scholarly journals Peak age of information in slotted ALOHA network

2021 ◽  
Author(s):  
Sepehr Asvadi ◽  
Farid Ashtiani
Keyword(s):  
Closed Form ◽  
Analytical Model ◽  
Discrete Time ◽  
Transmission Delay ◽  
Slotted Aloha ◽  
Achievable Throughput ◽  
Simulation Results ◽  
Age Of Information

<p>In this paper, we concentrate on the peak age of information (PAoI) in a discrete-time slotted ALOHA network comprised of <i>M</i> buffer-less nodes, capable of keeping just one packet at each time. In this network, whenever some nodes transmit their packets simultaneously, a collision happens, thus there is interaction among queues and transmission delay of a packet might prolong more than one slot. The packets are generated at each node stochastically and independently. The nodes follow preemptive queueing policy. In this network, we propose a new trellis-based analytical model to represent the interaction among queues and derive exact average PAoI in closed form. Furthermore, we find average PAoI-constrained regions and minimize average PAoI for a symmetric network, numerically. As a byproduct of our analysis, the achievable throughput region of two slotted ALOHA networks with unlimited buffer and buffer-less nodes are compared. We observe that the latter is superior not only in AoI, but also in achievable throughput region. Simulation results confirm our analysis.</p>

scholarly journals Peak age of information in slotted ALOHA network

2021 ◽  
Author(s):  
Sepehr Asvadi ◽  
Farid Ashtiani
Keyword(s):  
Closed Form ◽  
Analytical Model ◽  
Discrete Time ◽  
Transmission Delay ◽  
Slotted Aloha ◽  
Achievable Throughput ◽  
Simulation Results ◽  
Age Of Information

<p>In this paper, we concentrate on the peak age of information (PAoI) in a discrete-time slotted ALOHA network comprised of <i>M</i> buffer-less nodes, capable of keeping just one packet at each time. In this network, whenever some nodes transmit their packets simultaneously, a collision happens, thus there is interaction among queues and transmission delay of a packet might prolong more than one slot. The packets are generated at each node stochastically and independently. The nodes follow preemptive queueing policy. In this network, we propose a new trellis-based analytical model to represent the interaction among queues and derive exact average PAoI in closed form. Furthermore, we find average PAoI-constrained regions and minimize average PAoI for a symmetric network, numerically. As a byproduct of our analysis, the achievable throughput region of two slotted ALOHA networks with unlimited buffer and buffer-less nodes are compared. We observe that the latter is superior not only in AoI, but also in achievable throughput region. Simulation results confirm our analysis.</p>

scholarly journals Cheating at Craps

2021 ◽  
Vol 48 (4) ◽  
pp. 53-61
Author(s):  
Andrea Marin ◽  
Carey Williamson
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Modeling And Simulation ◽  
Analytical Model ◽  
Quantitative Evaluation ◽  
Mathematical Analysis ◽  
Simulation Modeling ◽  
Analytical Modeling ◽  
The World ◽  
Simulation Results

Craps is a simple dice game that is popular in casinos around the world. While the rules for Craps, and its mathematical analysis, are reasonably straightforward, this paper instead focuses on the best ways to cheat at Craps, by using loaded (biased) dice. We use both analytical modeling and simulation modeling to study this intriguing dice game. Our modeling results show that biasing a die away from the value 1 or towards the value 5 lead to the best (and least detectable) cheating strategies, and that modest bias on two loaded dice can increase the winning probability above 50%. Our Monte Carlo simulation results provide validation for our analytical model, and also facilitate the quantitative evaluation of other scenarios, such as heterogeneous or correlated dice.

scholarly journals Analytical Calculation for Capacitances of Electrode Patterns in Touch Panels

2017 ◽  
Vol 3 (1) ◽  
Author(s):  
Bau-Jy Liang ◽  
Don-Gey Liu ◽  
Chia-Hung Yeh ◽  
Hsiao-Chun Chen ◽  
Yu-Chen Fang ◽  
...  
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Analytical Method ◽  
Analytical Calculation ◽  
3 Dimensional ◽  
Simulation Results ◽  
Complex Patterns ◽  
Touch Panels

AbstractIn this paper, an accurate 3-dimensional (3-D) analytical solution is proposed to calculate the projective capacitances of touch panels. In this study, both simple and complex patterns were investigated for the calculation. We propose a partition strategy to divide a pattern into many rectangular or triangular sub-patterns. Each sub-pattern can be further cut into 2-D slices. The capacitance of a 2-D slice was then solved by our closed-form formulae. The total capacitance of a pattern was obtained by integrating up all the partial capacitances of the slices. In this study, the precision of our analytical method was examined by comparing the simulation results obtained from Q3D

A Direct Digital Control Algorithm for Control of a Single Environmental Space

1985 ◽  
Vol 107 (4) ◽  
pp. 324-331 ◽  
Author(s):  
D. B. Cherchas ◽  
A. Abdelmessih ◽  
M. Townsend
Keyword(s):  
Mathematical Model ◽  
Moisture Content ◽  
Discrete Time ◽  
Digital Control ◽  
Control Algorithm ◽  
Environmental Space ◽  
Practical Performance ◽  
Simulation Results ◽  
Time Form ◽  
Direct Digital Control

A direct digital control algorithm for control of dry bulb temperature in a single environmental space is developed. The algorithm is based on a bilinear mathematical model, developed in the paper, of the response of the space dry bulb temperature and moisture content. The algorithm is somewhat unique in that it includes feedback and feedforward terms in a manner respecting the bilinear nature of the controlled process and as well, minimizes a practical performance index. The discrete time form of the algorithm is presented and simulation results given.

Research and Implement of an Improved Frame-Slotted ALOHA Anti-Collision Algorithm

2014 ◽  
Vol 945-949 ◽  
pp. 2519-2522
Author(s):  
Li He ◽  
Gai Ping Liu ◽  
Chuan Yuan Han
Keyword(s):  
System Throughput ◽  
Slotted Aloha ◽  
C Language ◽  
Key Technology ◽  
Rfid System ◽  
Simulation Results

The anti-collision algorithm is the key technology of RFID system. Firstly, this paper studied frame-slotted ALOHA anti-collision algorithm, in order to solve the shortcomings of ALOHA algorithm, an improved anti-collision algorithm is proposed based on grouping mechanism, and it also carried out the simulation experiences using the C# language under the .NET platform. The simulation results indicate that the improved algorithms can increase RFID system throughput.

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