System Performance Measures Research Articles

Solution of an M/G/1 queueing model with k sequential heterogeneous service steps and vacations using the Tauberian property

This article studies a transient queueing model with k sequential heterogeneous service steps and vacations. Entrants arrive according to a Poisson process, and each arrival is serviced sequentially and consistently in k phases in the order of arrival. The service times follow a general distribution function. Upon completion of the service, the server could take a vacation with the probability θ and remains in the system to provide service to other customers with the probability For this model, first, we obtain the Laplace transform of the probability generating functions (PGFs) of system size, and then we obtain the PGFs for a special case in the transient state, and the corresponding steady state results explicitly. Also, we derive the system performance measures such as the means system size, waiting time, and busy period in a closed form.

A computational method for finding the availability of opportunistically maintained multi-state systems with non-exponential distributions

Availability is one of the most important performance measures of a repairable system. Among various mathematical methods, the method of supplementary variables is an effective way of modeling the steady-state availability of systems governed by non-exponential distributions. However, when all the underlying probability distributions are non-exponential (e.g., Weibull), the corresponding state equations are difficult to solve. To overcome this challenge, a new method is proposed in this article to determine the steady-state availability of a multi-state repairable system, where all the state sojourn times, as well as the maintenance times, are generally distributed. As an indispensable step, the well-posedness and stability of the system’s state equations are illustrated and proved using C0 operator semigroup theory. Afterwards, based on the generalized Integral Mean Value Theorem, the expression for system steady-state availability is derived as a function of state probabilities. Then, the original problem is transformed into a system of linear equations that can be easily solved. A simulation study and an instance studied in the literature are used to demonstrate the applications of the proposed method in practice. These numerical examples illustrate that the proposed method provides a new computational tool for effectively evaluating the availability of a repairable system without relying on simulation.

Modeling and analysis of carousel-based mixed-model flexible manufacturing system using colored Petri net

This study aims to model, analyze, and evaluate performance of a flexible manufacturing system, constituting a carousel-based manufacturing and assembly cells layout, configured to produce mixed-model multiple products employing inter-/intra-cellular routing flexibility in which manufacturing and assembly resources are subject to working and failure modes. A hierarchical colored Petri net model is developed to analyze performance of the flexible manufacturing system. Colored Petri net modeling experiments have been conducted to evaluate the system performance for throughput, cycle time, and work-in-process. The system performance has been investigated in relation to material supply and handling system, process execution, and production resources reliability variables. Different input factors are considered for simulation modeling such as mean machining time, mean loading/unloading time, mean assembly time, buffer capacity, material supply inter-arrival time, number of operations between failures, and mean time to repair for production resources; a variation in input factors has shown a significant impact on system performance measures. The colored Petri net–based modeling, simulation, and analysis approach has been demonstrated as an efficient method for carousel-based mixed-model configured flexible manufacturing system.

Comparison of predictive performance and measurement of off-grid 15 kWp solar power generation in Aceh Tamiang

In 2015, the Government, through a special allocation fund, has finished constructing an off-grid 15 KWp off-grid solar power plant in Paya Tampah Village, Aceh Tamiang district. The long-term reliability of solar power plants is highly reliant on on-site measurements because of the vagueness in some of the constantly-changing variables such as irradiation, drought rate, which possibly lead to cause significant power losses and which turn out to also affect the estimated cost of PV (kWh). With the aim of upgrading capabilities in off-grid solar power plant planning especially in the province of Aceh, this paper outlining detailed comparison of the results of calculating the performance of off-grid 15 KWp off-grid solar power among system performance measurement results after 2 years of operation. Performance calculations performed with the assistant of PVsyst software. The measurement results characterize the total power generated by the off-grid solar power plant is 15 kWp and used by 38 households. The result of this investigation is expected to be used by local governments to be a benchmark on the future planned off-grid solar power plant planning.

High-Speed Transmission Circuits Signaling in Optical Communication Systems

Abstract This paper has outlined high-speed transmission circuits signaling in guided or unguided optical communication systems. An efficient prediction scheme to predict the signal distortion caused by intersymbol interference. As high-speed digital signals exceed many gigabits per second speeds, eye diagrams provide the means to quickly and accurately measure signal quality and system performance. Semiconductor understands the capacitance constraints that designers are faced with when using these high-speed interfaces and offers a wide line of ultra-low capacitance electrical spectral density protection devices that service these interfaces, and the noise can be reduced at the optimum circuit at both bandwidths of 167 MHz, and bandwidth of 200 MHz.

Inventory Rationing on a One-for-One Inventory Model with Backorders and Lost Sales

In this study, we are primarily motivated by the research problem of recognizing heterogeneous customer behavior towards waiting for order fulfillment under the 'threshold rationing policy' (also known as the 'critical level policy'), and aim to find its effect on system stock levels and performance measures. We assume a continuous review one-for-one ordering policy with generally distributed lead times. In the first model, we consider the case in which low-priority customer class exhibits zero patience for waiting if the demand is not satisfied immediately (a lost sale), while the demand of high-priority customer class can be backordered. This is the first study in the literature to consider this model. We provide an exact analysis for the derivation of the steady-state probability distribution and the average infinite horizon cost per unit time. We then develop an efficient procedure to minimize the average expected cost rate by deriving bounds on the optimal cost, which reduces the enumeration space considerably. In the numerical study, we show the relative savings achieved by implementing the proposed threshold rationing policy over some of the traditional industry practices. In the second model, we study the opposite case in which the high-priority customer class exhibits zero patience for waiting. The existing study in the literature uses simulation to demonstrate that the performance of the critical level policy is robust with respect to the form and variability of the lead time distribution provided the mean lead times are identical. Then it proposes using the Continuous-Time Markov Chain (CTMC) equivalent of the model as an approximation. In this study, we establish a theoretical basis for the rationale of using the CTMC approach as an approximation. We show that under certain assumptions the steady-state probabilities of the system with generally distributed lead times are identical to the steady-state probabilities of the CTMC system with the same mean. This result enables us to link the dynamics of the studied model to the CTMC model, which then allows us to provide a theoretical explanation to the empirically observed phenomenon that why the steady-state probabilities and performance measures are near-insensitive to the form and variability of the lead time distribution as long as mean lead times are identical.

Dynamic Control of a Machine Repair Problem with Switching Failure and Unreliable Repairmen

This study examines the dynamic control of an M/M/2 machine repair system with R operating machines, S standbys, and two unreliable repairmen, wherein standbys are subject to switching failures. We apply the matrix analytic method to derive explicit expressions of the stationary probability distributions as well as matrix expressions of the system performance measures. We construct a cost model and determine the optimal dynamic operating policy to minimize the expected cost function per unit time. Sensitivity analysis is conducted using numerical examples. The results of sensitivity analysis indicate that the optimal thresholds and corresponding minimum expected cost increase as the number of operating machines or standbys increases. Moreover, the minimum expected cost is sensitive to the mean arrival and repair rates. The results provide managers with decision reference for productivity improvement and cost reduction.

Rainfall in Bangladesh: Is Rainwater Harvesting a Sustainable Approach for Governing Rainwater?

Global environmental change affects the intensity and frequency of rainfall that increases the necessity for sustainable management of rainwater. It is more important for rain intensive country like Bangladesh otherwise it creates further problems like water logging, flood, soil erosion, and water borne diseases. Based on the survey of 80 rainwater harvesters in the Coastal Bangladesh in 2017, this paper evaluates whether rainwater harvesting is sustainable approach to govern rainwater or not by using social and ecological performance measures of Social Ecological System (SES) of Elinor Ostrom. This study found that rainwater harvesting does not affect environment, it is an acceptable approach in family and society, help to develop biodiversity condition, create resilience to climate change impact, improve equitable access to water, efficient use of rainwater, improve women performance regarding water supply to the family, contribute in achieving sustainable development goal, and do not overharvest of rainwater that could create environmental problem. Beyond these measures, it needs rainwater harvesting controlling mechanism like formal operation rule or policy to avoid overharvesting and ensure more sustainability in governing rainwater.Keywords: Accountability; Biodiversity; Efficiency; Resilience; Equity; Global environmental change; Rainwater harvesting; Sustainable approach; Sustainable development goals; Sustainable management of rainwater

Energy-Efficient Power Allocation Maximization With Mixed Group Sum Power Bound and QoS Constraints

Energy efficiency (EE) is a critical performance measure in the next generation wireless communication systems, especially for battery-constrained Internet of Things (IoT) devices. We investigate the power allocation optimization problem in a multi-channel wireless system for EE maximization, subject to the sum power and the throughput constraints over each group of assigned channels, as well as the total power constraint. Resorting to geometric interpretation on the constraints, we propose the group virtually ceiled and bottomed water-filling (GVC-WF) algorithm to solve this EE maximization problem. Our proposed algorithm computes the exact optimal solution with a quadratic polynomial computational complexity. With the optimality and computational advantages, our proposed algorithm is suitable for power allocation in large-scale wireless systems. Simulation results demonstrate that our proposed power allocation algorithm improves the energy efficiency by more than 40%, as compared to the conventional Dinkelbach’s method with the same amount of computations.

Multi Node Tandem Queuing Model with Bulk Arrivals Having Geometric Arrival Distribution

In this paper a K-node forked queuing model with load dependent service rates is analysed. Here it is assumed that the customers arrive to the first queue in batches and wait for service. After getting service at first service station with some probability they may join any one of the (K-1) parallel queues which are connected to first queue in series and exit from the system after getting service. It is assumed that the arrival and service completions follow Poisson processes and service rates depend on number of customers in the queue connected to it. The influence of Geometrically distributed bulk arrivals on this queuing model is studied. Sensitivity analysis of the system behaviour with regards to the arrival rates and load dependent service distribution parameters is carried out. The influence of these parameters on system performance measures such as average number of customers, waiting time of customer, variation of number of customers in each queue, throughput of each service station, utilization of each server are derived explicitly when arrivals follow a Geometric distribution. Simulations are carried out to illustrate the result.

Simple Speech Transform Coding Scheme using Forward Adaptive Quantization for Discrete Input Signal

We propose a speech coding scheme based on the simple transform coding and forward adaptive quantization for discrete input signal processing in this paper. The quasi-logarithmic quantizer is applied to discretization of continuous input signal, i.e. for preparing discrete input. The application of forward adaptation based on the input signal variance provides more efficient bandwidth usage, whereas utilization of transform coding provides sub-sequences with more predictable signal characteristics that ensure higher quality of signal reconstruction at the receiving end. In order to provide additional compression, transform coding precedes adaptive quantization. As an objective measure of system performance we use signal-to-quantization-noise ratio. Sysem performance is discussed for two typical cases. In the first case, we consider that the information about continuous signal variance is available whereas the second case considers system performance estimation when we know only the information about discretized signal variance which means that there is a loss of input signal information. The main goal of such performance estimation comparison of the proposed speech signal coding model is to explore what is the objectivity of performance if we do not have information about a continuous source, which is a common phenomenon in digital systems.

Transient behaviour of an M/Ek/1 queue with vacations, balking and control of admission during vacations

This paper studies the transient behaviour of an M/Ek/1 queueing model with single and multiple vacations, balking and control of admission during vacations. An arriving customer undergoes k exponential phases of service before leaving the system. Whenever the system becomes empty, the server starts vacation (single or multiple). All the arriving customers are not allowed to join the queue during vacations. That is, they are either permitted to join the queue or rejected. During the vacation period, the permitted arrivals may either join the queue or balk. Using the method of generating function, the transient system size probabilities are derived for the proposed model in terms of generalised modified Bessel function of the second kind. The system performance measures such as average and variance of system size, probability of system empty and server idle are also obtained. Numerical illustrations are presented to analyse the influence of the system parameters.

A single server queue under random vacation policy

This paper deals with an M/G/1 queueing system with random vacation policy, in which the server takes the maximum number of random vacations till it finds minimum one message (customer) waiting in a queue at a vacation completion epoch. If no arrival occurs after completing maximum number of random vacations, the server stays dormant in the system and waits for the upcoming arrival. Here, we obtain steady state queue size distribution at an idle period completion epoch and service completion epoch. We also obtain the steady state system size probabilities and system state probabilities. Some significant measures such as a mean number of customers served during the busy period, Laplace-Stieltjes transform of unfinished work and its corresponding mean value and second moment have been obtained for the system. A cost optimal policy have been developed in terms of the average cost function to determine a locally optimal random vacation policy at a lower cost. Finally, we present various numerical results for the above system performance measures.

Mathematical Analysis of Queueing-Inventory Model with Compliment and Multiple Working Vacations

In this paper, we provide independent continuous review of stock for two commodities, namely commodity 1(C1) and 2 (C2). The type 1(T1) customer demands C1 and Type 2(T2) customer demands C2 but C2 is also given to T1 customer as a compliment (i.e. C2 is also given as a compliment to C1). The arrival pattern of customers is from a finite source of population. The ordering policies of both commodities are independent and also, each customer demands service with positive time. A single finite retrial orbit is allowed for any customer, when the demanding item is stocked out or the server is busy. The pre-emptive priority service policy is assigned to T1 customer over T2 customer. The server may go for the working vacation as C1 becomes zero, in which T2 customer who is taking his service is allowed to orbit whenever T1 customer demands the service with both commodities and when the orbit is not full. The joint limiting distributions of four random variables are studied under steady state. Long run expected total cost rate and measures of system performance are derived.

Computational Performance of a Single Server State Dependent Queue

In this article we consider a single server state dependent queuing system with the service rate varying according to types of customers like normal, tagged and heavy tailed. We develop a state dependent queuing model in which the service rate depends on customer type arrive to the system with quasi-birth-death environment structure and using matrix geometric method we develop the system performance measures. Also, we use these performance measures by utilizing the maximum potential of server and perform sensitivity analysis with numerical illustrations.

Comprehensive measurement of health system performance at district level in India: Generation of a composite index.

There have been limited attempts at measurement of health system performance at decentralized levels in low- and middle-income countries. This study was undertaken to develop a composite indicator to measure health system performance at district level in India. Primary data were collected from 377 public health facilities in 21 districts of Haryana state in India using health facility surveys. In addition, 1700 health care providers and 800 clients visiting health facilities were interviewed. Routine health management information system data at district and state level were also analyzed. These data were used for computing 67 input and process indicators covering six health system building blocks. Indicators were normalized and aggregated to generate domain-specific and overall composite health system performance index (HSPI) for each district. Several sensitivity analyses were performed to assess robustness of results. Overall, Panchkula and Ambala districts were found to be the best performing in the state (with HSPI scores of 0.64 and 0.62 out of 1), while Mewat, Faridabad, and Palwal districts had the poorest performance (with HSPI scores of 0.46, 0.49, and 0.48 out of 1). Significant variation in performance was observed for each health system building block. Sensitivity analyses results showed that study findings were robust to variations in methods of aggregation of indicators. Our study provides a framework and methods to measure health system performance at district level in a comprehensive manner. The composite indicator provides a summary snapshot to benchmark performance, while building block and domain scores provide critical information for programmatic action.

An integrated feature learning approach using deep learning for travel time prediction

Travel time data is a vital factor for numbers of performance measures in transportation systems. Travel time prediction is both a challenging and interesting problem in ITS, because of the underlying traffic and events’ hidden patterns. In this study, we propose a multi-step deep-learning-based algorithm for predicting travel time. Our algorithm starts with data pre-processing. Then, the data is augmented by incorporating external datasets. Moreover, extensive feature learning and engineering such as spatiotemporal feature analysis, feature extraction, and clustering algorithms is applied to improve the feature space. Furthermore, for representing features we used a deep stacked autoencoder with dropout layer as regularizer. Finally, a deep multi-layer perceptron is trained to predict travel times. For testing our predictive accuracy, we used a 5-fold cross validation to test the generalization of our predictive model. As we observed, the performance of the proposed algorithm is on average 4 min better than applying the deep neural network to the initial feature space. Furthermore, we have noticed that representation learning using stacked autoencoders makes our learner robust to overfitting. Moreover, our algorithm is capable of capturing the general dynamics of the traffic, however further works need to be done for some rare events which impact travel time prediction significantly.

M/M/1 Queueing system with Customer Balking and Reneging

This paper deals with an M/M/1 queueing system with customer balking and reneging. Balking and reneging of the customers are assumed to occur due to non-availability of the server during vacation and breakdown periods. Steady state probabilities for both the single and multiple vacation scenarios are obtained by employing probability generating functions. We evaluate the explicit expressions for various performance measures of the queueing system.

Joint decision-making of production and maintenance in mixed model assembly systems with delayed differentiation configurations

Mixed model assembly systems (MMASs) can simultaneously manufacture multiple product variants and are developed to satisfy customers’ increasing desire for products with a high variety. This paper investigates the joint decision-making of production and maintenance policies in MMASs with delayed differentiation configurations, where common operations are performed before differentiated processes. The problem is formulated as a Markov Decision Process (MDP) problem that minimises the average cost per unit time. Monte Carlo simulation is used to evaluate the system performance measures (e.g. volume mix ratio, product quality) under the optimal policy. Numerical examples are presented to illustrate the structure of the optimal policy and the impact of different factors on the system performance in an MMAS that produces two types of product variants. Techniques that can potentially solve the problem in large-sized MMASs are also discussed.

FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach

The present paper investigates the customers’ balking behavior in a double orbit retrial queueing system having two types of customers namely, ordinary and premium class customers. Upon finding the server busy, most of the arriving customers join ordinary orbit whereas a few of the customers join the premium orbit by paying extra amount. The steady state analytical solution for the probability distribution and system performance measures are derived by using probability generating function. A profit function based on customers’ reward-cost is constructed and analyzed using customers’ joining strategy. Markovian double orbit retrial model is then transformed into fuzzy FM/FM/1 queueing model with balking by using system parameters expressed as linguistic variables. Based on Zadeh's extension principle and α − cut method, parametric nonlinear programing (P-NLP) approach is used to determine fuzzified indices. Furthermore, the ranking index method is used to defuzzify the performance measures. The sensitivity analysis and cost optimization are performed for the crisp queueing model by taking a numerical illustration.