Properties and Moving Time Average for Lévy Walks with Power-Law Waiting-Time Distributions

2014 ◽  
Vol 580-583 ◽  
pp. 3079-3082
Author(s):  
Kai Ying Deng ◽  
Jing Wei Deng
Keyword(s):  
Power Law ◽  
Waiting Time ◽  
Waiting Times ◽  
Time Cost ◽  
Waiting Time Distributions ◽  
Time Average

Lévy walks are a natural model for the description of sub-ballistic, superdiffusive motion. The waiting times and jump lengths of Lévy walks are coupled in the form . The-coupling introduces a time cost for each jump in the form of the generalized velocity , such that long jumps get penalized by a higher time cost. In this paper, we firstly investigate the properties of Lévy walks with power-law waiting-time distributions; then discuss its moving time average.

Biased continuous-time random walks for ordinary and equilibrium cases: facilitation of diffusion, ergodicity breaking and ageing

2018 ◽  
Vol 20 (32) ◽  
pp. 20827-20848 ◽  
Author(s):  
Ru Hou ◽  
Andrey G. Cherstvy ◽  
Ralf Metzler ◽  
Takuma Akimoto
Keyword(s):  
Random Walks ◽  
Computer Simulations ◽  
Power Law ◽  
Waiting Time ◽  
Continuous Time ◽  
Zero Drift ◽  
Renewal Processes ◽  
Waiting Time Distributions ◽  
Continuous Time Random Walks ◽  
Ergodicity Breaking

We examine renewal processes with power-law waiting time distributions and non-zero drift via computing analytically and by computer simulations their ensemble and time averaged spreading characteristics.

The probability of large queue lengths and waiting times in a heterogeneous multiserver queue II: Positive recurrence and logarithmic limits

1995 ◽  
Vol 27 (2) ◽  
pp. 567-583 ◽  
Author(s):  
John S. Sadowsky
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Waiting Times ◽  
General Setting ◽  
Batch Arrival ◽  
Positive Recurrence ◽  
Waiting Time Distributions ◽  
Harris Recurrence ◽  
Stationary Queue Length ◽  
Queue Lengths

We continue our investigation of the batch arrival-heterogeneous multiserver queue begun in Part I. In a general setting we prove the positive Harris recurrence of the system, and with no additional conditions we prove logarithmic tail limits for the stationary queue length and waiting time distributions.

scholarly journals The Form of Waiting Time Distributions of Continuous Time Random Walk in Dead-End Pores

Geofluids ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Yusong Hou ◽  
Jianguo Jiang ◽  
J. Wu
Keyword(s):  
Power Law ◽  
Waiting Time ◽  
Power Index ◽  
Early Time ◽  
Anomalous Dispersion ◽  
Power Law Distribution ◽  
Waiting Time Distributions ◽  
Dead End ◽  
Exponential Decline ◽  
Power Law Distributions

Anomalous dispersion of solute in porous media can be explained by the power-law distribution of waiting time of solute particles. In this paper, we simulate the diffusion of nonreactive tracer in dead-end pores to explore the waiting time distributions. The distributions of waiting time in different dead-end pores show similar power-law decline at early time and transit to an exponential decline in the end. The transition time between these two decline modes increases with the lengths of dead-end pores. It is well known that power-law distributions of waiting time may lead to anomalous (non-Fickian) dispersion. Therefore, anomalous dispersion is highly dependent on the sizes of immobile zones. According to the power-law decline, we can directly get the power index from the structure of dead-end pores, which can be used to judge the anomalous degree of solute transport in advance.

The probability of large queue lengths and waiting times in a heterogeneous multiserver queue II: Positive recurrence and logarithmic limits

1995 ◽  
Vol 27 (02) ◽  
pp. 567-583 ◽  
Author(s):  
John S. Sadowsky
Keyword(s):  
Waiting Time ◽  
Queue Length ◽  
Waiting Times ◽  
General Setting ◽  
Batch Arrival ◽  
Positive Recurrence ◽  
Waiting Time Distributions ◽  
Harris Recurrence ◽  
Stationary Queue Length ◽  
Queue Lengths

We continue our investigation of the batch arrival-heterogeneous multiserver queue begun in Part I. In a general setting we prove the positive Harris recurrence of the system, and with no additional conditions we prove logarithmic tail limits for the stationary queue length and waiting time distributions.

scholarly journals Distributions of Patterns of Pair of Successes Separated by Failure Runs of Length at Least and at Most Involving Markov Dependent Trials: GERT Approach

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Kanwar Sen ◽  
Pooja Mohan ◽  
Manju Lata Agarwal
Keyword(s):  
Waiting Time ◽  
Generating Functions ◽  
Waiting Times ◽  
Waiting Time Distributions ◽  
Probability Generating Functions ◽  
Mean And Variance ◽  
Markov Dependent Trials

We use the Graphical Evaluation and Review Technique (GERT) to obtain probability generating functions of the waiting time distributions of 1st, and th nonoverlapping and overlapping occurrences of the pattern , involving homogenous Markov dependent trials. GERT besides providing visual picture of the system helps to analyze the system in a less inductive manner. Mean and variance of the waiting times of the occurrence of the patterns have also been obtained. Some earlier results existing in literature have been shown to be particular cases of these results.

On the tails of waiting-time distributions

1975 ◽  
Vol 12 (3) ◽  
pp. 555-564 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Limit Theorem ◽  
Waiting Time ◽  
Waiting Times ◽  
Waiting Time Distributions ◽  
Tail Behaviour

Results are given which relate the tail behaviour of the service and limiting waiting time distributions of a GI/G/1 queue. A limit theorem for the maxima of waiting times is given.

On the tails of waiting-time distributions

1975 ◽  
Vol 12 (03) ◽  
pp. 555-564 ◽  
Author(s):  
A. G. Pakes
Keyword(s):  
Limit Theorem ◽  
Waiting Time ◽  
Waiting Times ◽  
Waiting Time Distributions ◽  
Tail Behaviour

Results are given which relate the tail behaviour of the service and limiting waiting time distributions of a GI/G/1 queue. A limit theorem for the maxima of waiting times is given.

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