scholarly journals Rare events of transitory queues

2017 ◽  
Vol 54 (3) ◽  
pp. 943-962
Author(s):  
Harsha Honnappa
Keyword(s):  
Rare Events ◽  
Rare Event ◽  
Random Variables ◽  
General Distribution ◽  
Diffusion Approximations ◽  
Large Deviations Principle ◽  
Exponential Random Variables ◽  
Service Times ◽  
Ordered Statistics ◽  
And Diffusion

AbstractWe study the rare-event behavior of the workload process in a transitory queue, where the arrival epochs (or 'points') of a finite number of jobs are assumed to be the ordered statistics of independent and identically distributed (i.i.d.) random variables. The service times (or 'marks') of the jobs are assumed to be i.i.d. random variables with a general distribution, that are jointly independent of the arrival epochs. Under the assumption that the service times are strictly positive, we derive the large deviations principle (LDP) satisfied by the workload process. The analysis leverages the connection between ordered statistics and self-normalized sums of exponential random variables to establish the LDP. In this paper we present the first analysis of rare events in transitory queueing models, supplementing prior work that has focused on fluid and diffusion approximations.

scholarly journals Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times

2021 ◽  
Author(s):  
Dennis Schol ◽  
Maria Vlasiou ◽  
Bert Zwart
Keyword(s):  
Extreme Value Theory ◽  
Queue Length ◽  
Value Theory ◽  
Initial Number ◽  
Diffusion Approximations ◽  
Fluid Limit ◽  
Maximum Queue Length ◽  
Queue Lengths ◽  
Service Times ◽  
And Diffusion

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as [Formula: see text]. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.

scholarly journals Admission controls for Erlang's loss system with service times distributed as a finite sum of exponential random variables

1998 ◽  
Vol 2 (2) ◽  
pp. 119-132 ◽  
Author(s):  
Brian Moretta ◽  
Ilze Ziedins
Keyword(s):  
Optimal Policy ◽  
Random Variables ◽  
Loss System ◽  
Standard Assumption ◽  
Threshold Policy ◽  
Exponential Random Variables ◽  
Reservation Policy ◽  
Service Times ◽  
Trunk Reservation ◽  
Finite Sum

It is known that a threshold policy (or trunk reservation policy) is optimal for Erlang’s loss system under certain assumptions. In this paper we examine the robustness of this policy under departures from the standard assumption of exponential service times (call holding times) and give examples where the optimal policy has a generalized trunk reservation form.

Framework for rare event detection using Artificial Neural Network based context free grammar

2020 ◽  
Vol 39 (6) ◽  
pp. 8463-8475
Author(s):  
Palanivel Srinivasan ◽  
Manivannan Doraipandian
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Event Detection ◽  
Performance Metrics ◽  
Rare Events ◽  
Rare Event ◽  
Video Stream ◽  
Context Free Grammar ◽  
Artificial Neural ◽  
Context Free

Rare event detections are performed using spatial domain and frequency domain-based procedures. Omnipresent surveillance camera footages are increasing exponentially due course the time. Monitoring all the events manually is an insignificant and more time-consuming process. Therefore, an automated rare event detection contrivance is required to make this process manageable. In this work, a Context-Free Grammar (CFG) is developed for detecting rare events from a video stream and Artificial Neural Network (ANN) is used to train CFG. A set of dedicated algorithms are used to perform frame split process, edge detection, background subtraction and convert the processed data into CFG. The developed CFG is converted into nodes and edges to form a graph. The graph is given to the input layer of an ANN to classify normal and rare event classes. Graph derived from CFG using input video stream is used to train ANN Further the performance of developed Artificial Neural Network Based Context-Free Grammar – Rare Event Detection (ACFG-RED) is compared with other existing techniques and performance metrics such as accuracy, precision, sensitivity, recall, average processing time and average processing power are used for performance estimation and analyzed. Better performance metrics values have been observed for the ANN-CFG model compared with other techniques. The developed model will provide a better solution in detecting rare events using video streams.

scholarly journals Interspecies Chromosome Mapping in Caprimulgiformes, Piciformes, Suliformes, and Trogoniformes (Aves): Cytogenomic Insight into Microchromosome Organization and Karyotype Evolution in Birds

Cells ◽  
2021 ◽  
Vol 10 (4) ◽  
pp. 826
Author(s):  
Rafael Kretschmer ◽  
Marcelo Santos de Souza ◽  
Ivanete de Oliveira Furo ◽  
Michael N. Romanov ◽  
Ricardo José Gunski ◽  
...  
Keyword(s):  
Convergent Evolution ◽  
Karyotype Evolution ◽  
Rare Events ◽  
Rare Event ◽  
Chromosome Mapping ◽  
The Other ◽  
Other Hand ◽  
Interchromosomal Rearrangement ◽  
Insight Into ◽  
Phalacrocorax Brasilianus

Interchromosomal rearrangements involving microchromosomes are rare events in birds. To date, they have been found mostly in Psittaciformes, Falconiformes, and Cuculiformes, although only a few orders have been analyzed. Hence, cytogenomic studies focusing on microchromosomes in species belonging to different bird orders are essential to shed more light on the avian chromosome and karyotype evolution. Based on this, we performed a comparative chromosome mapping for chicken microchromosomes 10 to 28 using interspecies BAC-based FISH hybridization in five species, representing four Neoaves orders (Caprimulgiformes, Piciformes, Suliformes, and Trogoniformes). Our results suggest that the ancestral microchromosomal syntenies are conserved in Pteroglossus inscriptus (Piciformes), Ramphastos tucanus tucanus (Piciformes), and Trogon surrucura surrucura (Trogoniformes). On the other hand, chromosome reorganization in Phalacrocorax brasilianus (Suliformes) and Hydropsalis torquata (Caprimulgiformes) included fusions involving both macro- and microchromosomes. Fissions in macrochromosomes were observed in P. brasilianus and H. torquata. Relevant hypothetical Neognathae and Neoaves ancestral karyotypes were reconstructed to trace these rearrangements. We found no interchromosomal rearrangement involving microchromosomes to be shared between avian orders where rearrangements were detected. Our findings suggest that convergent evolution involving microchromosomal change is a rare event in birds and may be appropriate in cytotaxonomic inferences in orders where these rearrangements occurred.

scholarly journals Improving the Asmussen–Kroese-Type Simulation Estimators

2012 ◽  
Vol 49 (4) ◽  
pp. 1188-1193 ◽  
Author(s):  
Samim Ghamami ◽  
Sheldon M. Ross
Keyword(s):  
Monte Carlo ◽  
Nonnegative Integer ◽  
Rare Event ◽  
Random Variables ◽  
Random Variable ◽  
Heavy Tailed ◽  
Independent Identically Distributed

The Asmussen–Kroese Monte Carlo estimators of P(Sn > u) and P(SN > u) are known to work well in rare event settings, where SN is the sum of independent, identically distributed heavy-tailed random variables X1,…,XN and N is a nonnegative, integer-valued random variable independent of the Xi. In this paper we show how to improve the Asmussen–Kroese estimators of both probabilities when the Xi are nonnegative. We also apply our ideas to estimate the quantity E[(SN-u)+].

scholarly journals Distribution of Minimal Path Lengths when Edge Lengths are Independent Heterogeneous Exponential Random Variables

2012 ◽  
Vol 49 (3) ◽  
pp. 895-900
Author(s):  
Sheldon M. Ross
Keyword(s):  
Joint Distribution ◽  
Shortest Paths ◽  
Random Variables ◽  
Simulated Data ◽  
Minimal Path ◽  
Exponential Random Variables ◽  
Path Lengths

We find the joint distribution of the lengths of the shortest paths from a specified node to all other nodes in a network in which the edge lengths are assumed to be independent heterogeneous exponential random variables. We also give an efficient way to simulate these lengths that requires only one generated exponential per node, as well as efficient procedures to use the simulated data to estimate quantities of the joint distribution.

scholarly journals Uniform renewal theory with applications to expansions of random geometric sums

2007 ◽  
Vol 39 (4) ◽  
pp. 1070-1097 ◽  
Author(s):  
J. Blanchet ◽  
P. Glynn
Keyword(s):  
Asymptotic Expansion ◽  
Asymptotic Expansions ◽  
Random Variables ◽  
Renewal Theory ◽  
Random Variable ◽  
Higher Order ◽  
Order Correction ◽  
Diffusion Approximations ◽  
Geometric Sums ◽  
Correction Terms

Consider a sequence X = (Xn: n ≥ 1) of independent and identically distributed random variables, and an independent geometrically distributed random variable M with parameter p. The random variable SM = X1 + ∙ ∙ ∙ + XM is called a geometric sum. In this paper we obtain asymptotic expansions for the distribution of SM as p ↘ 0. If EX1 > 0, the asymptotic expansion is developed in powers of p and it provides higher-order correction terms to Renyi's theorem, which states that P(pSM > x) ≈ exp(-x/EX1). Conversely, if EX1 = 0 then the expansion is given in powers of √p. We apply the results to obtain corrected diffusion approximations for the M/G/1 queue. These expansions follow in a unified way as a consequence of new uniform renewal theory results that are also developed in this paper.

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