Probability Of Emptiness Research Articles

Selective Polling and Controlled Contention Based WLAN MAC Scheme for Low-Latency Applications

A novel medium access control scheme is proposed and investigated for central coordinated wireless local area networks to support future low-latency applications. The scheme divides each beacon interval into multiple service cycles, and each service cycle is composed of a polling period (PP) and a contention period (CP). By polling stations according to their latest channel accessing times during each PP and properly assigning backoff count for each station during each CP, the proposed scheme reduces the resource waste caused by polling empty stations and collisions, thereby achieving low-latency performance. In each service cycle, the number of stations to poll during the PP is calculated based on station empty probability, and the backoff count assigned to a station that has not been polled during the PP is unique and relatively small. Our simulation results show that the proposed scheme reduces uplink latency effectively, and can afford more traffic under the 0.5 ms uplink latency constraint compared to the conventional schemes.

Performance Analysis for Wireless Stochastic Networks With Dynamic Traffic and Packet Retransmission

In this paper, we analyze the system performance of a stochastic network, which is in the stationary state. Different from previous full-loaded assumptions that base stations (BSs) are always transmitting signals, which overestimates the inter-cell interference (ICI), dynamic traffic is considered in our model and BSs can be silent in some time slots. Packet retransmission is adopted, which brings a coupled relationship between the outage probability and the buffer empty probability. That is, as the outage probability increases, packets that are not successfully received will remain at the head of the buffer and be retransmitted until they are successfully received, which increases the proportion of active BSs and aggravates the ICI in turn. To better analyze this coupled relationship, the ICI is analyzed with the aid of the probability generating function and the Laplace transform. Then a queuing model is established to depict the packet arrival and departure processes. Some important system metrics, including the outage probability, the buffer empty probability, and the stable throughput region, are derived. Numerical results verify our theoretical analysis, and it is revealed that packet retransmission can enhance the system performance when the packet request rate is within the stable throughput region.

Empty Probability Distribution Considering Measurement Characteristics of Two-dimensional LRF for Autonomous Mobile Robots

Empty Probability Distribution Considering Measurement Characteristics of Two-dimensional LRF for Autonomous Mobile Robots

Stochastic Energy Harvesting and Relay Selection for Two-Way Dual-Relay Networks

The optimal transmission policy is investigated for two-way (TW) energy harvesting (EH) dual-relay networks with a stochastic EH model. There exist two solar-powered relays which have finite-sized batteries, and at most one relay is selected to facilitate the network’s information exchange. The objective is to optimize the network’s long-term outage performance by adapting the relay selection and power allocation to the system stochastic conditions. Thus, a Markov decision process (MDP) is utilized to formulate the design framework. From the MDP, the optimal transmission policy of the network is derived to indicate the adaptive relay selection and power allocation, and the computation of the network’s expected outage probability is presented. Further, the optimal transmission policy is asymptotically analyzed, and an active relaying property and a power convergency property of the optimal policy are pointed out. Moreover, according to the properties of the optimal policy, the long-term outage probabilities of the network are found to approach the limitation in sufficiently high SNRs, which is determined by the empty probability of the dual-battery under the optimal policy. Finally, computer simulations validate the analysis.

Forked queueing model with load dependent service rate and bulk arrivals

In this paper a forked two-node tandem queueing model with load dependent service rates having bulk arrivals is introduced and analysed under transient and equilibrium conditions. The system performance measures like probability of emptiness of the system, the probabilities of emptiness of marginal queues, the average number of customers in each queue, the average waiting time of the customer in each queue, the throughput of each node, the utility of servers and the variance of the number of customers in each queue are derived and analysed. The sensitivity analysis of a model reveals that the bulk size distribution parameters has a significant influence on system performance measures. Through numerical studies, it is observed that the load dependent service rates can reduce the congestion in queues and mean delay. A comparative study of the model with respect to equilibrium and transient conditions reveal that the time has significant influence on the performance measures. This model also includes some of the earlier models as particular cases for specific values of the parameters.

On Outage Probability for Two-Way Relay Networks With Stochastic Energy Harvesting

In this paper, we propose an optimal relay transmission policy by using a stochastic energy harvesting (EH) model for the EH two-way relay network, wherein the relay is solar-powered and equipped with a finite-sized battery. In this policy, the long-term average outage probability is minimized by adapting the relay transmission power to the wireless channel states, battery energy amount, and causal solar energy states. The designed problem is formulated as a Markov decision process (MDP) framework, and conditional outage probabilities for both decode-and-forward (DF) and amplify-and-forward (AF) cooperation protocols are adopted as the reward functions. We uncover a monotonic and bounded differential structure for the expected total discounted reward, and prove that such an optimal transmission policy has a threshold structure with respect to the battery energy amount in sufficiently high SNRs. Finally, the outage probability performance is analyzed and an interesting saturated structure for the outage performance is revealed, i.e., the expected outage probability converges to the battery empty probability in high SNR regimes, instead of going to zero. Furthermore, we propose a saturation-free condition that can guarantee a zero outage probability in high SNRs. Computer simulations confirm our theoretical analysis and show that our proposed optimal transmission policy outperforms other compared policies.

Stochastic Reservoir Systems with Different Assumptions for Storage Losses

Moran considered a dam whose inflow in a given interval of time is a continuous random variable. He then developed integral equations for the probabilities of emptiness and overflow. These equations are difficult to solve numerically; thus, approximations have been proposed that discretize the input. In this paper, extensions are considered for storage systems with different assumptions for storage losses. We also develop discrete approximations for the probabilities of emptiness and overflow.

Steady State Analysis of a Three Node Tandem Communication Network Model with DBA having Homogeneous Compound Poisson Direct Bulk Arrivals at Node 1 And Node 2

this paper, a three stage communication network model with two stage homogeneous bulk arrivals and dynamic bandwidth allocation under equilibrium condition is developed and analyzed. Consider a Communication network in which three nodes are in tandem and the messages arrive to the first node are converted into number of packets and stored in first buffer connected to the first node. After transmitting from the first node, the messages arrive to the second node from first node and the messages which are directly arriving to the second node are converted into number of packets and stored in second buffer connected to the second node. After transmitting from the second node, the messages arrive to the third node are converted into number of packets and stored in third buffer connected to the third node. Dynamic Bandwidth Allocation (DBA) is the strategy that the transmission rate at each node is adjusted depending upon the content of the buffer at every packet transmission. It is assumed that the arrival of packets follow compound Poisson processes and the transmission completions at each node follow Poisson processes. The steady state analysis of this model is carried by assuming that the system is stable under equilibrium. This model is more accurately fit into the realistic situation of the communication network having a predecessor and successor nodes for the middle node. Using the difference-differential equations, the joint probability generating function of the number of packets in each buffer is derived. The performance measures like, the probability of emptiness of the three buffers, the mean content in each buffer, mean delays in buffers, throughput etc. are derived explicitly under equilibrium or steady state conditions. This network model is much useful in communication systems. Keywordsstage communication networks, Dynamic bandwidth allocation, Batch arrivals and Steady state.

On Outage Probability for Stochastic Energy Harvesting Communications in Fading Channels

An optimal transmission policy is considered for energy harvesting (EH) wireless point-to-point communications, wherein the source node is solar-powered and equipped with a finite-sized battery. The long-term outage probability is minimized by adapting the transmission power to the causal energy arrival information, battery energy amount and channel fading through a Markov decision process (MDP) framework. We reveal an interesting saturated structure of the expected outage probability for which it eventually converges to a battery empty probability in high signal-to-noise power ratio (SNR). This phenomenon that links outage probability with EH capability is derived based on a monotonic and bounded differential structure of the long-term reward and a threshold structure of the optimal policy. Furthermore, a saturation-free condition on the outage performance is presented as well. Simulations confirm the theoretical analysis and the superiority of the proposed policy.

Tandem Communication Network Model with DBA having Non Homogeneous Poisson arrivals and Feedback for First Node

In this paper, we develop a two node tandem communication network model with dynamic bandwidth allocation and feedback for the first node. In most of the communication systems, the arrivals of packets follow Non-Homogeneous and arrival rate is time dependent. In this model, the transmission rate of each transmitter depends on the number of packets in the buffer connected it. The transmission rates at each transmitter are adjusted depending upon the content of the buffer connected to it. The packets transmitted through the first transmitter may be forwarded to the buffer connected to the second transmitter or returned back to the first buffer with certain probabilities. Using the difference-differential equations the performance measures including average number of packets in each buffer, the probability of emptiness of the network, the average waiting time in the buffer and in the network, the throughput of the transmitters, and the variance of the number of packets in the buffer are calculated. It is observed that the load dependent transmission can reduce the delays in the transmission and enhance the channel capacity.Â

Transient Analysis of Communication Network Model with Homogeneous Poisson arrivals and Dynamic Bandwidth Allocation

models play a dominant role in many communication systems for optimum utilization of the resources. In this paper, we develop and analyze a two node tandem communication network model with feedback for the first node, with an assumption that the arrivals follow homogeneous Poisson process. In this model, the service rates of each transmitter depends on the number of services in the buffer connected it. The model is analyzed using the difference-differential equations and a probability generating function of the number of packets in the buffer. Expressions are derived for performance measures including average number of packets in each buffer, the probability of emptiness of the network, the mean delay in the buffer and in the network, the throughput of the transmitters, and the variance of the number of packets in the buffer.

Queueing model with non-homogeneous bulk arrivals having state-dependent service rates

This paper considers a single-server queueing model with non-homogeneous bulk arrivals and state-dependent service rates. The bulk arrival queueing model is important in developing optimal operating policies for queueing in transportation systems and communication systems. Arrivals are assumed to be characterised by a non-homogeneous compound Poisson process, and the service rate depends on the content of the buffer connecting to the service station. Using difference-differential equations and a probability generating function, the system’s behaviour is analysed. Explicit expressions are derived for performance measures including average number of customers in the queue and probability of queue emptiness, etc. Sensitivity analysis of the model revealed that assuming non-homogeneous arrival significantly influences the system performance measures. The state-dependent service rate strategy can control queue congestion and mean delay in transmission. This model is effective in evaluating the performance of time-dependent communication systems.

Extremes of the time-average of stationary Gaussian processes

We study the exact asymptotics of P ( sup t ≥ 0 I Z ( t ) > u ) , as u → ∞ , where I Z ( t ) = { 1 t ∫ 0 t Z ( s ) d s for t > 0 Z ( 0 ) for t = 0 and { Z ( t ) : t ≥ 0 } is a centered stationary Gaussian process with covariance function satisfying some regularity conditions. As an application, we analyze the probability of buffer emptiness in a Gaussian fluid queueing system and the collision probability of differentiable Gaussian processes with stationary increments. Additionally, we find estimates for analogues of Piterbarg–Prisyazhnyuk constants, that appear in the form of the considered asymptotics.

On servers in series with losses in descrete time

We study a m-phase queueing system without buffers, operating in discrete time. The input flow is Bernoulli with parameter a. Service times in server i have geometric distribution with parameter b i. A customer, trying to enter a server at an instant, when it is busy, is lost. There have been obtained system of equilibrium equations and recurrence relations for its coefficients which enable us to formulate the algorithm to build the system. Recurrence formulas for computation of the empty system probability and some other performance characteristics of the system, are determined. The problem of optimal allocation of the servers is studied numerically.

One-Dimensional Lattice Dynamics of the Diffusion-Limited Reaction A +A A +S: Transient Behavior

We use a Boolean cellular automaton model to describe the diffusion-limited dynamics of the irreversible reaction A+A→A+S on a 1D lattice. We derive a set of equations for the dynamics of the empty interval probabilities from which explicit expressions for the particle concentration and the two-point correlation can be obtained. It is shown that the long-time dynamics is in agreement with the off-lattice solution. The early-time behavior, however, predicts a slower decay of the concentration.

Calculating the M/G/1 busy-period density and LIFO waiting-time distribution by direct numerical transform inversion

It is well known that the M/G/1 busy-period density can be characterized by the Kendall functional equation for its Laplace transform. The Kendall functional equation can be solved iteratively to obtain transform values to use in numerical inversion algorithms. However, we show that the busy-period density can also be numerically inverted directly, without iterating a functional equation, exploiting a contour integral representation due to Cox and Smith (1961). The contour integral representation was originally proposed as a basis for asymptotic approximations. We derive heavy-traffic expansions for the asymptotic parameters appearing there. We also use the integral representation to derive explicit series representations of the busy-period density for serval service-time distributions. In addition, we discuss related contour integral representations for the probability of emptiness, which is directly related to the waiting-time distribution with the LIFO discipline. The asymptotics and the numerical inversion reveal the striking difference between the waiting-time distributions for the FIFO and LIFO disciplines.

Six roads from Newton: great discoveries in physics

The Newtonian Universe Waves and Their Differences from Particles Fields: Space Is Not Empty Probability: What Does It Measure? Special Relativity: Only One Velocity Is Absolute Quantum Theory: New Phenomena, New Principles General Relativity: Gravity as Field Distortions A Look Down Further Roads Neither Determinism Nor Indeterminism Road to the Stars Appendices Index.

Reliable yield of reservoirs and possible effects of climatic change

Statistics of seasonal and daily rainfall in nine regions covering the United Kingdom are presented, together with the best currently available predictions of changes in rainfall and evaporation, based on various general circulation model (GCM) assessments of the climate 40 years ahead. On that basis, runoff sequences are generated for the region of northwest England with north Wales (NWE & NW, humid temperate) and for southeast England (SEE, temperate but less humid), both for the current climate and for the year 2030 estimate, the latter incorporating higher evaporation losses. The future annual runoff is reckoned as 8% less than the current average in the SEE region and 4% less than that in the NWE & NW region. Direct supply reservoir yield versus storage graphs are then derived in each case for a range of duration-based probability of emptiness, their yields (i.e. sustained draw-off rates) and storage capacities being expressed as proportions of current annual runoff. The year 2030 graphs fall systematically below those for the current climate, representing 8% to 15% loss of yield from existing storage in the SEE region and 4% to 25% loss of yield in the NWE & NW region.

An Infinite Dam with a Time-Dependent Release Rule

An infinite dam with discrete inputs arriving at times 0 = T0 < T1 <…< Tn <… is considered, where {Tn;n = 0,1,2,…} forms a renewal process. There is a random release from the dam during the interrenewal times which depends on the content as well as on the length of the time after the last input. A relation is derived that connects the content distribution at any time t to that when t is a renewal point. This relation is used to obtain the content distribution in the limiting case and in the transient case. The probability of emptiness is obtained and an integral equation is derived for the probability of first emptiness in a special case.

An infinite dam with random withdrawal policy

Most work in the theory of dams has dealt with deterministic withdrawals. Some more recent work, begun by Moran (1969), has been devoted to conditionally deterministic withdrawals which depend on the content of the dam, or in some cases on the last input. We consider in this paper an infinite dam fed by discrete additive inputs, under a totally random withdrawal policy. Explicit expressions are obtained for the time-dependent content distributions. Probabilities of emptiness are computed and stationary results are derived.