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Active queue management schemes are used to reduce the number of dropped packets at the routers. Random early detection uses dropping probability which is calculated based on the average queue size. Further it is modified according to the value of the count indicating the number of unmarked packets that have arrived after a marked packet. The impact of random variable i.e. number of packets arrived after a marked packet over the dropping pattern is investigated. The proposed model achieves smooth dropping pattern which results in improvement of quality of service parameters. A new model for dropping probability is proposed with different dropping function. The effect of new dropping probability results in the increase of the throughput and reduction of the expected end-to-end delay. An important finding is that the choice of modified dropping function significantly affects the performance measures of the networks.

The random early detection active queue management (AQM) scheme uses the average queue size to calculate the dropping probability in terms of minimum and maximum thresholds. The effect of heavy load enhances the frequency of crossing the maximum threshold value resulting in frequent dropping of the packets. An adaptive queue management with random dropping algorithm is proposed which incorporates information not just about the average queue size but also the rate of change of the same. Introducing an adaptively changing threshold level that falls in between lower and upper thresholds, our algorithm demonstrates that these additional features significantly improve the system performance in terms of throughput, average queue size, utilization and queuing delay in relation to the existing AQM algorithms.

A new theoretical probability distribution generalized Nakagami–generalized inverse Gaussian distribution (GN–GIGD) is proposed to model the backscattered echo envelope in ultrasound imaging. This new probability distribution is a composite distribution derived by compounding generalized Nakagami (GN) and generalized inverse Gaussian (GIG) distributions. It is known in the literature that GN distribution better captures the randomness in backscattered echo envelope where as GIG distribution provides better modeling of randomness in average power. The proposed distribution is a generalized distribution and several special cases results in several composite distributions in which some are able to characterize RF envelope in ultrasound imaging. The expression of signal to noise ratio for these relevant cases are obtained. The efficacy of proposed GN–GIGD in relation to Nakagami Gamma and Nakagami–generalized inverse Gaussian distributions is established by fitting these distributions over Field II simulation generated uncompressed echo envelope data of kidney and fetus phantoms for different scattering concentrations. It is found that the proposed GN–GIGD performs better then the other distributions in terms of Jensen Shannon divergence goodness of fit.

Recently, a dynamic adaptive queue management with random dropping (AQMRD) scheme has been developed to capture the time-dependent variation of average queue size by incorporating the rate of change of average queue size as a parameter. A major issue with AQMRD is the choice of parameters. In this paper, a novel online stochastic approximation based optimization scheme is proposed to dynamically tune the parameters of AQMRD and which is also applicable for other active queue management (AQM) algorithms. Our optimization scheme significantly improves the throughput, average queue size, and loss-rate in relation to other AQM schemes.

A unified approach based on truncated moment generating function (TMGF) is employed to derive the explicit expressions for channel capacity of log-normal channel under different adaptive transmission policy. The analysis is carried out assuming channel state information known to both transmitter and receiver. The efficacy of the approach is based on the fact it yields computationally convenient and efficient results in log-normal fading environment. Based on TMGF, a simple closed form expression for higher order moments of channel capacity for log-normal channels is obtained when channel state information is only known to receiver. Numerical computation in relation to simulation results for varying value of σdB over permissible range are carried out to validate the accuracy of derived expressions.

[This corrects the article DOI: 10.1371/journal.pone.0144378.].

A single neuronal model incorporating distributed delay (memory)is proposed. The stochastic model has been formulated as a Stochastic Integro-Differential Equation (SIDE) which results in the underlying process being non-Markovian. A detailed analysis of the model when the distributed delay kernel has exponential form (weak delay) has been carried out. The selection of exponential kernel has enabled the transformation of the non-Markovian model to a Markovian model in an extended state space. For the study of First Passage Time (FPT) with exponential delay kernel, the model has been transformed to a system of coupled Stochastic Differential Equations (SDEs) in two-dimensional state space. Simulation studies of the SDEs provide insight into the effect of weak delay kernel on the Inter-Spike Interval(ISI) distribution. A measure based on Jensen–Shannon divergence is proposed which can be used to make a choice between two competing models viz. distributed delay model vis-á-vis LIF model. An interesting feature of the model is that the behavior of (CV( t )) (ISI) (Coefficient of Variation) of the ISI distribution with respect to memory kernel time constant parameter η reveals that neuron can switch from a bursting state to non-bursting state as the noise intensity parameter changes. The membrane potential exhibits decaying auto-correlation structure with or without damped oscillatory behavior depending on the choice of parameters. This behavior is in agreement with empirically observed pattern of spike count in a fixed time window. The power spectral density derived from the auto-correlation function is found to exhibit single and double peaks. The model is also examined for the case of strong delay with memory kernel having the form of Gamma distribution. In contrast to fast decay of damped oscillations of the ISI distribution for the model with weak delay kernel, the decay of damped oscillations is found to be slower for the model with strong delay kernel.

The statistical characterization of channel capacity in slow fading environment modeled by log-normal probability density function is considered. The probability density function of channel capacity is found to be positively skewed and significantly departs from bell shaped curve for higher values of σdB. The computation of first two moments of channel capacity provides a measure for relative fluctuation in terms of coefficient of variation (CV). It is noted that the value of CV is quite high in lower range of SNR and starts declining with increasing SNR. This may question the applicability of average channel capacity as a performance measure in slow fading scenario and accordingly a more appropriate measure is based on outage capacity. A simple procedure based on three-point estimate is outlined to obtain the approximate expression for higher order moments of channel capacity and they are found to be in excellent agreement with exact results.

Wireless channel characteristics are random in nature. Consideration of shadowing and fading effect in the channel is necessary so as to capture the behavior of signal variation at the receiving end. The composite effect of the phenomenon is prominent in applications where receiving nodes are deployed in deep faded region with shadowed signal propagation. This becomes more important as the average power of the signal becomes random due to fading and shadowing effects. This effect is more prominent to capture the random behavior of the channel one has to adopt the probabilistic framework by using probability distributions. The Rayleigh–lognormal distribution (RLD), useful in characterizing fading and shadowing aspects of wireless communication channel, has a complex integral having no closed form. Noting that inverse Gaussian distribution closely approximates lognormal distribution, a better approximation is proposed by generalized inverse Gaussian distribution (GIGD). While different combination of compound probability distribution is capable of capturing the behavior of the channel, no such compound distributions work for the complete range of channel variations. Thus, the probability density function of the resulting Rayleigh–generalized inverse Gaussian distribution (RGIGD), besides having a closed form and being analytically tractable, is a more appropriate substitute for RLD. Based on Kullback–Leibler (K–L) measure to assess closeness of two probability distributions, it is found that the proposed RGIGD distribution is closer to the original RLD than other distributions, viz. RGD, RIGD. Further, the proposed distribution can be considered to provide a solution for a large range variation in the sense that RGD and RIGD become its special cases and yields more realistic values of quality of service parameters along with flexibility of covering a wide range of the signal variations through its special cases.

Besides the geometrical tortousity due to the extrasynaptic structures, macromolecular crowding and geometrical irregularities constituting the cleft composition at central excitatory synapses has a major and direct role in retarding the glutamate diffusion within the cleft space. However, the cleft composition may not only coarsely reduce the overall diffusivity of the glutamate but may also lead to substantial spatial variation in the diffusivity across the cleft space. Decrease in the overall diffusivity of the glutamate may have straightforward consequences to the glutamate transients in the cleft. However, how spatial variation in the diffusivity may further affect glutamate transients is an intriguing aspect. Therefore, to understand the role of cleft heterogeneity, the present study adopts a novel approach of glutamate diffusion which considers a gamma statistical distribution of the diffusion coefficient of glutamate (Dglut) across the cleft space, such that its moments discernibly capture the dual impacts of the cleft composition, and further applies the framework of superstatistics. The findings reveal a power law behavior in the glutamate transients, akin to the long-range anomalous subdiffusion, which leads to slower decay profile of cleft glutamate at higher intensity of cleft heterogeneity. Moreover, increase in the cleft heterogeneity is seen to eventually cause slower-rising excitatory postsynaptic currents with higher amplitudes, lesser noise, and prolonged duration of charge transfer across the postsynaptic membrane. Further, with regard to the conventional standard diffusion approach, the study suggests that the effective Dglut essentially derives from the median of the Dglut distribution and does not necessarily need to be the mean Dglut. Together, the findings indicate a strong implication of cleft heterogeneity to the metabolically cost-effective tuning of synaptic response during the phenomenon of plasticity at individual synapses and also provide an additional factor of variability in transmission across identical synapses.