Switchover Time Research Articles

Workload analysis of a two-queue fluid polling model

AbstractIn this paper, we analyze a two-queue random time-limited Markov-modulated polling model. In the first part of the paper, we investigate the fluid version: fluid arrives at the two queues as two independent flows with deterministic rate. There is a single server that serves both queues at constant speeds. The server spends an exponentially distributed amount of time in each queue. After the completion of such a visit time to one queue, the server instantly switches to the other queue, i.e., there is no switch-over time.For this model, we first derive the Laplace–Stieltjes transform (LST) of the stationary marginal fluid content/workload at each queue. Subsequently, we derive a functional equation for the LST of the two-dimensional workload distribution that leads to a Riemann–Hilbert boundary value problem (BVP). After taking a heavy-traffic limit, and restricting ourselves to the symmetric case, the BVP simplifies and can be solved explicitly.In the second part of the paper, allowing for more general (Lévy) input processes and server switching policies, we investigate the transient process limit of the joint workload in heavy traffic. Again solving a BVP, we determine the stationary distribution of the limiting process. We show that, in the symmetric case, this distribution coincides with our earlier solution of the BVP, implying that in this case the two limits (stationarity and heavy traffic) commute.

Assessment of Behavioural Preparedness on Recovery Outcomes in Patients Undergoing Abdominal Surgeries

Introduction: Behavioural preparedness is the process of preparing patients for the psychological and emotional challenges that may be encountered during and after surgery. This can include providing education about the surgical procedure and postoperative recovery, as well as training in coping strategies and techniques to manage anxiety, fear, and other negative emotions. Prior sensitisation is a form of behavioural preparedness that involves providing patients with information about the potential outcomes of their surgery in advance, in order to help them better understand and prepare for potential challenges. It has been suggested that providing this type of education and training may reduce patient anxiety, increase co-operation with medical staff, and improve recovery, potentially leading to shorter hospital stays and reduced medication needs. Aim: To assess the effects of behavioural preparedness and prior sensitisation on psychological aspects, recovery outcomes, and user satisfaction in patients undergoing abdominal surgeries. Materials and Methods: The study will be undertaken on patients in the Inpatient Department (IPD) of Department of Surgery in a rural tertiary care hospital in central India, during a period spanning two months. All adult patients (aged 18-60) undergoing elective abdominal surgical procedures under anaesthesia in the IPD of surgery will be eligible. The patients will be randomly selected and interviewed preoperatively, dividing them into two groups those receiving the intervention and those receiving standard care with no intervention. The investigator will provide an oral presentation to the intervention group regarding their recovery outcomes and expectations. Subjects will be evaluated with a Visual Analog Scale (VAS) scale for pain, RAND Short Form health Survey (SF36) questionnaire for physical mobility, RAND Patient Satisfaction Questionnaire III (PSQ-18) instrument for user satisfaction, length of hospital stay and analgesic switchover time on a survey form and the Spielberger State-Trait Anxiety Inventory (STAI) forms Y1 and Y2 for comparison of preoperative and postoperative negative affects. Effects of the intervention on recovery outcomes will be compared via the Chi-square test, the Mann-Whitney U test for comparison of qualitative data between the two groups and the Student’s Unpaired t-test for comparison of quantitative data between the groups. Wilcoxon’s Signed Rank test and the Student’s paired t-test will be used for analysing qualitative and quantitative input between preoperative and postoperative states. Conclusion: The study seeks to determine if a significant difference occurs from providing patients withprior knowledge about their outcomes and establishing the benefits of psychological preparedness as a cost-effective method in improving outcomes and postoperative recovery

Asymptotic optimality of the binomial-exhaustive policy for polling systems with large switchover times

We study an optimal-control problem of polling systems with large switchover times, when a holding cost is incurred on the queues. In particular, we consider a stochastic network with a single server that switches between several buffers (queues) according to a pre-specified order, assuming that the switchover times between the queues are large relative to the processing times of individual jobs. Due to its complexity, computing an optimal control for such a system is prohibitive, and so we instead search for an asymptotically optimal control. To this end, we first solve an optimal control problem for a deterministic relaxation (namely, for a fluid model), that is represented as a hybrid dynamical system. We then “translate” the solution to that fluid problem to a binomial-exhaustive policy for the underlying stochastic system, and prove that this policy is asymptotically optimal in a large-switchover-time scaling regime, provided a certain uniform integrability (UI) condition holds. Finally, we demonstrate that the aforementioned UI condition holds in the following cases: (i) the holding cost has (at most) linear growth, and all service times have finite second moments; (ii) the holding cost grows at most at a polynomial rate (of any degree), and the service-time distributions possess finite moment generating functions.

A Linear-Array Receiver AFE Circuit Embedded 8-to-1 Multiplexer for Direct ToF Imaging LiDAR Applications

To increase the light detection and ranging (LiDAR) system spatial resolution, the multiple photodetectors are typically deployed in the receiver. An equivalent linear-array receiver with multiplexing operation scheme is presented for the direct time of flight (dToF) LiDAR applications. In particular, the analog front-end (AFE) circuit of the proposed receiver mainly consists of eight transimpedance preamplifiers (preTIAs), a dummy preTIA, a post amplifier (PA) with an 8-to-1 multiplexer, an analog output buffer and a timing discriminator. The proposed AFE circuit, which achieves a transimpedance gain of ~106 dB <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Omega $ </tex-math></inline-formula> , a bandwidth of ~220 MHz, an equivalent input-referred noise current of ~5.1 pA/Hz0.5 and a channel switchover time of 6 ns, was fabricated in a 65 nm standard CMOS technology. The associated DC power consumption is 137 mW with a power supply of 2.5 V. The total area of the proposed AFE circuit, which includes the circuit core, bias circuits and I/O PADs, is approximately equal to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1.2\times 1.2$ </tex-math></inline-formula> mm2.

An improved nonlinear path following method with on-line transition trajectory generation for fixed-wing unmanned aerial vehicles

To enhance the path following ability for fixed-wing unmanned aerial vehicles, and solve the stability and high-accuracy tracking problems due to inappropriate route switchover time during intense maneuvers, an improved nonlinear path following method with on-line transition trajectory generation was proposed in the article. Firstly, the influence of the guidance distance to the nonlinear path following method was verified through a flight experiment, and the importance of the critical time for route switchover was deduced. The on-line transition trajectory generation was expected to realize the automation of the switchover process, including the computation of the critical switchover time and desired paths. Secondly, to generate the on-line transition trajectory, the computation method was derived for typical intense maneuvers, such as the turning maneuver for square trajectory, or the converging maneuver to the expected trajectory under initial numerous errors (such as modifying the waypoint during a flight mission). Finally, to solve the situations in which the transition trajectory does not exist, an adaptive guidance distance algorithm was proposed to improve the flight stability and accuracy. From the simulation and flight experiment results, stability and high accuracy can be guaranteed for different situations with the proposed methods. The path following error is smaller than 1.0 m when it is converged (in downwind or upwind situations), which is important for the method to be used widely.

Calibration of cavity pressure simulation using autoencoder and multilayer perceptron neural networks

AbstractNumerical simulations of polymer melt flow behavior in cavities help predict and optimize injection molding process parameters. However, simulation and actual results may differ because of simplified mathematical models, inaccurate processing conditions, material property settings, and machine aging, among other factors. Therefore, simulated optimal process parameters cannot be directly applied in practice. This study applied machine learning to generate a virtual–actual correction model to improve the accuracy of simulation results, especially the cavity pressure profile, a key indicator of injection‐molding quality for identifying ideal process parameter settings such as filling‐to‐packing switchover time and holding pressure. This method does not require big data for model training to enhance its practicality. Therefore, the correction model is only suitable for specific settings. A set of injection molding machines, molds, and processed materials were used for experimental verification. An autoencoder model was used to extract the features of simulation and actual cavity pressure curves. Then, a multilayer perceptron model was used to determine a relationship between simulation and actual features. The autoencoder was used to decode simulated features into cavity pressure curves. The proposed method was verified with dumbbell‐shaped specimens; the correlation between simulated and actual cavity pressures was greatly improved from 81% to 98%.

Optimal Profit Analysis of Machine Repair Problem with Repair in Phases and Organizational Delay

In this article, we study machine repair problems (MRP) consisting of the finite number of operating machines with the provisioning of the finite number of warm standby machines under the care of a single unreliable server. For the machining system’s uninterrupted functioning, an operating machine is immediately replaced with the available warm standby machine in negligible switchover time whenever it fails. The concept of threshold vacation policy: N-policy is also considered. Under this vacation policy, the server starts to serve the failed machines on the accumulation of a pre-specified number of failed machines in the system. The server continues until the system is empty from the failed machines; after that, the server goes for vacation. The notion of an organizational delay, server breakdown, and repair in multiple phases is also conceptualized to build the studied model more realistic. The recursive matrix method is used to find steady-state queue size distribution, and subsequently, various system performance measures are also developed to validate the studied model. The optimal analysis has been performed to identify the critical design parameters for the governing model. The state-of-the-art of the present study is its mathematical modeling of the multi-machine stochastic problem with varied limitations and strategies. The methodology to obtain queue size distribution, optimal design parameters, is beneficial for dealing with other complex and sophisticated real-time machining problems in the service system, computer and communication system, manufacturing and production system, etc. The present problem is limited to fewer machines, which can be extended to more machines with different topologies with high computational facilities.

Effect of polarity shift on the performance of electrocoagulation process for the treatment of produced water

A novel electrocoagulation (EC) system for the treatment of produced water (PW), with a provision to shift polarity is designed with the aim of reducing the problems resulting from electrode passivation. The enhancement of performance in terms of the rate and completion of the pollutant removal, energy and electrode consumption, sludge formation and ultimately the operating cost has been investigated by performing statistically designed experiments using RSM. The switching mode operation of EC had brought about significant improvement in the oil removal than the conventional mode. The polarity changeover in short span of batch recirculation time (BRT) was found to be more effective. Greater current density (CD) and supporting electrolyte concentration (SC) were found to enable a still lower switchover time (SOT) so that changeover frequency can further be increased. It was possible to remove a maximum of 99% COD and 98% Oil & Grease from a PW sample having initial concentration of 360 mgL−1of oil (1280 mgL− 1COD) at BRT of 15 min, CD of 1.6 Adm−2, SC of 3 gL-1 and SOT of 1 min. The combination of operating variables (BRT- 3 min, CD- 2.14 Adm−2SC- 3 gL−1and SOT- 1.9 min) giving minimum operating cost (0.65 US$/kg COD removed) achieving oil removal (88%) meeting discharge standards was found out by optimizing the RSM models for cost and oil removal. The method can be considered as an effective alternative for treating PW especially in offshore oil basins where time and space are the major constraints.

Reliability Prediction of Computing Network with Software and Hardware Failures

In this paper, we investigate the reliability and queueing performance indices for the fault-tolerant computing network having a finite number of unreliable operating components with the provision of warm standby components. Operating and standby components are governed by dedicated software which is also prone to random failure. On failure of operating components, available standby component(s) may switch from the standby state to operating state with negligible switchover time. The switchover process may also fail due to some automation hindrance. The computing network is also subjected to common cause failure in lieu of external cause. The studied redundant fault-tolerant computing network is framed as a Markovian machine interference model with exponentially distributed inter-failure times and service times. For the reliability prediction of the computing network, various performance measures, namely, mean-time-to-failure (MTTF), reliability/availability, failure frequency, etc., have been formulated in terms of transient-state probabilities which we have obtained using the spectral method. To show the practicability of the developed model, numerical simulation has been done. Sensitivity analysis of reliability and other indices of the computing network with respect to different network parameters has been presented, and results are summarized in the tables and graphs. Finally, future scope and concluding remarks have been included.

Computing the Moments of Polling Models with Batch Poisson Arrivals by Transform Inversion

A polling model is defined as a queueing station with a single server serving multiple queues following a certain rule to determine when to stop serving one queue and which queue to serve next. The key to much of the analysis of these systems is to obtain the first two moments of queue lengths at polling instants, which are defined as the instants when the server starts to serve each queue. This study develops a novel approach, in which the generating functions of queue lengths at polling instants are computed iteratively. Transform inversion is then applied to invert these generating functions to obtain their first two moments efficiently. Because the expected waiting time of each queue depends on some basic distributions, such as the service time distributions, the switchover distributions, and the arrival batch distributions only through their first two moments, this study proposes a new transform inversion technique that is called “the pseudotransform inversion algorithm” by introducing “pseudotransforms” of these distributions, which are simply approximations to the transforms with Taylor’s expansions that agree up to a certain order. Then, the expected waiting times can be computed using transform inversion, because they are simply functions of two moments. This study also discusses the special case involving zero switchover times. The strongest benefit of the pseudotransform inversion algorithm over current approaches is that it significantly decreases the computation effort when the number of queues is large. Several numerical examples are devised to validate our approach and show its efficiency in analyzing polling models. The results show that the pseudotransform inversion algorithm is indeed quite efficient for analyzing polling stations. Although polling models are the best example that we have found to date, in any situation where the quantity to be computed depends only on the first several moments of the input distributions, the pseudotransform inversion algorithm holds promise as a computational algorithm.

Performance of large-scale polling systems with branching-type and limited service

Motivated by emerging Internet-of-Things (IoT) applications and smart building environments, we analyze the performance of large-scale symmetric polling systems where the number of queues grows large. We consider a scenario in which the total arrival rate is kept fixed and the individual switch-over time and service time distributions remain the same. This asymptotic regime leads to cycles of infinite length and queue lengths with non-trivial distributions. We show that for most traditional service policies the scaled cycle times converge to a deterministic value in the limit, which in turn implies that the queue lengths at the various nodes become asymptotically independent. Using these insights, we find that the behavior of individual queues simplifies to that of a discrete-time bulk service queue in the limit, so that the marginal queue length and waiting-time distributions become considerably easier to analyze. Additionally, we propose a new flexible k-limited service discipline aimed at striking a good balance between short mean queue lengths and predictable cycle times for deadline-critical applications.

Mathematical modelling of the vitamin C clock reaction.

Chemical clock reactions are characterized by a relatively long induction period followed by a rapid ‘switchover’ during which the concentration of a clock chemical rises rapidly. In addition to their interest in chemistry education, these reactions are relevant to industrial and biochemical applications. A substrate-depletive, non-autocatalytic clock reaction involving household chemicals (vitamin C, iodine, hydrogen peroxide and starch) is modelled mathematically via a system of nonlinear ordinary differential equations. Following dimensional analysis, the model is analysed in the phase plane and via matched asymptotic expansions. Asymptotic approximations are found to agree closely with numerical solutions in the appropriate time regions. Asymptotic analysis also yields an approximate formula for the dependence of switchover time on initial concentrations and the rate of the slow reaction. This formula is tested via ‘kitchen sink chemistry’ experiments, and is found to enable a good fit to experimental series varying in initial concentrations of both iodine and vitamin C. The vitamin C clock reaction provides an accessible model system for mathematical chemistry.

A mine main fans switchover system with lower air flow volatility based on improved particle swarm optimization algorithm

A reliable ventilation system is essential for maintaining a comfortable working environment and ensuring safety production in an underground coal mine. The automated fan switchover technique was developed for changing the main fan for maintenance with lower air flow volatility of underground mine in the switchover process. This article established the optimization model in the main fans switchover process, used the improved particle swarm optimization algorithm to solve the model, and achieved minimum air flow volatility in the fans switchover process. Compared to previous studies, computer simulations have shown that the proposed algorithm can effectively find the global optimal solution with less initial parameters and achieved lower air flow volatility in underground mine. The particle swarm optimization solution, searching diversity, prevents it from confining to local optimal solutions and enhances convergence. The reasonable step length is beneficial to reduce the air flow volatility and main fans switchover time. The air flow volatility is larger comparatively when some doors are nearly open or closed fully at the start–stop phase of the switchover process. A case application in a China’s domestic coal mine shows that the air flow volatility of the underground mine in the main fans switchover process is no more than 0.4%.

Equilibrium Strategies of a Polling Network with Non-zero Switch-over Times

In this paper, we consider a cyclic two-queue polling system with non-zero switchover times under exhaustive service discipline. Arriving customers decide whether to join queue 1 ( Q1 ) or queue 2 ( Q2 ) under two different information levels: fully unobservable case and fully observable case. With the help of the waiting costs, we study the equilibrium strategies for arriving customers in both cases. Furthermore, we analyze the expected waiting cost of an arriving customer in fully unobservable case by numerical examples.

A review of assessment of the machinery tillage tools’ performance for higher crop production efficiencies

The efficiency of crop production technologies to a great extent depends on the selected tillage tools and their performance. The aim of this study was to assess general quantitative performance of various machinery tillage tools. At first stage of study, the general assessment of soil tillage tools with regard to crop yielding capacity was assessed. The task of the second stage of study was to assess the performance of modern tillage tools from the perspective capacity of tractors. The study showed that the most rational practice was alternation of soil tillage tools for different crops grown under various crop rotations. At the same time, the energy-saturated aggregates, on an average, showed the same indicators of specific fuel consumption, running speed and switch-over time utilization coefficient as that of the aggregates with tillage tools of less operating width. The primary advantage of the wide-cut aggregates was narrowed to reduction of labour input, the value of which was reciprocally proportional to the operating width of the given tool. The gain in specific materials consumption of the tillage tools outruned the intensity of their operating width, which had a non-linear increase in the machinery cost, the level of its negative impact on the territory, and it's more complicated exploitation. These drawbacks were compensated with a series of advantages with the decrease in the labour input. In case of introducing driverless tractors, the profit from the diligence of the aggregates with an increased operating width was to a great extent smoothed over. Thus, hypothetically the development of site-specific crop growing and automation of the agricultural processes will lead to the limitation of tractor capacity and operating width of the tools aggregated with them.

Optimal routeing in two-queue polling systems

AbstractWe consider a polling system with two queues, exhaustive service, no switchover times, and exponential service times with rate µ in each queue. The waiting cost depends on the position of the queue relative to the server: it costs a customercper time unit to wait in the busy queue (where the server is) anddper time unit in the idle queue (where there is no server). Customers arrive according to a Poisson process with rate λ. We study the control problem of how arrivals should be routed to the two queues in order to minimize the expected waiting costs and characterize individually and socially optimal routeing policies under three scenarios of available information at decision epochs: no, partial, and complete information. In the complete information case, we develop a new iterative algorithm to determine individually optimal policies (which are symmetric Nash equilibria), and show that such policies can be described by a switching curve. We use Markov decision processes to compute the socially optimal policies. We observe numerically that the socially optimal policy is well approximated by a linear switching curve. We prove that the control policy described by this linear switching curve is indeed optimal for the fluid version of the two-queue polling system.

Alternating server with non-zero switch-over times and opposite-queue threshold-based switching policy

A single server alternates between two Markovian queues with non-zero switch-over times. The server’s switching instants are determined by the number of customers accumulated at the unattended queue. Specifically, when queue i(i=1,2) is attended and the number of customers in queue j(j=1,2;j≠i) reaches a threshold, the server starts an exponentially distributed switch-over time to queue j, unless the number of customers in queue i is equal to or above queue i’s threshold. However, if during a switch-over period from queue i to queue j the former reaches its threshold, the switch-over is aborted, and the server immediately returns to queue i and continues to serve the customers there. We analyze the system mainly via Matrix Geometric (MG) methods while deriving explicitly the rate matrix R, and thus eliminating the need for successive substitutions. We further reveal connections between the entries of R and the roots of polynomials related to the Probability Generating Functions (PGFs) of the system states. Expressions for the system’s performance measures are obtained (e.g. mean queue size and mean sojourn time in queue 1, PGF and mean of the queue size in queue 2, as well as the Laplace Stieltjes transform and mean of the sojourn time in queue 2). Numerical results are presented and the effects of the various parameters, as well as the switch-over times, on the performance measures are examined. Seemingly counter-intuitive phenomena are discussed. Finally, various extreme cases are investigated.

On stabilizability of fluid multi-server polling systems with setups

A time-invariant fluid model of a polling system is considered. It consists of finitely many servers and buffers with unlimited sizes. The buffers receive inflows of work from the outside, work leaves the system after processing by a server. Every server works only with buffers from an associated zone of service, which may overlap for various servers, is able to serve at most one buffer at a time and so has to switch, from time to time, among buffers, the switch-over times are nonzero. We present a criterion for existence of a scheduling and service protocol that makes the system stable in the sense that the total amount of work in the buffers remains bounded as time progresses. The necessity part of this result is concerned with the widest class of protocols, including dynamic ones that are centralized and have access to the full information about the events in the system. Meanwhile, we show that every stabilizable system can be stabilized in a fully decentralized fashion via a simple static protocol, e.g., by a protocol that is based on independent round robin scheduling of the servers and for every server, employs only time measurement.

On a 2-class polling model with reneging and $$k_i$$ k i -limited service

This paper analyzes a 2-class, single-server polling model operating under a $$k_i$$ -limited service discipline with class-dependent switchover times. Arrivals to each class are assumed to follow a Poisson process with phase-type distributed service times. Within each queue, customers are impatient and renege (i.e., abandon the queue) if the time before entry into service exceeds an exponentially distributed patience time. We model the queueing system as a level-dependent quasi-birth-and-death process, and the steady-state joint queue length distribution as well as the per-class waiting time distributions are computed via the use of matrix analytic techniques. The impacts of reneging and choice of service time distribution are investigated through a series of numerical experiments, with a particular focus on the determination of $$(k_1,k_2)$$ which minimizes a cost function involving the expected time a customer spends waiting in the queue and an additional penalty cost should reneging take place.

Decision process of allocating projects to project managers

Allocating projects to project managers (PM) is a crucial decision in project management. Choosing the PM must be undertaken in a structured way, and thereby take into account the needs of the project and the PM’s competences and availability. The proposed model optimises the total time that PMs have available and takes into account the constraint of the switchover time loss within the mathematical programming. It model is part of a three-stage approach where: (1) projects are sorted using a multicriteria approach; (2) PMs are sorted using a multicriteria approach; and (3) the final allocation to intra-classes of projects is made using the optimisation model. This proposal contributes to aiding decision-makers involved in allocating projects: by respecting the limit of the time that PMs have available, or by extrapolating PMs’ available hours in which case overtime will have to be used. The model is applied in a Brazilian Energy Company.