scholarly journals Overflow behavior in queues with many long-tailed inputs

2000 ◽  
Vol 32 (4) ◽  
pp. 1150-1167 ◽  
Author(s):  
Michel Mandjes ◽  
Sem Borst
Keyword(s):  
Buffer Size ◽  
Qualitative Behavior ◽  
Input Rate ◽  
Substantial Fraction ◽  
Fluid Queue ◽  
Overflow Probability ◽  
Typical Time ◽  
Link Rate ◽  
Regularly Varying ◽  
Insight Into

We consider a fluid queue fed by the superposition of n homogeneous on-off sources with generally distributed on and off periods. The buffer space B and link rate C are scaled by n, so that we get nb and nc, respectively. Then we let n grow large. In this regime, the overflow probability decays exponentially in the number of sources n. We specifically examine the scenario where b is also large. We obtain explicit asymptotics for the case where the on periods have a subexponential distribution, e.g., Pareto, Lognormal, or Weibull.The results show a sharp dichotomy in the qualitative behavior, depending on the shape of the function v(t) := - logP(A* > t) for large t, A* representing the residual on period. If v(.) is regularly varying of index 0 (e.g., Pareto, Lognormal), then, during the path to overflow, the input rate will only slightly exceed the link rate. Consequently, the buffer will fill ‘slowly’, and the typical time to overflow will be ‘more than linear’ in the buffer size. In contrast, if v(.) is regularly varying of index strictly between 0 and 1 (e.g., Weibull), then the input rate will significantly exceed the link rate, and the time to overflow is roughly proportional to the buffer size.In both cases there is a substantial fraction of the sources that remain in the on state during the entire path to overflow, while the others contribute at their mean rates. These observations lead to approximations for the overflow probability. The approximations may be extended to the case of heterogeneous sources. The results provide further insight into the so-called reduced-load approximation.

scholarly journals Fluid queues driven by anM/M/1/Nqueue

2000 ◽  
Vol 6 (5) ◽  
pp. 439-460 ◽  
Author(s):  
R. B. Lenin ◽  
P. R. Parthasarathy
Keyword(s):  
Distribution Function ◽  
Buffer Capacity ◽  
Input Rate ◽  
Fluid Queue ◽  
Buffer Occupancy ◽  
Fluid Queues ◽  
Markovian Queue ◽  
Service Rates ◽  
Queue Model ◽  
Number Of Customers

In this paper, we consider fluid queue models with infinite buffer capacity which receives and releases fluid at variable rates in such a way that the net input rate of fluid into the buffer (which is negative when fluid is flowing out of the buffer) is uniquely determined by the number of customers in anM/M/1/Nqueue model (that is, the fluid queue is driven by this Markovian queue) with constant arrival and service rates. We use some interesting identities of tridiagonal determinants to find analytically the eigenvalues of the underlying tridiagonal matrix and hence the distribution function of the buffer occupancy. For specific cases, we verify the results available in the literature.

Markov-renewal fluid queues

2004 ◽  
Vol 41 (3) ◽  
pp. 746-757 ◽  
Author(s):  
Guy Latouche ◽  
Tetsuya Takine
Keyword(s):  
Markov Process ◽  
Exponential Distribution ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Input Rate ◽  
Fluid Queue ◽  
Birth And Death Processes ◽  
Fluid Queues ◽  
Semi Markov Process ◽  
Semi Markov Processes

We consider a fluid queue controlled by a semi-Markov process and we apply the Markov-renewal approach developed earlier in the context of quasi-birth-and-death processes and of Markovian fluid queues. We analyze two subfamilies of semi-Markov processes. In the first family, we assume that the intervals during which the input rate is negative have an exponential distribution. In the second family, we take the complementary case and assume that the intervals during which the input rate is positive have an exponential distribution. We thoroughly characterize the structure of the stationary distribution in both cases.

scholarly journals A fluid queue with a finite buffer and subexponential input

2000 ◽  
Vol 32 (1) ◽  
pp. 221-243 ◽  
Author(s):  
A. P. Zwart
Keyword(s):  
Stationary Distribution ◽  
Fluid Model ◽  
Buffer Size ◽  
Finite Buffer ◽  
Asymptotic Results ◽  
Fluid Queue ◽  
Buffer Content ◽  
The Mean ◽  
Heavy Tailed ◽  
Finite Dam

We consider a fluid model similar to that of Kella and Whitt [32], but with a buffer having finite capacity K. The connections between the infinite buffer fluid model and the G/G/1 queue established by Kella and Whitt are extended to the finite buffer case: it is shown that the stationary distribution of the buffer content is related to the stationary distribution of the finite dam. We also derive a number of new results for the latter model. In particular, an asymptotic expansion for the loss fraction is given for the case of subexponential service times. The stationary buffer content distribution of the fluid model is also related to that of the corresponding model with infinite buffer size, by showing that the two corresponding probability measures are proportional on [0,K) if the silence periods are exponentially distributed. These results are applied to obtain large buffer asymptotics for the loss fraction and the mean buffer content when the fluid queue is fed by N On-Off sources with subexponential on-periods. The asymptotic results show a significant influence of heavy-tailed input characteristics on the performance of the fluid queue.

scholarly journals Busy periods in fluid queues with multiple emptying input states

2010 ◽  
Vol 47 (2) ◽  
pp. 474-497 ◽  
Author(s):  
A. J. Field ◽  
P. G. Harrison
Keyword(s):  
Busy Period ◽  
Arrival Rate ◽  
Random Variable ◽  
Input Rate ◽  
Output Rate ◽  
Fluid Queue ◽  
Fluid Queues ◽  
The Laplace Transform ◽  
Constant Output ◽  
Positive Input

A semi-numerical method is derived to compute the Laplace transform of the equilibrium busy period probability density function in a fluid queue with constant output rate when the buffer is nonempty. The input process is controlled by a continuous-time semi-Markov chain (CTSMC) with n states such that in each state the input rate is constant. The holding time in states with net positive output rate - so-called emptying states - is assumed to be an exponentially distributed random variable, whereas in states with net positive input rate - so-called filling states - it may have an arbitrary probability distribution. The result is demonstrated by applying it to various systems, including fluid queues with two on-off input sources. The latter exercise in part shows consistency with prior results but also solves the problem in the case where there are two emptying states. Numerical results are presented for selected examples which expose discontinuities in the busy period distribution when the number of emptying states changes, e.g. as a result of increasing the fluid arrival rate in one or more states of the controlling CTSMC.

Application of Harmonic Wavelet Analysis to Soil Motion Data

2001 ◽  
Author(s):  
Berrak Teymur ◽  
S. P. Gopal Madabhushi
Keyword(s):  
Wavelet Analysis ◽  
Centrifuge Modeling ◽  
Complex Data ◽  
Time Frequency ◽  
Motion Data ◽  
Signal Features ◽  
Typical Time ◽  
Harmonic Wavelet ◽  
Shear Beam ◽  
Insight Into

Abstract This paper presents techniques which employ frequency response and wavelet analysis to identify damage in soils. Experimental data is obtained by dynamic centrifuge modeling. Dynamic centrifuge model experiments generate complex data. Harmonic wavelet analysis provides a good way to analyse them. In this paper the experimental technique will be explained along with typical time-frequency maps. With harmonic wavelet analysis, the signal features that cannot be observed from classical Fourier analysis were seen. Harmonic wavelet analysis provide a new insight into the boundary effects in the Equivalent Shear Beam (ESB) model container used in the experimental work.

Markov-renewal fluid queues

2004 ◽  
Vol 41 (03) ◽  
pp. 746-757
Author(s):  
Guy Latouche ◽  
Tetsuya Takine
Keyword(s):  
Markov Process ◽  
Exponential Distribution ◽  
Stationary Distribution ◽  
Markov Processes ◽  
Input Rate ◽  
Fluid Queue ◽  
Birth And Death Processes ◽  
Fluid Queues ◽  
Semi Markov Process ◽  
Semi Markov Processes

We consider a fluid queue controlled by a semi-Markov process and we apply the Markov-renewal approach developed earlier in the context of quasi-birth-and-death processes and of Markovian fluid queues. We analyze two subfamilies of semi-Markov processes. In the first family, we assume that the intervals during which the input rate is negative have an exponential distribution. In the second family, we take the complementary case and assume that the intervals during which the input rate is positive have an exponential distribution. We thoroughly characterize the structure of the stationary distribution in both cases.

scholarly journals easyCLIP Quantifies RNA-Protein Interactions and Characterizes Recurrent PCBP1 Mutations in Cancer

2019 ◽  
Author(s):  
Douglas F. Porter ◽  
Paul A. Khavari
Keyword(s):  
Protein Interactions ◽  
Rna Binding ◽  
Cellular Protein ◽  
Good Efficiency ◽  
Cellular Processes ◽  
Simple Protocol ◽  
Link Rate ◽  
Cross Links ◽  
Rna Interaction ◽  
Insight Into

ABSTRACTRNA-protein interactions mediate a host of cellular processes, underscoring the need for methods to quantify their occurrence in living cells. RNA interaction frequencies for the average cellular protein are undefined, however, and there is no quantitative threshold to define a protein as an RNA-binding protein (RBP). Ultraviolet (UV) cross-linking immunoprecipitation (CLIP)-sequencing, an effective and widely used means of characterizing RNA-protein interactions, would particularly benefit from the capacity to quantitate the number of RNA cross-links per protein per cell. In addition, CLIP-seq methods are difficult, have high experimental failure rates and many ambiguous analytical decisions. To address these issues, the easyCLIP method was developed and used to quantify RNA-protein interactions for a panel of known RBPs as well as a spectrum of random non-RBP proteins. easyCLIP provides the advantages of good efficiency compared to current standards, a simple protocol with a very low failure rate, troubleshooting information that includes direct visualization of prepared libraries without amplification, and a new form of analysis. easyCLIP, which uses sequential on-bead ligation of 5’ and 3’ adapters tagged with different infrared dyes, classified non-RBPs as those with a per protein RNA cross-link rate of <0.1%, with most RBPs substantially above this threshold, including Rbfox1 (18%), hnRNPC (22%), CELF1 (11%), FBL (2%), and STAU1 (1%). easyCLIP with the PCBP1L100 RBP mutant recurrently seen in cancer quantified increased RNA binding compared to wild-type PCBP1 and suggested a potential mechanism for this RBP mutant in cancer. easyCLIP provides a simple, efficient and robust method to both obtain both traditional CLIP-seq information and to define actual RNA interaction frequencies for a given protein, enabling quantitative cross-RBP comparisons as well as insight into RBP mechanisms.

scholarly journals FAST SIMULATION OF A QUEUE FED BY A SUPERPOSITION OF MANY (HEAVY-TAILED) SOURCES

2002 ◽  
Vol 16 (2) ◽  
pp. 205-232 ◽  
Author(s):  
Nam Kyoo Boots ◽  
Michel Mandjes
Keyword(s):  
Short Range ◽  
Fast Simulation ◽  
Change Of Measure ◽  
Simulation Techniques ◽  
Performance Metric ◽  
Overflow Probability ◽  
Link Rate ◽  
Heavy Tailed ◽  
Exponential Change ◽  
Optimal Change

We consider a queue fed by a large number, say n, on–off sources with generally distributed on- and off-times. The queueing resources are scaled by n: The buffer is B ≡ nb and the link rate is C ≡ nc. The model is versatile. It allows one to model both long-range-dependent traffic (by using heavy-tailed on-periods) and short-range-dependent traffic (by using light-tailed on-periods). A crucial performance metric in this model is the steady state buffer overflow probability.This probability decays exponentially in n. Therefore, if n grows large, naive simulation is too time-consuming and fast simulation techniques have to be used. Due to the exponential decay (in n), importance sampling with an exponential change of measure goes through, irrespective of the on-times being heavy or light tailed. An asymptotically optimal change of measure is found by using large deviations arguments. Notably, the change of measure is not constant during the simulation run, which is different from many other studies (usually relying on large buffer asymptotics).Numerical examples show that our procedure improves considerably over naive simulation. We present accelerations, we discuss the influence of the shape of the distributions on the overflow probability, and we describe the limitations of our technique.

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