BLOCKCHAIN DOUBLE-SPEND ATTACK DURATION

2020 ◽  
pp. 1-9
Author(s):  
Mark Brown ◽  
Erol Peköz ◽  
Sheldon Ross
Keyword(s):  
Poisson Process ◽  
Closed Form ◽  
Exact Expression ◽  
Computational Power ◽  
Efficient Simulation ◽  
Analytic Approximations

Many cryptocurrencies including Bitcoin are susceptible to a so-called double-spend attack, where someone dishonestly attempts to reverse a recently confirmed transaction. The duration and likelihood of success of such an attack depends on the recency of the transaction and the computational power of the attacker, and these can be related to the distribution of time for counts from one Poisson process to exceed counts from another by some desired amount. We derive an exact expression for this distribution and show how it can be used to obtain efficient simulation estimators. We also give closed-form analytic approximations and illustrate their accuracy.

Radial generation of n-dimensional poisson processes

1984 ◽  
Vol 21 (03) ◽  
pp. 548-557
Author(s):  
M. P. Quine ◽  
D. F. Watson
Keyword(s):  
Poisson Process ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Simulation Studies ◽  
Simple Method ◽  
Efficient Simulation ◽  
Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in ann-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

scholarly journals Optimal Layer Reinsurance for Compound Fractional Poisson Model

2019 ◽  
Vol 2019 ◽  
pp. 1-8
Author(s):  
Jiesong Zhang
Keyword(s):  
Poisson Process ◽  
Closed Form ◽  
Compound Poisson Process ◽  
Poisson Model ◽  
Adjustment Coefficient ◽  
Compound Poisson ◽  
Numerical Examples ◽  
Fractional Poisson Process ◽  
Reinsurance Treaty

In this paper, we study the optimal retentions for an insurer with a compound fractional Poisson surplus and a layer reinsurance treaty. Under the criterion of maximizing the adjustment coefficient, the closed form expressions of the optimal results are obtained. It is demonstrated that the optimal retention vector and the maximal adjustment coefficient are not only closely related to the parameter of the fractional Poisson process, but also dependent on the time and the claim intensity, which is different from the case in the classical compound Poisson process. Numerical examples are presented to show the impacts of the three parameters on the optimal results.

Effect of Surface Roughness on Adhesion and Friction of Microfibers in Side Contact

2008 ◽  
Author(s):  
Mircea Teodorescu ◽  
Carmel Majidi ◽  
Homer Rahnejat ◽  
Ronald S. Fearing
Keyword(s):  
Mathematical Model ◽  
Surface Roughness ◽  
Closed Form ◽  
Contact Mechanics ◽  
Elastic Contact ◽  
Linear Elastic ◽  
Multi Scale ◽  
Analytic Approximations ◽  
Effect Of Surface

A multi-scale mathematical model is used to study the effect of surface roughness on the adhesion and friction of microfibers engaged in side contact. Results are compared to closed-form analytic approximations derived from linear elastic contact mechanics.

The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process

2001 ◽  
Vol 38 (1) ◽  
pp. 255-261 ◽  
Author(s):  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Closed Form ◽  
Queueing System ◽  
Heavy Traffic ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Maximum Workload ◽  
Busy Cycle

We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

scholarly journals Physical-Layer Security Analysis over M-Distributed Fading Channels

Entropy ◽  
2019 ◽  
Vol 21 (10) ◽  
pp. 998 ◽  
Author(s):  
Sheng-Hong Lin ◽  
Rong-Rong Lu ◽  
Xian-Tao Fu ◽  
An-Ling Tong ◽  
Jin-Yuan Wang
Keyword(s):  
Lower Bound ◽  
Closed Form ◽  
Fading Channels ◽  
Physical Layer Security ◽  
Physical Layer ◽  
Exact Expression ◽  
Closed Form Expression ◽  
Secrecy Outage Probability ◽  
Secrecy Capacity ◽  
Special Cases

In this paper, the physical layer security over the M-distributed fading channel is investigated. Initially, an exact expression of secrecy outage probability (SOP) is derived, which has an integral term. To get a closed-form expression, a lower bound of SOP is obtained. After that, the exact expression for the probability of strictly positive secrecy capacity (SPSC) is derived, which is in closed-form. Finally, an exact expression of ergodic secrecy capacity (ESC) is derived, which has two integral terms. To reduce its computational complexity, a closed-from expression for the lower bound of ESC is obtained. As special cases of M-distributed fading channels, the secure performance of the K, exponential, and Gamma-Gamma fading channels are also derived, respectively. Numerical results show that all theoretical results match well with Monte-Carlo simulation results. Specifically, when the average signal-to-noise ratio of main channel is larger than 40 dB, the relative errors for the lower bound of SOP, the probability of SPSC, and the lower bound of ESC are less than 1.936%, 6.753%, and 1.845%, respectively. This indicates that the derived theoretical expressions can be directly used to evaluate system performance without time-consuming simulations. Moreover, the derived results regarding parameters that influence the secrecy performance will enable system designers to quickly determine the optimal available parameter choices when facing different security risks.

Response times in M/M/s fork-join networks

2004 ◽  
Vol 36 (3) ◽  
pp. 854-871 ◽  
Author(s):  
Sung-Seok Ko ◽  
Richard F. Serfozo
Keyword(s):  
Response Time ◽  
Poisson Process ◽  
Closed Form ◽  
Queue Length ◽  
Response Times ◽  
Statistical Tests ◽  
Queueing Systems ◽  
Kolmogorov Smirnov ◽  
Processing Network ◽  
Closed Form Formula

We study a fork-join processing network in which jobs arrive according to a Poisson process and each job splits into m tasks, which are simultaneously assigned to m nodes that operate like M/M/s queueing systems. When all of its tasks are finished, the job is completed. The main result is a closed-form formula for approximating the distribution of the network's response time (the time to complete a job) in equilibrium. We also present an analogous approximation for the distribution of the equilibrium queue length (the number of jobs in the system), when each node has one server. Kolmogorov-Smirnov statistical tests show that these formulae are good fits for the distributions obtained from simulations.

Radial generation of n-dimensional poisson processes

1984 ◽  
Vol 21 (3) ◽  
pp. 548-557 ◽  
Author(s):  
M. P. Quine ◽  
D. F. Watson
Keyword(s):  
Poisson Process ◽  
Poisson Processes ◽  
Three Dimensions ◽  
Simulation Studies ◽  
Simple Method ◽  
Efficient Simulation ◽  
Nearest Neighbours

A simple method is proposed for the generation of successive ‘nearest neighbours' to a given origin in an n-dimensional Poisson process. It is shown that the method provides efficient simulation of random Voronoi polytopes. Results are given of simulation studies in two and three dimensions.

Response times in M/M/s fork-join networks

2004 ◽  
Vol 36 (03) ◽  
pp. 854-871 ◽  
Author(s):  
Sung-Seok Ko ◽  
Richard F. Serfozo
Keyword(s):  
Response Time ◽  
Poisson Process ◽  
Closed Form ◽  
Queue Length ◽  
Response Times ◽  
Statistical Tests ◽  
Queueing Systems ◽  
Kolmogorov Smirnov ◽  
Processing Network ◽  
Closed Form Formula

We study a fork-join processing network in which jobs arrive according to a Poisson process and each job splits into m tasks, which are simultaneously assigned to m nodes that operate like M/M/s queueing systems. When all of its tasks are finished, the job is completed. The main result is a closed-form formula for approximating the distribution of the network's response time (the time to complete a job) in equilibrium. We also present an analogous approximation for the distribution of the equilibrium queue length (the number of jobs in the system), when each node has one server. Kolmogorov-Smirnov statistical tests show that these formulae are good fits for the distributions obtained from simulations.

The busy cycle of the reflected superposition of Brownian motion and a compound Poisson process

2001 ◽  
Vol 38 (01) ◽  
pp. 255-261
Author(s):  
David Perry ◽  
Wolfgang Stadje
Keyword(s):  
Brownian Motion ◽  
Poisson Process ◽  
Closed Form ◽  
Queueing System ◽  
Heavy Traffic ◽  
Compound Poisson Process ◽  
Compound Poisson ◽  
Maximum Workload ◽  
Busy Cycle

We consider a reflected superposition of a Brownian motion and a compound Poisson process as a model for the workload process of a queueing system with two types of customers under heavy traffic. The distributions of the duration of a busy cycle and the maximum workload during a cycle are determined in closed form.

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