The Waiting Time Distribution of a Pareto Service Self-Similar Queuing Model for Wireless Network Nodes

2006 ◽  
Author(s):  
Sheng Xu ◽  
Bugong Xu ◽  
Dazhou Peng
Keyword(s):  
Wireless Network ◽  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Queuing Model ◽  
Network Nodes ◽  
Self Similar

scholarly journals Queuing models of gene expression: Analytical distributions and beyond

2020 ◽  
Author(s):  
C. Shi ◽  
Y. Jiang ◽  
T. Zhou
Keyword(s):  
Gene Expression ◽  
Waiting Time ◽  
Time Distribution ◽  
Biochemical Process ◽  
Waiting Time Distribution ◽  
Molecular Memory ◽  
Queuing Model ◽  
Analytical Expression ◽  
Intermediate Reaction ◽  
Insight Into

ABSTRACTActivation of a gene is a multistep biochemical process, involving recruitments of transcription factors and histone kinases as well as modification of histones. Many of these intermediate reaction steps would have been unspecified by experiments. Therefore, classical two-state models of gene expression established based on the memoryless (or Markovian) assumption would not well describe the reality in gene expression. In fact, recent experimental data have indicated that the inactive phases of gene promoters are differently distributed, showing strong memory. Here, we use a non-exponential waiting-time distribution to model the complex activation process of a gene, and analyze a queuing model of stochastic transcription. We successfully derive the analytical expression for the mRNA distribution, which provides insight into the effect of molecular memory created by complex activating events on the mRNA expression. We find that the reduction in the waiting-time noise may result in the increase in the mRNA noise, contrary to the previous conclusion. Based on the derived distribution, we also develop a method to infer the waiting-time distribution from a known mRNA distribution. Data analysis on a realistic example verifies the validity of this method.SIGNIFICANCEActivation of a gene is a complex biochemical process and involve several intermediate reaction steps, many of which have been unspecified by experiments. Stochastic models of gene expression that were previously established based on the constant reaction rates would not well reflect the reality in gene expression. To this end, we study a queuing model of stochastic transcription which assume that the reaction waiting time follows a general distribution and derive the analytical expression for mRNA distribution. Our results provide insight into the role of molecular memory in fine-tuning the gene expression noise, and can be used to infer the underlying molecular mechanism.

Some analyses on the control of queues using level crossings of regenerative processes

1980 ◽  
Vol 17 (3) ◽  
pp. 814-821 ◽  
Author(s):  
J. G. Shanthikumar
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Queueing Systems ◽  
Density Functions ◽  
Waiting Time Distribution ◽  
Regenerative Processes ◽  
Stieltjes Transform ◽  
Expected Number ◽  
Control Of Queues ◽  
Special Case

Some properties of the number of up- and downcrossings over level u, in a special case of regenerative processes are discussed. Two basic relations between the density functions and the expected number of upcrossings of this process are derived. Using these reults, two examples of controlled M/G/1 queueing systems are solved. Simple relations are derived for the waiting time distribution conditioned on the phase of control encountered by an arriving customer. The Laplace-Stieltjes transform of the distribution function of the waiting time of an arbitrary customer is also derived for each of these two examples.

scholarly journals Role of the Solar Minimum in the Waiting Time Distribution Throughout the Heliosphere

2021 ◽  
Author(s):  
Yosia I Nurhan ◽  
Jay Robert Johnson ◽  
Jonathan R Homan ◽  
Simon Wing
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Solar Minimum ◽  
Waiting Time Distribution

CONTINUOUS-TIME FINANCE AND THE WAITING TIME DISTRIBUTION: MULTIPLE CHARACTERISTIC TIMES

2012 ◽  
Vol 26 (23) ◽  
pp. 1250151 ◽  
Author(s):  
KWOK SAU FA
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Waiting Time ◽  
Continuous Time ◽  
Probability Distribution Function ◽  
Time Distribution ◽  
Waiting Time Distribution ◽  
Exponential Functions ◽  
Multiple Characteristic ◽  
Sum Of Products

In this paper, we model the tick-by-tick dynamics of markets by using the continuous-time random walk (CTRW) model. We employ a sum of products of power law and stretched exponential functions for the waiting time probability distribution function; this function can fit well the waiting time distribution for BUND futures traded at LIFFE in 1997.

Part Waiting Time Distribution in a Two-Machine Line

2012 ◽  
Vol 45 (6) ◽  
pp. 457-462 ◽  
Author(s):  
Chuan Shi ◽  
Stanley B. Gershwin
Keyword(s):  
Waiting Time ◽  
Time Distribution ◽  
Waiting Time Distribution
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