Tandem Network Research Articles

Conditioned tandem networks.

Conditioned tandem networks.

Benchmarking deep learning-based models on nanophotonic inverse design problems

Photonic inverse design concerns the problem of finding photonic structures with target optical properties. However, traditional methods based on optimization algorithms are time-consuming and computationally expensive. Recently, deep learning-based approaches have been developed to tackle the problem of inverse design efficiently. Although most of these neural network models have demonstrated high accuracy in different inverse design problems, no previous study has examined the potential effects under given constraints in nanomanufacturing. Additionally, the relative strength of different deep learning-based inverse design approaches has not been fully investigated. Here, we benchmark three commonly used deep learning models in inverse design: Tandem networks, Variational Auto-Encoders, and Generative Adversarial Networks. We provide detailed comparisons in terms of their accuracy, diversity, and robustness. We find that tandem networks and Variational Auto-Encoders give the best accuracy, while Generative Adversarial Networks lead to the most diverse predictions. Our findings could serve as a guideline for researchers to select the model that can best suit their design criteria and fabrication considerations. In addition, our code and data are publicly available, which could be used for future inverse design model development and benchmarking.

Conditional Waiting Time Analysis in Tandem Polling Queues

We analyze a tandem network of polling queues with two product types and two stations. We assume that external arrivals to the network follow a Poisson process, and service times at each station are exponentially distributed. For this system, we determine the mean conditional waiting time for an arriving customer using a sample path analysis approach. The approach classifies system state upon arrival into scenarios and exploits an inherent structure in the sequence of events that occur till the customer departs to obtain conditional waiting time estimates. We conduct numerical studies to show both the accuracy of our conditional waiting time estimates and their practical importance.

An improved tandem neural network for the inverse design of nanophotonics devices

The tandem neural network with a modified loss function is used to inversely design the nanophotonic device from a desired spectrum, to obtain the corresponding structural parameters. High prediction accuracy is demonstrated on the inverse design of grating coupler examples, etc. Different activation functions and loss functions used in the tandem network are compared to find the optimum scheme. The method can be readily applied to many other cases in order to obtain the design parameters instantaneously from the device response curves.

Thiol-Substituted Poly(2-oxazoline)s with Photolabile Protecting Groups-Tandem Network Formation by Light.

Herein, we present a novel polymer architecture based on poly(2-oxazoline)s bearing protected thiol functionalities, which can be selectively liberated by irradiation with UV light. Whereas free thiol groups can suffer from oxidation or other spontaneous reactions that degrade polymer performance, this strategy with masked thiol groups offers the possibility of photodeprotection on demand with spatio-temporal control while maintaining polymer integrity. Here, we exploit this potential for a tandem network formation upon irradiation with UV light by thiol deprotection and concurrent crosslinking via thiol-ene coupling. The synthesis of the novel oxazoline monomer 2-{2-[(2-nitrobenzyl)thio]ethyl}-4,5-dihydrooxazole (NbMEtOxa) carrying 2-nitrobenzyl-shielded thiol groups and its cationic ring-opening copolymerization at varying ratios with 2-ethyl-2-oxazoline (EtOxa) is described. The tandem network formation was exemplarily demonstrated with the photoinitator 2-hydroxy-2-methylpropiophenone (HMPP) and pentaerythritol tetraacrylate (PETA), a commercially available, tetrafunctional vinyl crosslinker. The key findings of the conducted experiments indicate that a ratio of ~10% NbMEtOxa repeat units in the polymer backbone is sufficient for network formation and in-situ gelation in N,N-dimethylformamide.

A semi-product-form for a pair of queues with finite batches: Equilibrium state probabilities and response time densities

A Markovian network of two queues, with finite size batch Poisson arrivals and departures, is solved approximately, but to arbitrary accuracy, for its equilibrium state probabilities. Below a pair of thresholds on the queue lengths, a modification of the Spectral Expansion Method is used to construct a semi-product-form at all lengths of one queue in a finite lattice strip defined by the threshold of the other queue. No additional special arrival streams are required, for example at empty queues, from which it is already known that a product-form can be constructed. Hence the first exact closed form solution for the equilibrium probabilities in an unmodified Markovian queueing network with batches is obtained, the only constraint being finiteness of the batches. The method is illustrated numerically, first in a tandem network and then in a two-node network with feedback. Simulation results confirm convincingly the precision of the method, and partial batch forwarding and discarding are thereby compared quantitatively. Response time distributions are derived using the generating function method, which complements well the semi-product form of the equilibrium state probabilities. Again, agreement with simulation is excellent. The regenerative simulation method was used, so that no warm-up period was needed, and the statistical estimates for the 95% confidence bands are explained for the different cases of state occupancy and response time prediction at equilibrium.

A Survey on Network Calculus Tools for Network Infrastructure in Real-Time Systems

Network Calculus is an established analytical framework which can provide deterministic estimates of latency and buffer requirements for feed-forward packet-switched communication networks. Researchers find it useful in analyzing network performance in real-time systems. As there are several Network Calculus tools and software packages for estimating network performance, it is important to select suitable Network Calculus tools for network analysis problems. This article introduces twelve established tools for Network Calculus analysis and compares their advantages and disadvantages in terms of their applicability for various systems and analysis needs. We also provide recommendations for users to select the suitable tools for research. Five public tools, namely DiscoDNC, RTC Toolbox, Deborah, CyNC, and nc-tandem-tight, are chosen to analyze end-to-end delay in a series of tandem networks for their performance demonstration. Simulations of the same tandem networks are implemented to compare with the analytical results achieved by the Network Calculus tools. To our best knowledge, this is the first comprehensive study that compares existing tools of Network Calculus analysis for real-time system network infrastructure. Our aim is to provide quick guidance to research communities for selecting suitable tools to analyze delay performance of networks.

On tandem stochastic networks with time-deteriorating product quality

We consider an n-site tandem stochastic production network where each product moves sequentially through the sites, and the product's quality deteriorates with its sojourn time in the system. At each site the product goes through two stages: the first stage is a processing operation with a generally-distributed random duration. This operation either does or does not conclude successfully; in the latter case, the operation is repeated immediately. Once the processing operation concludes successfully, the product goes through an inspection stage lasting a generally-distributed random duration. At the end of the inspection the product's state is determined as follows: either (i) it requires additional processing and moves forward to the next site; or (ii) it is found ‘good’ and exits the network with quality value depending on its total sojourn time in the system; or (iii) it is declared ‘failed’, discarded, and exits the network with zero quality value. Two scenarios are analysed: (i) a new product enters the system only after the preceding product has exited and (ii) the network is a tandem Jackson-type system. For each scenario, we construct both time-dependent and quality-dependent performance measures. In the case where the sites can be arranged in an arbitrary order, we derive easy to implement optimal index-type policies of ordering the sites so as to maximise the quality rate of the production network.

Three Node Tandem Communication Network Model with Duane Arrival Process having Phase Type Service

Three Node Tandem Communication Network Model with Duane Arrival Process having Phase Type Service

Minimum carbon dioxide emission based selection of traffic route with unsignalised junctions in tandem network

PurposeThe purpose of this paper is to provide a traffic route selection strategy based on minimum carbon dioxide (CO2) emission by vehicles over different route choices.Design/methodology/approachThe study used queuing theory for Markovian M/M/1 model over the road junctions to assess total time spent over each of the junctions for a route with junctions in tandem. With parameters of distance, mean service rate at the junction, the number of junctions and fuel consumption rate, which is a function of variable average speed, the CO2 emission is estimated over each of the junction in tandem and collectively over each of the routes.FindingsThe outcome of the study is a mathematical formulation, using queuing theory to estimate CO2 emissions over different route choices. Research finding estimated total time spent and subsequent CO2 emission for mean arrival rates of vehicles at junctions in tandem. The model is validated with a pilot study, and the result shows the best vehicular route choice with minimum CO2 emissions.Research limitations/implicationsProposed study is limited to M/M/1 model at each of the junction, with no defection of vehicles. The study is also limited to a constant mean arrival rate at each of the junction.Practical implicationsThe work can be used to define strategies to route vehicles on different route choices to reduce minimum vehicular CO2 emissions.Originality/valueProposed work gives a solution for minimising carbon emission over routes with unsignalised junctions in the tandem network.

Time-varying many-server finite-queues in tandem: Comparing blocking mechanisms via fluid models

This paper focuses on the mechanism of Blocking Before Service (BBS), in time-varying many-server queues in tandem. BBS arises in telecommunication networks, production lines and healthcare systems. We model a stochastic tandem network under BBS and develop its corresponding fluid limit, which includes reflection due to jobs lost. Comparing our fluid model against simulation shows that the model is accurate and effective. This gives rise to design/operational insights regarding network throughput, under both BBS and BAS (Blocking After Service).

Cooperation and sharing costs in a tandem queueing network

We consider a tandem network of queues with a Poisson arrival process to the first queue. Service times are assumed to be exponential. In cases where they are not, we additionally assume a processor sharing service discipline in all servers. Consecutive servers may cooperate by pooling resources which leads to the formation of a single combined server that satisfies the aggregated service demands with a greater service rate. On this basis we define a cooperative game with transferable utility, where the cost of a coalition is the steady-state mean total number of customers in the system formed by its members. We show that the game is subadditive, leading to full cooperation being socially optimal. We then show the non-emptiness of the core, despite the characteristic function being neither monotone, nor concave. Finally, we derive several well-known solution concepts, including the Shapley value, the Banzhaf, value and the nucleolus, for the case where servers have equal mean service demands. In particular, we show that all three values coincide in this case.

Queues on a Dynamically Evolving Graph

This paper considers a population process on a dynamically evolving graph, which can be alternatively interpreted as a queueing network. The queues are of infinite-server type, entailing that at each node all customers present are served in parallel. The links that connect the queues have the special feature that they are unreliable, in the sense that their status alternates between ‘up’ and ‘down’. If a link between two nodes is down, with a fixed probability each of the clients attempting to use that link is lost; otherwise the client remains at the origin node and reattempts using the link (and jumps to the destination node when it finds the link restored). For these networks we present the following results: (a) a system of coupled partial differential equations that describes the joint probability generating function corresponding to the queues’ time-dependent behavior (and a system of ordinary differential equations for its stationary counterpart), (b) an algorithm to evaluate the (time-dependent and stationary) moments, and procedures to compute user-perceived performance measures which facilitate the quantification of the impact of the links’ outages, (c) a diffusion limit for the joint queue length process. We include explicit results for a series relevant special cases, such as tandem networks and symmetric fully connected networks.

Time-varying tandem queues with blocking: modeling, analysis, and operational insights via fluid models with reflection

In this paper, we develop time-varying fluid models for tandem networks with blocking. Beyond having their own intrinsic value, these mathematical models are also limits of corresponding many-server stochastic systems. We begin by analyzing a two-station tandem network with a general time-varying arrival rate, a finite waiting room before the first station, and no waiting room between the stations. In this model, customers that are referred from the first station to the second when the latter is saturated (blocked) are forced to wait in the first station while occupying a server there. The finite waiting room before the first station causes customer loss and, therefore, requires reflection analysis. We then specialize our model to a single station (many-server fluid limit of the $$G_t/M/N/(N +H)$$ queue), generalize it to k stations in tandem, and allow finite internal waiting rooms. Our models yield operational insights into network performance, specifically on the effects of line length, bottleneck location, waiting room size, and the interaction among these effects.

Traffic Allocation for Low-Latency Multi-Hop Networks With Buffers

For buffer-aided tandem networks consisting of relay nodes and multiple channels per hop, we consider two traffic allocation schemes, namely local allocation and global allocation, and investigate the end-to-end latency of a file transfer. We formulate the problem for generic multi-hop queuing systems and subsequently derive closed-form expressions of the end-to-end latency. We quantify the advantages of the global allocation scheme relative to its local allocation counterpart, and we conduct an asymptotic analysis on the performance gain when the number of channels in each hops increases to infinity. The traffic allocations and the analytical delay performance are validated through simulations. Furthermore, taking a specific two-hop network with millimeter-wave (mm-wave) as an example, we derive lower bounds on the average end-to-end latency, where Nakagami- $m$ fading is considered. Numerical results demonstrate that, compared with the local allocation scheme, the advantage of global allocation grows as the number of relay nodes increases, at the expense of higher complexity that linearly increases with the number of relay nodes. It is also demonstrated that a proper deployment of relay nodes in a linear mm-wave network plays an important role in reducing the average end-to-end latency, and the average latency decays as the mm-wave channels become more deterministic. These findings provide insights for designing multi-hop mm-wave networks with low end-to-end latency.

SIEGMUND DUALITY FOR MARKOV CHAINS ON PARTIALLY ORDERED STATE SPACES

For a Markov chain on a finite partially ordered state space, we show that its Siegmund dual exists if and only if the chain is Möbius monotone. This is an extension of Siegmund's result for totally ordered state spaces, in which case the existence of the dual is equivalent to the usual stochastic monotonicity. Exploiting the relation between the stationary distribution of an ergodic chain and the absorption probabilities of its Siegmund dual, we present three applications: calculating the absorption probabilities of a chain with two absorbing states knowing the stationary distribution of the other chain; calculating the stationary distribution of an ergodic chain knowing the absorption probabilities of the other chain; and providing a stable simulation scheme for the stationary distribution of a chain provided we can simulate its Siegmund dual. These are accompanied by concrete examples: the gambler's ruin problem with arbitrary winning/losing probabilities; a non-symmetric game; an extension of a birth and death chain; a chain corresponding to the Fisher–Wright model; a non-standard tandem network of two servers, and the Ising model on a circle. We also show that one can construct a strong stationary dual chain by taking the appropriate Doob transform of the Siegmund dual of the time-reversed chain.

Pooling in tandem queueing networks with non-collaborative servers

Abstract This paper considers pooling several adjacent stations in a tandem network of single-server stations with finite buffers. When stations are pooled, we assume that the tasks at those stations are pooled but the servers are not. More specifically, each server at the pooled station picks a job from the incoming buffer of the pooled station and conducts all tasks required for that job at the pooled station before that job is placed in the outgoing buffer. For such a system, we provide sufficient conditions on the buffer capacities and service times under which pooling increases the system throughput by means of sample-path comparisons. Our numerical results suggest that pooling in a tandem line generally improves the system throughput—substantially in many cases. Finally, our analytical and numerical results suggest that pooling servers in addition to tasks results in even larger throughput when service rates are additive and the two systems have the same total number of storage spaces.

Minimum Flow Time in a Tandem Two-Server Fluid Network

We consider a tandem two-server fluid network with two fluid types. Each server in the network has two buffers, one for each fluid, and the capacity of each server can be shared among the fluids. An initial amount of fluids is to be processed by both servers and drained through the system. We determine the processing rates for which the servers' capacity is optimally shared, with the objective of minimizing the total flow time. Three cases of the optimal strategy are discussed.

On a tandem queue with batch service and its applications in wireless sensor networks

We present a tandem network of queues 0,dots , s-1. Customers arrive at queue 0 according to a Poisson process with rate lambda . There are s independent batch service processes at exponential rates mu _0, dots , mu _{s-1}. Service process i, i=0, dots , s-1, at rate mu _i is such that all customers of all queues 0, dots , i simultaneously receive service and move to the next queue. We show that this system has a geometric product-form steady-state distribution. Moreover, we determine the service allocation that minimizes the waiting time in the system and state conditions to approximate such optimal allocations. Our model is motivated by applications in wireless sensor networks, where s observations from different sensors are collected for data fusion. We demonstrate that both optimal centralized and decentralized sensor scheduling can be modeled by our queueing model by choosing the values of mu _i appropriately. We quantify the performance gap between the centralized and decentralized schedules for arbitrarily large sensor networks.

Decentralized Estimation With Dependent Gaussian Observations

This paper considers decentralized estimation with correlated noises under the Bayesian framework. For a tandem network with correlated additive Gaussian noises, we establish that threshold quantizers on local observations are optimal in the sense of maximizing Fisher information at the fusion center; this is true despite the fact that subsequent estimators may differ at the fusion center, depending on the statistical distribution of the parameter to be estimated. In addition, it is always beneficial to have the better sensor, i.e., the one with higher signal-to-noise ratio, serve as the fusion center in a tandem network. Finally, we identify different correlation regimes in terms of their impact on the estimation performance. These include the well-known case where negatively correlated noise benefits estimation performance as it facilitates noise cancellation, as well as two distinct regimes with positively correlated noises.