Exponential bounds for the waiting time distribution in Markovian queues, with applications to TES/GI/1 systems

Exponential bounds for the stationary waiting-time distribution of the type ae–θt are considered. These bounds are obtained by the use of Kingman's method of ‘integral inequalities’. Approximations of Θ and a are given which are useful especially if the service and/or inter-arrival time distribution functions are NBUE or NWUE.

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On exponential bounds for the waiting-time distribution function in GI/G/1

Journal of Applied Probability ◽

10.1017/s0021900200094535 ◽

1976 ◽

Vol 13 (02) ◽

pp. 411-417

Author(s):

R. Bergmann ◽

D. Stoyan

Keyword(s):

Distribution Function ◽

Waiting Time ◽

Time Distribution ◽

Arrival Time ◽

Distribution Functions ◽

Integral Inequalities ◽

Arrival Time Distribution ◽

Waiting Time Distribution ◽

Exponential Bounds ◽

Stationary Waiting Time

Exponential bounds for the stationary waiting-time distribution of the type ae–θt are considered. These bounds are obtained by the use of Kingman's method of ‘integral inequalities’. Approximations of Θ and a are given which are useful especially if the service and/or inter-arrival time distribution functions are NBUE or NWUE.

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Hopping in a supercooled Lennard-Jones liquid: Metabasins, waiting time distribution, and diffusion

Physical Review E ◽

10.1103/physreve.67.030501 ◽

2003 ◽

Vol 67 (3) ◽

Cited By ~ 132

Author(s):

B. Doliwa ◽

A. Heuer

Keyword(s):

Waiting Time ◽

Time Distribution ◽

Waiting Time Distribution ◽

Lennard Jones ◽

And Diffusion

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

Journal of Applied Probability ◽

10.2307/3212974 ◽

1980 ◽

Vol 17 (3) ◽

pp. 814-821 ◽

Cited By ~ 20

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.

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

10.1002/essoar.10507138.1 ◽

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

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

Modern Physics Letters B ◽

10.1142/s0217984912501515 ◽

2012 ◽

Vol 26 (23) ◽

pp. 1250151 ◽

Cited By ~ 7

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.

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