Random Arrival Times Research Articles

Traffic Signal Timing Optimization for Heterogeneous Traffic Conditions Using Modified Webster’s Delay Model

Indian traffic is typically composed of different vehicle classes like motorized two-wheelers, three-wheelers, four-wheelers, and non-motorized modes, which vary widely in their static and dynamic characteristics. Such diverse group of vehicle classes sharing of the same right-of-way (ROW) results in a type of traffic behaviour called “gap filling” and “virtual lane”. At signalized intersections, this behaviour is manifested by the Probably-First-In-Probably-First-Out (PFIPFO) queuing behaviour, which has been defined and described in this paper. A literature review of the topic reveals that previous delay models have focused on homogeneous traffic conditions and cannot be used for the heterogeneous traffic conditions in countries like India without significant modifications. Basic Webster’s delay model is among the most widely used around the world, including India, for designing and evaluation of signalized intersections. In this model, the signalized intersection is treated as an M/D/1 queuing system with constant (or deterministic) service times and random arrival times. While this is a reasonable model for lane-disciplined, car-dominated traffic, its suitability for the heterogeneous traffic in India is dubious, as the service times are also rendered random in this case by the differences in vehicle characteristics. Hence an M/M/1 or M/M/N queuing model is more appropriate in such scenario. Considering these points, it is therefore necessary to modify Webster’s basic delay model to make it suitable for heterogeneous, weakly lane-disciplined, saturated traffic conditions in India. In the present study, a new model for random delay component using multichannel queuing theory and PFIPFO queuing behaviour is derived for Indian traffic conditions. The proposed model is validated using the results from a micro-simulation and finally it is used to optimize the traffic signal timing for three intersections in Bangalore city.

Capacity Limits of Diffusion-Based Molecular Timing Channels With Finite Particle Lifetime

This paper introduces capacity limits for molecular timing (MT) channels, where information is modulated in the release timing of small information particles with finite lifetime, and decoded from the time of arrivals at the receiver. It is shown that the random time of arrival can be represented as an additive noise channel, and for the diffusion-based MT (DBMT) channel this noise is distributed according to the Levy distribution. Lower and upper bounds on the capacity of the DBMT channel are derived for the case where the delay associated with the propagation of the information particles in the channel is finite, namely, when the information particles dissipate after a finite time interval. For the case where a single particle is released per channel use, these bounds are shown to be tight. When the transmitter simultaneously releases a large number of particles, the detector at the receiver may not be able to precisely detect the arrival time of all the particles. Therefore, two alternative models are considered: 1) detection based on the particle that arrives first or 2) detection based on the average arrival times. Lower and upper bounds on the capacities of these two models are derived, and the lower bound also provides a lower bound for the capacity of the DBMT channel. It is shown that by controlling the lifetime of the information particles, the capacity can increase polylogarithmically with the number of released particles. As each particle takes a random independent path, this diversity of paths is analogous to receiver diversity and can be used to considerably increase the achievable data rates.

Optimal Detection for One-Shot Transmission Over Diffusion-Based Molecular Timing Channels

This paper studies optimal detection for communication over diffusion-based molecular timing (DBMT) channels. The transmitter simultaneously releases multiple information particles, where the information is encoded in the time of release. The receiver decodes the transmitted information based on the random time of arrival of the information particles, which is modeled as an additive noise channel. For a DBMT channel without flow, this noise follows the Levy distribution. Under this channel model, the maximum-likelihood (ML) detector is derived and shown to have high computational complexity. It is also shown that under ML detection, releasing multiple particles improves performance, while for any additive channel with $\boldsymbol {\alpha }$ -stable noise where $\boldsymbol {\alpha }\boldsymbol { (such as the DBMT channel), under linear processing at the receiver, releasing multiple particles degrades performance relative to releasing a single particle . Hence, a new low-complexity detector, which is based on the first arrival (FA) among all the transmitted particles, is proposed. It is shown that for a small number of released particles, the performance of the FA detector is very close to that of the ML detector. On the other hand, error exponent analysis shows that the performance of the two detectors differ when the number of released particles is large.

Exploiting Diversity in One-Shot Molecular Timing Channels via Order Statistics

We study diversity in one-shot communication over molecular timing channels. We consider a channel model where the transmitter simultaneously releases a large number of information particles, while the information is encoded in the time of release . The receiver decodes the information based on the random time of arrival of the information particles. The random propagation is characterized by the general class of right-sided unimodal densities. We characterize the asymptotic exponential decrease rate of the probability of error as a function of the number of released particles, and denote this quantity as the system diversity gain . Four types of detectors are considered: 1) the maximum-likelihood (ML) detector; 2) a linear detector; 3) a detector that is based on the first arrival (FA) among all the transmitted particles; and 4) a detector based on the last arrival (LA). When the density characterizing the random propagation is supported over a large interval, we show that the simple FA detector achieves a diversity gain very close to that of the ML detector. On the other hand, when the density characterizing the random propagation is supported over a small interval, we show that the simple LA detector achieves a diversity gain very close to that of the ML detector.

Stochastic single-machine scheduling with random resource arrival times

Scheduling in an uncertain environment remains a meaningful yet challenging direction of research. In this paper, we consider a new scheduling setting from practical complex business applications, where resources (e.g., raw materials) used for processing jobs arrive randomly, due to reasons such as unstable transportation service caused by extreme weather conditions, unreliable suppliers, unpredictable industrial actions, etc. Further, jobs must be processed one by one and preemption is not allowed. The processing times of jobs are not known but their distribution. We incorporate these factors into a stochastic single-machine scheduling model and examine two different common types of objectives: minimizing total expected weighted completion time and minimizing total expected weighted squared completion time. We derive and prove a natural and intuitive optimal policy for the model with the first objective. Besides, we find that, under some mild conditions, the well-known policy in stochastic scheduling, WSEPT (weighted shortest expected processing time), still holds optimal for achieving either of objectives. The numerical example further supports and illustrates our results, which provide decision-makers insights into tricky uncertain scheduling problems.

A biophysical model examining the role of low-voltage-activated potassium currents in shaping the responses of vestibular ganglion neurons.

The vestibular nerve is characterized by two broad groups of neurons that differ in the timing of their interspike intervals; some fire at highly regular intervals, whereas others fire at highly irregular intervals. Heterogeneity in ion channel properties has been proposed as shaping these firing patterns (Highstein SM, Politoff AL. Brain Res 150: 182-187, 1978; Smith CE, Goldberg JM. Biol Cybern 54: 41-51, 1986). Kalluri et al. (J Neurophysiol 104: 2034-2051, 2010) proposed that regularity is controlled by the density of low-voltage-activated potassium currents (IKL). To examine the impact of IKL on spike timing regularity, we implemented a single-compartment model with three conductances known to be present in the vestibular ganglion: transient sodium (gNa), low-voltage-activated potassium (gKL), and high-voltage-activated potassium (gKH). Consistent with in vitro observations, removing gKL depolarized resting potential, increased input resistance and membrane time constant, and converted current step-evoked firing patterns from transient (1 spike at current onset) to sustained (many spikes). Modeled neurons were driven with a time-varying synaptic conductance that captured the random arrival times and amplitudes of glutamate-driven synaptic events. In the presence of gKL, spiking occurred only in response to large events with fast onsets. Models without gKL exhibited greater integration by responding to the superposition of rapidly arriving events. Three synaptic conductance were modeled, each with different kinetics to represent a variety of different synaptic processes. In response to all three types of synaptic conductance, models containing gKL produced spike trains with irregular interspike intervals. Only models lacking gKL when driven by rapidly arriving small excitatory postsynaptic currents were capable of generating regular spiking.

Fully Bayesian inference for α-stable distributions using a Poisson series representation

In this paper we develop an approach to Bayesian Monte Carlo inference for skewed α-stable distributions. Based on a series representation of the stable law in terms of infinite summations of random Poisson process arrival times, our framework leads to a simple representation in terms of conditionally Gaussian distributions for certain latent variables. Inference can therefore be carried out straightforwardly using techniques such as auxiliary variables versions of Markov chain Monte Carlo (MCMC) methods. The Poisson series representation (PSR) is further extended to practical application by introducing an approximation of the series residual terms based on exact moment calculations. Simulations illustrate the proposed framework applied to skewed α-stable simulated and real-world data, successfully estimating the distribution parameter values and being consistent with other (non-Bayesian) approaches. The methods are highly suitable for incorporation into hierarchical Bayesian models, and in this case the conditionally Gaussian structure of our model will lead to very efficient computations compared to other approaches.

Dynamic Antenna Management for Uplink Energy Efficiency on 802.11n Mobile Devices

An increasing number of mobile devices are being equipped with 802.11n interfaces to support bandwidth-intensive applications; however, the improved bandwidth increases power consumption. To address the issue, researchers are focusing on antenna management. In this paper, we present a dynamic antenna management (DAM) scheme to improve the uplink energy efficiency on mobile devices whose packet workloads may vary significantly and frequently. First, we model antenna management as an optimization problem, with the objective of minimizing the energy required to transmit a sequence of variable-length packets with random arrival times. Then, we propose an optimal offline algorithm to solve the problem, as well as a competitive online algorithm that has a provable performance guarantee and allows compatible implementations on 802.11n mobile devices. To evaluate our scheme, we conducted extensive simulations based on real mobile user traces and application transmission patterns. Nearly all commercial 802.11n mobile devices support the power save mode (PSM). Our results demonstrate that DAM can improve the energy efficiency of PSM significantly at a cost of slight throughput degradation.

The use of segmented cathodes to determine the spoke current density distribution in high power impulse magnetron sputtering plasmas

The localized target current density associated with quasi-periodic ionization zones (spokes) has been measured in a high power impulse magnetron sputtering (HiPIMS) discharge using an array of azimuthally separated and electrical isolated probes incorporated into a circular aluminum target. For a particular range of operating conditions (pulse energies up to 2.2 J and argon pressures from 0.2 to 1.9 Pa), strong oscillations in the probe current density are seen with amplitudes up to 52% above a base value. These perturbations, identified as spokes, travel around the discharge above the target in the E×B direction. Using phase information from the angularly separated probes, the spoke drift speeds, angular frequencies, and mode number have been determined. Generally, at low HiPIMS pulse energies Ep < 0.8 J, spokes appear to be chaotic in nature (with random arrival times), however as Ep increases, coherent spokes are observed with velocities between 6.5 and 10 km s−1 and mode numbers m = 3 or above. At Ep > 1.8 J, the plasma becomes spoke-free. The boundaries between chaotic, coherent, and no-spoke regions are weakly dependent on pressure. During each HiPIMS pulse, the spoke velocities increase by about 50%. Such an observation is explained by considering spoke velocities to be determined by the critical ionization velocity, which changes as the plasma composition changes during the pulse. From the shape of individual current density oscillations, it appears that the leading edge of the spoke is associated with a slow increase in local current density to the target and the rear with a more rapid decrease. The measurements show that the discharge current density associated with individual spokes is broadly spread over a wide region of the target.

Asynchronous Adaptation and Learning Over Networks—Part III: Comparison Analysis

In Part II [3] we carried out a detailed mean-square-error analysis of the performance of asynchronous adaptation and learning over networks under a fairly general model for asynchronous events including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. In this Part III, we compare the performance of synchronous and asynchronous networks. We also compare the performance of decentralized adaptation against centralized stochastic-gradient (batch) solutions. Two interesting conclusions stand out. First, the results establish that the performance of adaptive networks is largely immune to the effect of asynchronous events: the mean and mean-square convergence rates and the asymptotic bias values are not degraded relative to synchronous or centralized implementations. Only the steady-state mean-square-deviation suffers a degradation in the order of $\nu$, which represents the small step-size parameters used for adaptation. Second, the results show that the adaptive distributed network matches the performance of the centralized solution. These conclusions highlight another critical benefit of cooperation by networked agents: cooperation does not only enhance performance in comparison to stand-alone single-agent processing, but it also endows the network with remarkable resilience to various forms of random failure events and is able to deliver performance that is as powerful as batch solutions.

Asynchronous Adaptation and Learning Over Networks—Part II: Performance Analysis

In Part I of this paper, also in this issue, we introduced a fairly general model for asynchronous events over adaptive networks including random topologies, random link failures, random data arrival times, and agents turning on and off randomly. We performed a stability analysis and established the notable fact that the network is still able to converge in the mean-square-error sense to the desired solution. Once stable behavior is guaranteed, it becomes important to evaluate how fast the iterates converge and how close they get to the optimal solution. This is a demanding task due to the various asynchronous events and due to the fact that agents influence each other. In this Part II, we carry out a detailed analysis of the mean-square-error performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We derive analytical expressions for the mean-square convergence rate and the steady-state mean-square-deviation. The expressions reveal how the various parameters of the asynchronous behavior influence network performance. In the process, we establish the interesting conclusion that even under the influence of asynchronous events, all agents in the adaptive network can still reach an O(ν <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1 + γo'</sup> ) near-agreement with some γo <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">'</sup> > 0 while approaching the desired solution within O(ν) accuracy, where ν is proportional to the small step-size parameter for adaptation.

Asynchronous Adaptation and Learning Over Networks—Part I: Modeling and Stability Analysis

In this work and the supporting Parts II [2] and III [3], we provide a rather detailed analysis of the stability and performance of asynchronous strategies for solving distributed optimization and adaptation problems over networks. We examine asynchronous networks that are subject to fairly general sources of uncertainties, such as changing topologies, random link failures, random data arrival times, and agents turning on and off randomly. Under this model, agents in the network may stop updating their solutions or may stop sending or receiving information in a random manner and without coordination with other agents. We establish in Part I conditions on the first and second-order moments of the relevant parameter distributions to ensure mean-square stable behavior. We derive in Part II expressions that reveal how the various parameters of the asynchronous behavior influence network performance. We compare in Part III the performance of asynchronous networks to the performance of both centralized solutions and synchronous networks. One notable conclusion is that the mean-square-error performance of asynchronous networks shows a degradation only of the order of $O(\nu)$, where $\nu$ is a small step-size parameter, while the convergence rate remains largely unaltered. The results provide a solid justification for the remarkable resilience of cooperative networks in the face of random failures at multiple levels: agents, links, data arrivals, and topology.

Protecting dissipative quantum state preparation via dynamical decoupling

We show that dissipative quantum state preparation processes can be protected against qubit dephasing by interlacing the state preparation control with dynamical decoupling (DD) control consisting of a sequence of short $\ensuremath{\pi}$ pulses. The inhomogeneous broadening can be suppressed to second order of the pulse interval, and the protection efficiency is nearly independent of the pulse sequence but determined by the average interval between pulses. The DD protection is numerically tested and found to be efficient against inhomogeneous dephasing on two exemplary dissipative state preparation schemes that use collective pumping to realize many-body singlets and linear cluster states, respectively. Numerical simulation also shows that the state preparation can be efficiently protected by $\ensuremath{\pi}$ pulses with completely random arrival time. Our results make possible the application of these state preparation schemes in inhomogeneously broadened systems. DD protection of state preparation against dynamical noises is also discussed using the example of Gaussian noise with a semiclasscial description.

Cross-Layer Design and Optimization of CDMA Networks in Frequency-Selective Fading Channels

The cross-layer optimization technique in a recent paper [1] is extended and analyzed for frequency-selective channels with maximum ratio combining (MRC) coherent RAKE receiver. We assume random arrival time for a new user within a frame, and consider discrete spreading factors as a practical case. We show that the optimum outer-loop SNR-target does not depend on the received number of paths (Lp), and neither is dependent on the Uniformly-distributed arrival time of new users. Furthermore, an increase in Lp reduces the sum-throughput and the achievable gain in sum-throughput through our optimization approach.

CORRELATION OFCHANDRAPHOTONS WITH THE RADIO GIANT PULSES FROM THE CRAB PULSAR

No apparent correlation was found between giant pulses (GPs) and X-ray photons from the Crab pulsar during 5.4 hours of simultaneous observations with the Green Bank Telescope at 1.5 GHz and Chandra X-Ray Observatory primarily in the energy range 1.5-4.5 keV. During the Crab pulsar periods with GPs the X-ray flux in radio emission phase windows does not change more than by +-10% for main pulse (MP) GPs and +-30% for interpulse (IP) GPs. During giant pulses themselves, the X-ray flux does not change more than by two times for MP GPs and 5 times for IP GPs. All limits quoted are compatible with 2-sigma fluctuations of the X-ray flux around the sets of false GPs with random arrival times. The results speak in favor of changes in plasma coherence as the origin of GPs. However, the results do not rule out variations in the rate of particle creation if the particles that emit coherent radio emission are mostly at the lowest Landau level.

Liquidity cost of market orders in the Taiwan Stock Market: A study based on an order-driven agent-based artificial stock market

We developed an order-driven agent-based artificial stock market to analyze the liquidity costs of market orders in the Taiwan Stock Market (TWSE). The agent-based stock market was based on the DFGIS model proposed by Daniels, Farmer, Gillemot, Iori and Smith (Daniels et al., 2003). We also improved the DFGIS model by using two average order size parameters. When tested on 10 stocks and securities in the market, the model-simulated liquidity costs were higher than those of the TWSE data. We identified some possible factors that have contributed to this result: 1) the overestimated effective market order size, which can be improved by using two average order size parameters; 2) the random market order arrival time designed in the DFGIS model; 3) the zero-intelligence of the artificial agents in our model; and 4) the price of the effective market order. We continued improving the model so that it could be used to study liquidity costs and to devise liquidation strategies for stocks and securities traded in the Taiwan Stock Market.

Diverse Path Routing with Interference and Reusability Consideration in Wireless Mesh Networks

Multipath routing has been extensively employed in wireless mesh networks (WMNs) for providing network reliability and survivability, therefore, improves energy consumptions. To provide network survivability, each user should be protected against failures, either node or link failures. For each request, a primary path is set up for normal transmission, and an alternate path (protection path) should also be provided to protect the request in case of network failure. In this paper, we study how to provide survivability using multi-path scheme for dynamic network traffic, where users' requests have random arrival times. Compared with previous work, our scheme considers interference and reusability factors when providing multiple paths for each request. By applying our scheme, the numerical results show that we can accommodate about 17% more requests than previous schemes. Meanwhile, the results show that our scheme not only accommodates more requests, but also takes less running time to find a solution for each request.

Nonuniform Linear Regression With Block-Wise Sample-Minimum Preprocessing

We analyze the statistical properties of slope estimates obtained from linear regression with sample-minimum Erlang variates. The sample-minimum of sequential blocks has the effect of introducing nonuniform time samples. We show that this nonuniformity has negligible effect on the slope estimate variance, but introduces a spurious low-frequency component in the power spectrum, which can be detrimental for low-bandwidth tracking applications. The analysis shows that this effect can be moderated by choosing a sufficiently large number of sample-minimum output samples in the linear regression. These results are useful, for example, in clock synchronization over packet networks, where the random variates model packet arrival times.

Engineering atomic quantum reservoirs for photons

We present protocols for creating entangled states of two modes of the electromagnetic field by using a beam of atoms crossing microwave resonators. The atoms are driven by a transverse, classical field and pump correlated photons into (i) two modes of a cavity and (ii) the modes of two distant cavities. The protocols are based on a stochastic dynamics, characterized by random arrival times of the atoms and by random interaction times between atoms and cavity modes. The resulting effective model yields a master equation, whose steady state is an entangled state of the cavity modes. In this respect, the atoms act like a quantum reservoir, pulling the cavity modes into an entangled, Einstein-Podolski-Rosen state, whose degree of entanglement is controlled by the intensity and the frequency of the transverse field. This scheme is robust against stochastic fluctuations in the atomic beam, and it does not require atomic detection nor velocity selection.

Performance of the CMS drift-tube chamber local trigger with cosmic rays

The performance of the Local Trigger based on the drift-tube system of the CMS experiment has been studied using muons from cosmic ray events collected during the commissioning of the detector in 2008. The properties of the system are extensively tested and compared with the simulation. The effect of the random arrival time of the cosmic rays on the trigger performance is reported, and the results are compared with the design expectations for proton-proton collisions and with previous measurements obtained with muon beams.