approximation in single-server queues. With robust optimization techniques, the underlying stochastic processes are replaced by samples from suitably defined uncertainty sets and the worst-case scenario is analyzed. We show that this worst-case characterization of the performance measure is asymptotically exact for approximating the mean steady-state workload in G/G/1 models in both the light-traffic and heavy-traffic limits, under mild regularity conditions. In our non-parametric Robust Queueing formulation, we focus on the customer flows, defined as the continuous-time processes counting customers in or out of the network, or flowing from one queue to another. Each flow is partially characterized by a continuous function that measures the change of stochastic variability over time. This function is called the index of dispersion for counts. The Robust Queueing algorithm converts the index of dispersion for counts into approximations of the performance measures. We show the advantage of using index of dispersion for counts in queueing approximation by a renewal process characterization theorem and the ordering of the mean steady-state workload in GI/M/1 models.
To develop generalized algorithm for open queueing networks, we first establish the heavy-traffic limit theorem for the stationary departure flows from a GI/GI/1 model. We show that the index of dispersion for counts function of the stationary departure flow can be approximately characterized as the convex combination of the arrival index of dispersion for counts and service index of dispersion for counts with a time-dependent weight function, revealing the non-trivial impact of the traffic intensity on the departure processes. This heavy-traffic limit theorem is further generalized into a joint heavy-traffic limit for the stationary customer flows in generalized Jackson networks, where the external arrival are characterized by independent renewal processes and the service times are independent and identically distributed random variables, independent of the external arrival processes.
We show how these limiting theorems can be exploited to establish a set of linear equations, whose solution serves as approximations of the index of dispersion for counts of the flows in an open queueing network. We prove that this set of equations is asymptotically exact in approximating the index of dispersion for counts of the stationary flows. With the index of dispersion for counts available, the network is decomposed into single-server queues and the Robust Queueing algorithm can be applied to obtain performance approximation. This algorithm is referred to as the Robust Queueing Network Analyzer.
We perform extensive simulation study to validate the effectiveness of our algorithm. We show that our algorithm can be applied not only to models with non-exponential distirbutions but also to models with more complex arrival processes than renewal processes, including those with Markovian arrival processes
Global Sensitivity Analysis of Stochastic Computer Models with joint metamodels
The global sensitivity analysis method, used to quantify the influence of
uncertain input variables on the response variability of a numerical model, is
applicable to deterministic computer code (for which the same set of input
variables gives always the same output value). This paper proposes a global
sensitivity analysis methodology for stochastic computer code (having a
variability induced by some uncontrollable variables). The framework of the
joint modeling of the mean and dispersion of heteroscedastic data is used. To
deal with the complexity of computer experiment outputs, non parametric joint
models (based on Generalized Additive Models and Gaussian processes) are
discussed. The relevance of these new models is analyzed in terms of the
obtained variance-based sensitivity indices with two case studies. Results show
that the joint modeling approach leads accurate sensitivity index estimations
even when clear heteroscedasticity is present
Style rotation and performance persistence of mutual funds
Most academic studies on performance persistence in monthly mutual fund returns do not find evidence for timing skills of fund managers. Furthermore, realized returns are undoubtedly driven by the investment style of a fund. We propose a new holdings-based measure of style rotation to investigate the relation between performance persistence and changes in style. For a large sample of U.S. domestic equity mutual funds we find that top and bottom performing decile portfolios, sorted on past one-year returns and risk djusted excess performance from a 4-factor model, are subject to a higher degree of style rotation than middle deciles. Style inconsistent funds with high values for the style rotation measure in turn exhibit less persistence in decile rankings over subsequent years than style consistent funds. Hence, it is important for delegated portfolio management to consider style rotation when selecting managers based on past performance.mutual fund, performance persistence, style rotation.
Compound Markov counting processes and their applications to modeling infinitesimally over-dispersed systems
We propose an infinitesimal dispersion index for Markov counting processes.
We show that, under standard moment existence conditions, a process is
infinitesimally (over-) equi-dispersed if, and only if, it is simple
(compound), i.e. it increases in jumps of one (or more) unit(s), even though
infinitesimally equi-dispersed processes might be under-, equi- or
over-dispersed using previously studied indices. Compound processes arise, for
example, when introducing continuous-time white noise to the rates of simple
processes resulting in Levy-driven SDEs. We construct multivariate
infinitesimally over-dispersed compartment models and queuing networks,
suitable for applications where moment constraints inherent to simple processes
do not hold.Comment: 26 page
First-Passage Time and Large-Deviation Analysis for Erasure Channels with Memory
This article considers the performance of digital communication systems
transmitting messages over finite-state erasure channels with memory.
Information bits are protected from channel erasures using error-correcting
codes; successful receptions of codewords are acknowledged at the source
through instantaneous feedback. The primary focus of this research is on
delay-sensitive applications, codes with finite block lengths and, necessarily,
non-vanishing probabilities of decoding failure. The contribution of this
article is twofold. A methodology to compute the distribution of the time
required to empty a buffer is introduced. Based on this distribution, the mean
hitting time to an empty queue and delay-violation probabilities for specific
thresholds can be computed explicitly. The proposed techniques apply to
situations where the transmit buffer contains a predetermined number of
information bits at the onset of the data transfer. Furthermore, as additional
performance criteria, large deviation principles are obtained for the empirical
mean service time and the average packet-transmission time associated with the
communication process. This rigorous framework yields a pragmatic methodology
to select code rate and block length for the communication unit as functions of
the service requirements. Examples motivated by practical systems are provided
to further illustrate the applicability of these techniques.Comment: To appear in IEEE Transactions on Information Theor
Contributions to modelling of internet traffic by fractal renewal processes.
The principle of parsimonious modelling of Internet traffic states that a minimal
number of descriptors should be used for its characterization. Until early 1990s,
the conventional Markovian models for voice traffic had been considered suitable
and parsimonious for data traffic as well. Later with the discovery of strong
correlations and increased burstiness in Internet traffic, various self-similar count
models have been proposed. But, in fact, such models are strictly mono-fractal
and applicable at coarse time scales, whereas Internet traffic modelling is about
modelling traffic at fine and coarse time scales; modelling traffic which can be
mono and multi-fractal; modelling traffic at interarrival time and count levels;
modelling traffic at access and core tiers; and modelling all the three structural
components of Internet traffic, that is, packets, flows and sessions.
The philosophy of this thesis can be described as: “the renewal of renewal theory
in Internet traffic modelling”. Renewal theory has a great potential in modelling
statistical characteristics of Internet traffic belonging to individual users, access
and core networks. In this thesis, we develop an Internet traffic modelling
framework based on fractal renewal processes, that is, renewal processes with
underlying distribution of interarrival times being heavy-tailed. The proposed
renewal framework covers packets, flows and sessions as structural components
of Internet traffic and is applicable for modelling the traffic at fine and coarse
time scales. The properties of superposition of renewal processes can be used
to model traffic in higher tiers of the Internet hierarchy. As the framework is
based on renewal processes, therefore, Internet traffic can be modelled at both
interarrival times and count levels
- …