2,318 research outputs found
Rare-event analysis of mixed Poisson random variables, and applications in staffing
A common assumption when modeling queuing systems is that arrivals behave
like a Poisson process with constant parameter. In practice, however, call
arrivals are often observed to be significantly overdispersed. This motivates
that in this paper we consider a mixed Poisson arrival process with arrival
rates that are resampled every time units, where and a
scaling parameter. In the first part of the paper we analyse the asymptotic
tail distribution of this doubly stochastic arrival process. That is, for large
and i.i.d. arrival rates , we focus on the evaluation of
, the probability that the scaled number of arrivals exceeds .
Relying on elementary techniques, we derive the exact asymptotics of :
For we identify (in closed-form) a function
such that tends to as .
For and we find a partial
solution in terms of an asymptotic lower bound. For the special case that the
s are gamma distributed, we establish the exact asymptotics across all . In addition, we set up an asymptotically efficient importance sampling
procedure that produces reliable estimates at low computational cost. The
second part of the paper considers an infinite-server queue assumed to be fed
by such a mixed Poisson arrival process. Applying a scaling similar to the one
in the definition of , we focus on the asymptotics of the probability
that the number of clients in the system exceeds . The resulting
approximations can be useful in the context of staffing. Our numerical
experiments show that, astoundingly, the required staffing level can actually
decrease when service times are more variable
Scaling limits for infinite-server systems in a random environment
This paper studies the effect of an overdispersed arrival process on the
performance of an infinite-server system. In our setup, a random environment is
modeled by drawing an arrival rate from a given distribution every
time units, yielding an i.i.d. sequence of arrival rates
. Applying a martingale central limit theorem, we
obtain a functional central limit theorem for the scaled queue length process.
We proceed to large deviations and derive the logarithmic asymptotics of the
queue length's tail probabilities. As it turns out, in a rapidly changing
environment (i.e., is small relative to ) the overdispersion
of the arrival process hardly affects system behavior, whereas in a slowly
changing random environment it is fundamentally different; this general finding
applies to both the central limit and the large deviations regime. We extend
our results to the setting where each arrival creates a job in multiple
infinite-server queues
Malware in the Future? Forecasting of Analyst Detection of Cyber Events
There have been extensive efforts in government, academia, and industry to
anticipate, forecast, and mitigate cyber attacks. A common approach is
time-series forecasting of cyber attacks based on data from network telescopes,
honeypots, and automated intrusion detection/prevention systems. This research
has uncovered key insights such as systematicity in cyber attacks. Here, we
propose an alternate perspective of this problem by performing forecasting of
attacks that are analyst-detected and -verified occurrences of malware. We call
these instances of malware cyber event data. Specifically, our dataset was
analyst-detected incidents from a large operational Computer Security Service
Provider (CSSP) for the U.S. Department of Defense, which rarely relies only on
automated systems. Our data set consists of weekly counts of cyber events over
approximately seven years. Since all cyber events were validated by analysts,
our dataset is unlikely to have false positives which are often endemic in
other sources of data. Further, the higher-quality data could be used for a
number for resource allocation, estimation of security resources, and the
development of effective risk-management strategies. We used a Bayesian State
Space Model for forecasting and found that events one week ahead could be
predicted. To quantify bursts, we used a Markov model. Our findings of
systematicity in analyst-detected cyber attacks are consistent with previous
work using other sources. The advanced information provided by a forecast may
help with threat awareness by providing a probable value and range for future
cyber events one week ahead. Other potential applications for cyber event
forecasting include proactive allocation of resources and capabilities for
cyber defense (e.g., analyst staffing and sensor configuration) in CSSPs.
Enhanced threat awareness may improve cybersecurity.Comment: Revised version resubmitted to journa
Exact asymptotics in an infinite-server system with overdispersed input
This short communication considers an infinite-server system with
overdispersed input. The objective is to identify the exact tail asymptotics of
the number of customers present at a given point in time under a specific
scaling of the model (which involves both the arrival rate and time). The
proofs rely on a change-of-measure approach. The results obtained are
illustrated by a series of examples.Comment: Short communicatio
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the TakĂĄcs Award for outstanding PhD thesis on "Queueing Theory and its Applications"
High-Dimensional Fixed Effects Profiling Models and Applications in End-Stage Kidney Disease Patients: Current State and Future Directions
Profiling analysis aims to evaluate health care providers, including hospitals, nursing homes, or dialysis facilities among others with respect to a patient outcome, such as 30-day unplanned hospital readmission or mortality. Fixed effects (FE) profiling models have been developed over the last decade, motivated by the overall need to (a) improve accurate identification or âflaggingâ of under-performing providers, (b) relax assumptions inherent in random effects (RE) profiling models, and (c) take into consideration the unique disease characteristics and care/treatment processes of end-stage kidney disease (ESKD) patients on dialysis. In this paper, we review the current state of FE methodologies and their rationale in the ESKD population and illustrate applications in four key areas: profiling dialysis facilities for (1) patient hospitalizations over time (longitudinally) using standardized dynamic readmission ratio (SDRR), (2) identification of dialysis facility characteristics (e.g., staffing level) that contribute to hospital readmission, and (3) adverse recurrent events using standardized event ratio (SER). Also, we examine the operating characteristics with a focus on FE profiling models. Throughout these areas of applications to the ESKD population, we identify challenges for future research in both methodology and clinical studies
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