Poisson Input Research Articles

The effects of dynamical synapses on firing rate activity: a spiking neural network model.

Accumulating evidence relates the fine-tuning of synaptic maturation and regulation of neural network activity to several key factors, including GABAA signaling and a lateral spread length between neighboring neurons (i.e., local connectivity). Furthermore, a number of studies consider short-term synaptic plasticity (STP) as an essential element in the instant modification of synaptic efficacy in the neuronal network and in modulating responses to sustained ranges of external Poisson input frequency (IF). Nevertheless, evaluating the firing activity in response to the dynamical interaction between STP (triggered by ranges of IF) and these key parameters invitro remains elusive. Therefore, we designed a spiking neural network (SNN) model in which we incorporated the following parameters: local density of arbor essences and a lateral spread length between neighboring neurons. We also created several network scenarios based on these key parameters. Then, we implemented two classes of STP: (1) short-term synaptic depression (STD) and (2) short-term synaptic facilitation (STF). Each class has two differential forms based on the parametric value of its synaptic time constant (either for depressing or facilitating synapses). Lastly, we compared the neural firing responses before and after the treatment with STP. We found that dynamical synapses (STP) have a critical differential role on evaluating and modulating the firing rate activity in each network scenario. Moreover, we investigated the impact of changing the balance between excitation (E) and inhibition (I) on stabilizing this firing activity.

STDP Allows Close-to-Optimal Spatiotemporal Spike Pattern Detection by Single Coincidence Detector Neurons

Repeating spatiotemporal spike patterns exist and carry information. How this information is extracted by downstream neurons is unclear. Here we theoretically investigate to what extent a single cell could detect a given spike pattern and what the optimal parameters to do so are, in particular the membrane time constant τ. Using a leaky integrate-and-fire (LIF) neuron with homogeneous Poisson input, we computed this optimum analytically. We found that a relatively small τ (at most a few tens of ms) is usually optimal, even when the pattern is much longer. This is somewhat counter-intuitive as the resulting detector ignores most of the pattern, due to its fast memory decay. Next, we wondered if spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimum. We simulated a LIF equipped with additive STDP, and repeatedly exposed it to a given input spike pattern. As in previous studies, the LIF progressively became selective to the repeating pattern with no supervision, even when the pattern was embedded in Poisson activity. Here we show that, using certain STDP parameters, the resulting pattern detector is optimal. These mechanisms may explain how humans learn repeating sensory sequences. Long sequences could be recognized thanks to coincidence detectors working at a much shorter timescale. This is consistent with the fact that recognition is still possible if a sound sequence is compressed, played backward, or scrambled using 10-ms bins. Coincidence detection is a simple yet powerful mechanism, which could be the main function of neurons in the brain.

Engineering Approach to Calculating QoS of Server with Self-Similar Incoming Traffic Based on Recursive Scalable Poisson Model

To date the prospects for using the accumulated over many years mathematical and software for the modeling of telecommunications with the Poisson input flow are under a big question. The matter is that a new fractal queuing theory is already on the threshhold. This article formulates and solves the problem of application of a queuing system model with a Poisson incoming flow for the purposes of server modeling described by QS with self-similar incoming traffic of the "fractal Brownian motion" type (according to Norros). Based on the results of the morphological analysis, the Norros model was decomposed into Poisson components connected by a scalable recurrence scheme. The variance of the number of packets in the server, raised to the power determined by the Hurst parameter acts as the similarity coefficient of fractal and Poisson QSs. The method for rescaling Poisson solutions into fractal solutions was constructed on the basis of the similarity coefficient. According to this method in order to find the fractal delay of access, the Poisson delay should be multiplied by the similarity coefficient, and to estimate the probability of packet loss, it is necessary to extract a root of degree equal to the similarity coefficient from classical exponential losses. The scope of the re-scaling method focuses on the pre-project stages of creating telecommunications, where there is no need for high accuracy of simulation results.

On the effect of stabilizing mean firing rate of a neuron due to STDP

We show by numerical simulations that a neuron with additive Spike-Timing-Dependent Plasticity with restricted symmetric nearest-neighbor spike pairing scheme, receiving Poisson input, establishes mean firing rate that does not depend on input rates, in a sufficiently high range of input rates. The established rate also does not depend on the number of inputs and the existence of inhibitory inputs, and depends only on the neuron and STDP parameters. A possible way to utilize this effect in learning is shown.

Two-phase queueing system optimization in applications to data transmission control

We consider the controlled tandem queuing network with two single-server finite-length queues with non-stationary Poisson input flow of packets. The first station controls the service rate and drops any incoming packet if its buffer is full. The second station controls the packet acceptance probability. The tandem is described by a controlled finite-state Markov process and optimized on a fixed time interval by minimizing average number of dropped packets with constraints on the average sojourn time and energy consumption.

Reneging in a batch arrival two phases queue with random feedback and Coxian-2 vacation

In this system we consider a batch arrival Poisson input with two phases of heterogeneous service with random feedback in each servivce. The first phase of service is essential for all customers, but with a probability tagged customer chose second phase, feedback to tail of original queue or leave the system. Also, after completion of the second phase, with a probability the customer leaves the system, or feedback to tail of original queue. At each service completion epoch, the server may apt to take a vacation with a probability or continue to be available in the system for the next service. The service times are assumed to be general. The vacation period of the server has two heterogeneous phases with Coxian-2 distribution. The vacation times are assumed to be general. When the server goes for vacation, service become unavailable and customers may decide to renege at each vacation times. We assume reneging follow exponential distribution. All stochastic processes involved in this system (service and vacation times) are independent of each other. We derive the PGF’s of the system and by using them the performance measures are obtained. Some numerical approch are examined the validity of results.

Gaussian and Diffusion Limits for Multi-Channel Stochastic Networks

In the paper the multichannel stochastic networks are considered. A non-homogeneous Poisson input flow of calls arrives at each node. An approximate method of investigation of the service process in heavy traffic is developed. For the multichannel Markovian networks the limit process is represented as a multidimensional diffusion.

Queueing System with Preemptive Resume Service Discipline and Unreliable Server*

We consider a single server queue with an unreliable server and two Poisson input flows. For this system we find stability conditions and obtain the limit distribution of the number of customers in the system.

Queues with advanced reservations: an infinite-server proxy for the bookings diary

Abstract Queues with advanced reservations are endemic in the real world. In such a queue, the 'arrival' process is an incoming stream of customer 'booking requests', rather than actual customers requiring immediate service. We consider a model with a Poisson booking request process with rate λ. Associated with each request is a pair of independent random variables (Ri, Si) constituting a request for service over a period Si, starting at a time Ri into the future. Our interest is in the probability that a customer will be rejected due to capacity constraints. We present a simulation of a finite-capacity queue in which we record the proportion of rejected customers, and then move to an analysis of a queue with infinitely-many servers. Obviously no customers are rejected in the latter case. However, the event that the arrival of the extra customer will cause the number of customers in the queue to exceed C at some point during its service can be used as a proxy for the event that the customer would have been rejected in a system with finite capacity C. We start by calculating the transient and stationary distributions for some performance measures for the infinite-server queue. By observing that the stationary measure for the bookings diary (that is, the list of customers currently on hand, together with their start times and service times) is the same as the law for the entire sample path of an infinite server queue with a specified nonhomogenous Poisson input process, which we call the bookings queue, we are able to write down expressions for the abovementioned probability that, at some time during a requested service, the number of customers exceeds C. This measure serves as a bound for the probability that an incoming arrival would be refused admission in a system with C servers and, for a well-dimensioned system, it is to be hoped that it is a good approximation. We test the quality of this approximation by comparing our analytical results for the infinite-server case against simulation results for the finite-server case.

Stability of Constant Retrial Rate Systems with NBU Input*

We study the stability of a single-server retrial queueing system with constant retrial rate, general input and service processes. First, we present a review of some relevant recent results related to the stability criteria of similar systems. Sufficient stability conditions were obtained by Avrachenkov and Morozov (2014), which hold for a rather general retrial system. However, only in the case of Poisson input is an explicit expression provided; otherwise one has to rely on simulation. On the other hand, the stability criteria derived by Lillo (1996) can be easily computed but only hold for the case of exponential service times. We present new sufficient stability conditions, which are less tight than the ones obtained by Avrachenkov and Morozov (2010), but have an analytical expression under rather general assumptions. A key assumption is that interarrival times belongs to the class of new better than used (NBU) distributions. We illustrate the accuracy of the condition based on this assumption (in comparison with known conditions when possible) for a number of non-exponential distributions.

ALGORITHMS OF EVALUATION OF THE WAITING TIME AND THE MODELLING OF THE TERMINAL ACTIVITY BASED ON THE TRAFFIC COEFFICIENT OF SHIPS IN THE SEAPORT

Ponte Academic JournalAug 2016, Volume 72, Issue 8 ALGORITHMS OF EVALUATION OF THE WAITING TIME AND THE MODELLING OF THE TERMINAL ACTIVITY BASED ON THE TRAFFIC COEFFICIENT OF SHIPS IN THE SEAPORTAuthor(s): Costea Alina ,Gheorghe Miscoi, Ionela Rodica Ticu, Catalin pomazanJ. Ponte - Aug 2016 - Volume 72 - Issue 8 doi: 10.21506/j.ponte.2016.8.17 Abstract:This paper approaches the application of the waiting model with Poisson inputs and priorities in the port activity. The arrival of ships in the maritime terminal is numerically modelled, and specific parameters for the distribution functions of service and of inputs are determined, in order to establish the waiting time of ships in the seaport and a stationary process. The modelling is based on waiting times and on the coefficient of traffic. Download full text:Check if you have access through your login credentials or your institution Username Password

Steady-state simulation of reflected Brownian motion and related stochastic networks

This paper develops the first class of algorithms that enable unbiased estimation of steady-state expectations for multidimensional reflected Brownian motion. In order to explain our ideas, we first consider the case of compound Poisson (possibly Markov modulated) input. In this case, we analyze the complexity of our procedure as the dimension of the network increases and show that, under certain assumptions, the algorithm has polynomial-expected termination time. Our methodology includes procedures that are of interest beyond steady-state simulation and reflected processes. For instance, we use wavelets to construct a piecewise linear function that can be guaranteed to be within $\varepsilon$ distance (deterministic) in the uniform norm to Brownian motion in any compact time interval.

Lateral Inhibition as the organizer of the bottom-up attentional modulation in the primary visual cortex

Lateral inhibition is known to occur at all levels of processing of visual information: from retinal ganglion cells, through principal cells in LGN to primary cortical areas [1]. The role of this connectivity module is to contrast lateral variation within the simultaneously processed upstream information. Our work is based on local field potential (LFP) multichannel signal data [2] recorded from the cats visual cortices activated by attentional tasks: voluntary (top-down) and stimulus driven (bottom-up). These experiments showed that enhanced beta signals (16-24 Hz) serve as a carrier for distributing attentional activation across the visual system. By measuring the correlation strengths between spontaneous LFP signals in different cortical recording sites it was also found that beta activation maps were organized in a mosaic-like pattern within the visual cortex during bottom-up task, whereas top-down task resulted in spatially homogeneous cortical beta excitation. It was hypothesized that the reason for these different cortical activation patterns was due to lateral inhibition raised by salient visual stimulus during bottom-up task [2]. This work aims to verify a role played by lateral inhibition in producing specific spatial activation patterns found in top-down and bottom-up experimental paradigms by means of computational modelling. We have constructed a model of neuronal network comprised of single compartment excitatory and inhibitory cells activated according to extended Hodgkin-Huxley dynamics. The network consists of 16 domains representing cortical patches [3], where the neuronal connections keep the anatomical weights, proportions and local structure according to experimental data: neurons are more likely to form synapses with neighboring cells within one domain. Additionally, the domains are more likely to be interconnected with adjacent than with distant ones. LFPs are modelled as a sum of synaptic currents taking into account their distances from a point of measurement. The modelled neurons receive two kinds of Poisson inputs, which represent the feed-forward input from the thalamus and feed-back activation from higher order cortical regions. The reinforcement of the latter causes widespread increase in beta band power of LFP and represents diffuse, top-down attentional modulating signal. The input from the thalamus arriving to one or more domains represents bottom-up attentional activation of excitatory and inhibitory neurons evoked by salient visual stimulus. The cortical domains activated by this salient input exert additional lateral inhibition on neighboring domains. Our model shows that the spatial heterogeneity of cortical activation resulting in local decrease of correlation in bottom-up task and homogeneity in top-down task, can be mediated by feed-forward lateral inhibitory influences at the cortical level. The higher cross-correlation variance observed experimentally during bottom-up than in top-down attentional paradigm is also observed in the model. This modelling study, confirmed that mechanism of lateral inhibition may be sufficient in explaining spatial differences in organization of beta activities in visual cortical areas observed during bottom-up and top-down attentional paradigms. The network was modelled by means of PyNEST package.

Sufficient stability conditions for multi-class constant retrial rate systems

We study multi-class retrial queueing systems with Poisson inputs, general service times, and an arbitrary numbers of servers and waiting places. A class-i blocked customer joins orbit i and waits in the orbit for retrial. Orbit i works like a single-server $$\cdot /M/1$$·/M/1 queueing system with exponential retrial time regardless of the orbit size. Such retrial systems are referred to as retrial systems with constant retrial rate. Our model is not only motivated by several telecommunication applications, such as wireless multi-access systems, optical networks, and transmission control protocols, but also represents independent theoretical interest. Using a regenerative approach, we provide sufficient stability conditions which have a clear probabilistic interpretation. We show that the provided sufficient conditions are in fact also necessary, in the case of a single-server system without waiting space and in the case of symmetric classes. We also discuss a very interesting case, when one orbit is unstable, whereas the rest of the system is stable.

Limit theorems for an infinite-server queuing system

We consider an infinite-server queuing system with a doubly stochastic Poisson input flow. Assuming that the service time does not have expectation, we prove limit theorems for the number of occupied servers. As a consequence, we obtain limit theorems for systems in which the input flow intensity is a regenerative process.

Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis

Abstract We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s). We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD). The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn ]/E[Yn ]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.

A batch arrival multi phase queueing system with random feedback in service and single vacation policy

We study a batch arrival Poisson input, k phases heterogeneous services with randomly feedback in services. The first phase of service is essential for all customers, but with probability γ1 a tagged customer chose second phase, with probability α1 feedback to tail of original queue or with probability β1 = 1 − γ1 − α1 leave the system. Also, after completion of the second phase, with probability γ2 the customer leads to the third service, or with probability α2 feedback to tail of original queue, or leaves the system with probability β2 = 1 − γ2 − α2. Like that, in kth phase feedback with probability αk or leaves the system with probability 1 − αk. After completion of each phases, the server either goes for a vacation with probability 𝜃(0 ≤ 𝜃 ≤ 1), or may continue to serve the next unit with probability 1 − 𝜃, if any. Otherwise, it remains in the system until a customer arrives, which is single vacation policy. We assume restricted admissibility of arriving batches in which not all batches are allowed to join the system at all times. In this paper we derive the steady- state equations, PGF’s of the system, and measures of sysytem.

Algorithm for computing the queue length distribution at various time epochs in DMAP/G(1, a, b)/1/N queue with batch-size-dependent service time

Abstract This paper presents a discrete-time single-server finite-buffer queue with Markovian arrival process and generally distributed batch-size-dependent service time. Given that infinite service time is not commonly encountered in practical situations, we suppose that the distribution of the service time has a finite support. Recently, a similar continuous-time system with Poisson input process was discussed by Banerjee and Gupta (2012). But unfortunately, their method is hard to apply in the analysis of discrete-time case with versatile Markovian point process due to the fact that the difference equation governing the boundary state probabilities is more complex than the continuous one. If we follow their ideas, we will eventually find that some important joint queue length distributions cannot be computed and thus some key performance measures cannot be derived. In this paper, replacing the finite support renewal distribution with an appropriate phase-type distribution, the joint state probabilities at various time epochs (arbitrary, pre-arrival and departure) have been obtained by using matrix analytic method and embedded Markov chain technique. Furthermore, UL-type RG-factorization is employed in numerical computation of block-structured Markov chains with finitely-many levels. Some numerical examples are presented to demonstrate the feasibility of the proposed algorithm for several service time distributions. Moreover, the impact of the correlation factor on loss probability and mean sojourn time is also investigated.

Congestion Probabilities in CDMA-Based Networks Supporting Batched Poisson Input Traffic

We propose a new multirate teletraffic loss model for the calculation of time and call congestion probabilities in CDMA-based networks that accommodate calls of different service-classes. The call arrival process follows a batched Poisson process, which is more “peaked” and “bursty” than the ordinary Poisson process. The call-admission-control policy is based on the partial batch blocking discipline. This policy accepts a part of the batch (one or more calls) and discards the rest, if the available resources are not enough to accept the whole batch. The proposed model takes into account multiple access interference, both the notion of local (soft) and hard blocking, the user’s activity, as well as interference cancellation. Although the analysis of the model does not lead to a product form solution of the steady state probabilities, we show that the call-level performance metrics, time and call congestion probabilities can be efficiently calculated based on approximate but recursive formulas. The accuracy of the proposed formulas are verified through simulation and found to be quite satisfactory. Comparison of the proposed model with that of Poisson input shows the necessity of the new model. We also show the consistency of the new model over changes of its parameters.

On the Evolution and Asymptotic Analysis of Open Markov Populations: Application to Consumption Credit

In this paper, we study, by means of randomized sampling, the long-run stability of some open Markov population fed with time-dependent Poisson inputs. We show that state probabilities within transient states converge—even when the overall expected population dimension increases without bound—under general conditions on the transition matrix and input intensities.Following the convergence results, we obtain ML estimators for a particular sequence of input intensities, where the sequence of new arrivals is modeled by a sigmoidal function. These estimators allow for the forecast, by confidence intervals, of the evolution of the relative population structure in the transient states.Applying these results to the study of a consumption credit portfolio, we estimate the implicit default rate.