Finite Buffer Capacity Research Articles

A Computational Analysis of Long Transfer Line Behavior

Meeting customer demands for order-based production and make‐to‐stock production policies against holding and non-holding costs are fundamental functions for businesses to ensure. For these policies, finite capacity buffers between machines is of great importance. WIP, production rate, and profit values, which are the key performance indicators of the transfer line, affect the sustainable economics of companies. It is important to investigate how the production rate, one of the most important performance indicators, and its calculation time are affected by the reliability parameters of the machines, the convergence rate and the analytical methods applied. In this study, the theoretical computational analysis of Dallery-David-Xie (DDX) algorithm on unreliable transfer line with finite buffers. The results show that the performance of the DDX algorithm is very sensitive to the convergence rate. Also, initial buffer configuration allocations to maximize the profit value in the transfer line are investigated.

A Discrete-Time Queueing Model of a Bottleneck with an Energy-Saving Mechanism Based on Setup and Shutdown Times

Producers are encouraged to reduce their energy consumption of manufacturing systems by applying less-energy-intensive modern technologies and advanced machine tools and operating methods at the system level. In the paper, organizational and analytical solutions are combined to model the sustainable production system. Managers can study the behavior of a production system organized using energy-saving rules by changing key parameters of the input model (arrival intensity, bottleneck service rate, buffer size, setup and shutdown time) to analyze the queue size of the production system and therefore performance. A discrete-time queueing model of a single-bottleneck production line with a finite input buffer capacity is proposed. Jobs occur according to a binomial process and are processed individually, one by one, according to the natural FIFO service discipline, with a general discrete-type cumulative distribution function. The total number of jobs present in the system is bounded by a non-random fixed value N. Every time the system becomes empty, an energy-saving mechanism is started: the processing machine (server) is turned off during a geometrically distributed shutdown time. Similarly, the first job arriving into the empty system initializes a geometrically distributed setup time. Identifying renewal moments in the evolution of the model, a system of difference equations is built for the transient queue-size distribution conditioned by the state of the system at the opening. The solution is obtained explicitly in terms of probability-generating functions. In addition, the Drum-Buffer-Rope concept is proposed to reduce the energy consumption of the production line. The throughput of the production system is maximized by adjusting the time between the order arrivals and the size of the input buffer to the capacity of the bottleneck. Turning off a machine under certain conditions and slowing down non-critical machines are strategies to reduce energy consumption. A detailed illustrating numerical and simulation study of the considered model is attached as well, in which the sensitivity of the queue-size behavior to changes of the key input model parameters is investigated.

Two commodity queueing inventory system with random common lifetime, two demand classes and pool of customers

This paper analyzes a two-commodity perishable queueing inventory system with random common lifetimes commodity-wise, positive service time, and individual ordering policy. We have considered two types of customers: priority customers and non-priority customers. There is a buffer of finite capacity for the priority customers and a pool with infinite capacity made available for the non-priority customers. The arrival of these customers is occurred by two independent Poisson processes. The lifetimes of each of the commodities and service times follow independent exponential distributions. The matrix geometric approach is used to analyze the model's steady-state behavior and we computed various system performance measures. This article examines the effects of the common lifetime parameters on the measures of performance, such as average cycle time, the average number of reorders due to the realization of the common lifetime of commodities, etc. Also, a sensitivity analysis of the system parameters on the performance measures is carried out. Further, a cost function is constructed based on the performance measures, and its convexity is examined numerically.

Queueing system with server breakdowns and individual customer abandonment

ABSTRACT We consider a single server queueing system with a finite capacity buffer in which the server is subject to breakdowns and repairs. At the time of a breakdown, the customers, if any, present in the system will either decide to stay or abandon according to a probabilistic mechanism. This decision is made by every customer present in the system independent of the others. We assume that the arrivals of customers occur according to a Markovian arrival process (MAP). The shocks that create breakdowns of the servers are also assumed to follow a MAP independent of the other MAP. The service and the repair times of the server are assumed to follow (possibly) different phase type (PH) distributions. An arriving customer finding the buffer full will be lost. Further, an arriving customer finding the server under repair may decide to balk or join the queue at that instant. This queueing system, which generalizes some of the well-known queueing models in the literature, is studied as a GI/ M/ 1- type with a finite state space. The model is analyzed in steady-state and illustrative numerical examples including an optimization problem of interest are presented.

A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input

In this paper, we discuss the waiting-time distribution for a finite-space, single-server queueing system, in which customers arrive singly following a Poisson process and the server operates under (a,b)-bulk service rule. The queueing system has a finite-buffer capacity ‘N’ excluding the batch in service. The service-time distribution of batches follows a general distribution, which is independent of the arrival process. We first develop an alternative approach of obtaining the probability distribution for the queue length at a post-departure epoch of a batch and, subsequently, the probability distribution for the queue length at a random epoch using an embedded Markov chain, Markov renewal theory and the semi-Markov process. The waiting-time distribution (in the queue) of a random customer is derived using the functional relation between the probability generating function (pgf) for the queue-length distribution and the Laplace–Stieltjes transform (LST) of the queueing-time distribution for a random customer. Using LSTs, we discuss the derivation of the probability density function of a random customer’s waiting time and its numerical implementations.

Transient Behavior of a Queueing Model with Hyper-Exponentially Distributed Processing Times and Finite Buffer Capacity.

In the paper, a finite-capacity queueing model is considered in which jobs arrive according to a Poisson process and are being served according to hyper-exponential service times. A system of equations for the time-sensitive queue-size distribution is established by applying the paradigm of embedded Markov chain and total probability law. The solution of the corresponding system written for Laplace transforms is obtained via an algebraic approach in a compact form. Numerical illustration results are attached as well.

Optimal replacement policy for multi-state manufacturing system with economic and resource dependence under epistemic uncertainty

This paper develops an optimal replacement policy V* for a multi-state manufacturing system. The manufacturing system would be repaired imperfectly once its performance cannot meet the production demand, and would be replaced when the production demand is not met for the V*-th time. Due to imprecise state assignments and unpredictable external working conditions, the performance and transition intensity of the multi-state machine cannot be accurately identified and then inevitably lead to epistemic uncertainty. In addition, the economic dependence and resource dependence that prevailed in the manufacturing system should be considered. In this paper, economic dependence is described as the time and cost saved by simultaneously repairing multiple identical machines, and resource dependence is caused by finite capacity buffers. To take these into account, the fuzzy Markov model and fuzzy stochastic flow manufacturing network (FSFMN) are tailored to evaluate the fuzzy reliability of machines and manufacturing systems, respectively. To obtain the optimal replacement policy V*, we derive the expression of the long run fuzzy profit rate under epistemic uncertainty. The replacement policy is demonstrated on the ferrite phase shifting unit manufacturing system, and the results of the subsequent comparative study and sensitivity analysis show that this policy is more effective.

Analysis of a production line subject to degradation and preventive maintenance

This paper considers a continuous flow manufacturing system with two machines subjected to condition-based preventive maintenance, and separated by an intermediate buffer of finite capacity. Each machine can degrade into several discrete states characterized by different degradation levels and performance parameters, ranging from perfect functioning to complete failure. Unlike the existing literature, the proposed approach considers various side effect costs, including the cost related to quality deterioration. A methodology is developed to describe the degradation stochastic process, and to analyze the complex trade-off between the condition-based preventive maintenance and the buffer capacity. The obtained results show the importance of considering quality-related and other possible costs when selecting preventive maintenance policy to optimize the performance of the manufacturing system. It is also shown that the selection of preventive maintenance actions should be considered from the view of the whole system, rather than individual machines. The optimal solution depends on the different degradation levels of the upstream and downstream machines.

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

Non-stationary departure process in a batch-arrival queue with finite buffer capacity and threshold-type control mechanism

A Multi-criteria Production Planning Approach for Aircraft Manufacturing Flow Lines

We consider a two-stage low-volume manufacturing system motivated by settings found in the aerospace industry. The first stage is given by parallel mixed-model assembly lines. The second stage consists of parallel paint stations. The two stages are decoupled by a finite-capacity buffer. Jobs have to be assigned to the assembly lines and must be sequenced on the lines. Afterwards, they must be assigned to paint stations and have to be sequenced at these stations. The conflicting performance measures are the total weighted tardiness (TWT) of the jobs at the second stage, whereas labor and inventory costs are considered at the first stage. We are interested in determining the set of Pareto-optimal solutions. We propose a hybrid metaheuristic based on the non-dominated sorting genetic algorithm (NSGA)-II to tackle large-sized problem instances. Results of computational experiments based on randomly generated problem instances are presented. The results demonstrate that the hybrid heuristic is able to quickly compute high-quality solutions.

On Local Optima Distribution in Buffer Allocation Problem for Production Line with Unreliable Machines

In this paper, we consider a buffer allocation problem in manufacturing flow lines with series-parallel network structure where nodes correspond to buffers of finite capacity, and arcs correspond to the machines. The machines are supposed to be unreliable, their time to failure and repair time are assumed to be exponentially distributed. Different machines may have different production rates and the production rates of all machines are assumed to be deterministic. The buffer allocation problem is to determine the capacities of all buffers with respect to a given optimality criterion, which is a function of the average production rate of the line, the buffer acquisition and installation cost and the inventory cost. In search for the optimum, the tentative solutions are evaluated by means of an approximate method based on the Markov models aggregation. We carry out computational experiments with the local search and genetic algorithms. It turns out that the “massif central” or “big valley” structure of the fitness landscape is present but only partially: The fitness of the local optima is negatively correlated with the distance to the best found solution, yet the set of local optima can not be encompassed by a ball of relatively small radius. Moreover, we show that in many problem instances, several clusters of local optima can be identified. The symmetries of the fitness function are discussed and suggested as the possible cause of the local optima clustering. Finally the performance of genetic algorithms is bfiefly discussed with respect to solutions clustering.

Analysis of Energy Efficient Scheduling of the Manufacturing Line with Finite Buffer Capacity and Machine Setup and Shutdown Times

The aim of this paper is to present a model of energy efficient scheduling for series production systems during operation, including setup and shutdown activities. The flow shop system together with setup, shutdown times and energy consumption are considered. Production tasks enter the system with exponentially distributed interarrival times and are carried out according to the times assumed as predefined. Tasks arriving from one waiting queue are handled in the order set by the Multi Objective Immune Algorithm. Tasks are stored in a finite-capacity buffer if machines are busy, or setup activities are being performed. Whenever a production system is idle, machines are stopped according to shutdown times in order to save energy. A machine requires setup time before executing the first batch of jobs after the idle time. Scientists agree that turning off an idle machine is a common measure that is appropriate for all types of workshops, but usually requires more steps, such as setup and shutdown. Literature analysis shows that there is a research gap regarding multi-objective algorithms, as minimizing energy consumption is not the only factor affecting the total manufacturing cost—there are other factors, such as late delivery cost or early delivery cost with additional storage cost, which make the optimization of the total cost of the production process more complicated. Another goal is to develop previous scheduling algorithms and research framework for energy efficient scheduling. The impact of the input data on the production system performance and energy consumption for series production is investigated in serial, parallel or serial–parallel flows. Parallel flow of upcoming tasks achieves minimum values of makespan criterion. Serial and serial–parallel flows of arriving tasks ensure minimum cost of energy consumption. Parallel flow of arriving tasks ensures minimum values of the costs of tardiness or premature execution. Parallel flow or serial–parallel flow of incoming tasks allows one to implement schedules with tasks that are not delayed.

Energy-Efficient Control Policy for Parallel and Identical Machines With Availability Constraint

Energy efficiency is becoming a key subject in manufacturing, especially if related to the major environmental impact of machining activities. Nowadays, great research efforts are performed to find new methodologies to improve sustainability of manufacturing processes. Energy consumption can be lowered controlling machine state during idle periods. This can be achieved with Energy-Efficient Control (EEC) policies that switch off/on the machine. The same approach can be applied simultaneously to more identical devices in a parallel machines workstation. This letter presents a novel model to identify EEC policies for manufacturing systems composed of parallel and identical machines with finite buffer capacity. In this configuration, each machine can be switched on with a stochastic startup time and switched off instantaneously also considering an availability constraint. The proposed model reduces energy consumption while assuring a target availability level. The control is executed using buffer level information. Numerical results confirm model benefits when applied to a real industrial system from the automotive sector.

Performance evaluation of asynchronous two-stage manufacturing lines fabricating discrete parts

Asynchronous systems with deterministic processing times are critical for fabricating discrete parts, especially in countries offering high salaries. Despite their widespread application, it is difficult to analyze these systems using conventional analytical modeling tools as commonly used hypotheses for these models consider different conditions compared to real behaviors. This paper presents a new analytical model for the performance evaluation of asynchronous two-stage manufacturing lines fabricating discrete parts with finite buffer capacity. A continuous-time Markov chain flow model that mimics the behavior of discrete asynchronous manufacturing systems by employing threshold-based control mechanisms is presented. The results obtained with the proposed model are compared with those using discrete event simulation, and they show good agreement. The model proposed in this paper can be used as a building block for the evaluation of longer asynchronous lines.

On Time-Dependent Queue-Size Distribution in a Model With Finite Buffer Capacity and Deterministic Multiple Vacations With Applications to LTE DRX Mechanism Modeling

A finite-capacity queueing model with the arrival stream of messages governed by the compound Poisson process and generally-distributed processing times is investigated. Whenever the system becomes empty (the server becomes idle), a number of deterministic independent vacations of equal length are initialized as far as at least one message is detected in the accumulating buffer at the completion epoch of one of them. During vacations the service process is suspended completely, while after finishing the last vacation it restarts normally. Identifying Markov moments in the evolution of the system and using the Korolyuk’s potential method, the compact-form representation for the transient queue-size distribution conditioned by the initial buffer state is found in terms of its Laplace transform. The considered model has potential applications in modeling the energy saving LTE DRX mechanism. A detailed simulation and numerical study is attached.

A unified approach for an approximation of tandem queues with failures and blocking under several types of service-failure interactions

We consider tandem queues with failures and a buffer of finite capacity at each service station. The service and repair time distributions of each server is of the phase type. A unified method for approximating the system under three types of service-failure interactions is presented. The approximation is based on the decomposition method. Some numerical examples are presented to investigate the effectiveness of the approximation and the effects of the system characteristics, such as failure rates, service time, repair time and service-failure interactions.

Real-Time Bottleneck in Serial Production Lines With Bernoulli Machines: Theory and Case Study

In production systems, the bottleneck is typically understood as the operation that affects the system performance in the strongest manner. Identification and mitigation of bottleneck are among the most important problems in production systems research and practice. The current literature offers numerous methods for the identification of production bottlenecks. Most of these methods focus on steady-state system behavior under constant parameters, and the corresponding mitigation approach is typically to prioritize the improvement of that particular operation. This applies when the improvement cannot be dynamically reallocated to other operations in the system, and the improvement is to be fixed to an operation for a long period of time. In this article, we attempt to study the bottleneck problem in a dynamic environment. Especially, we consider serial production lines with finite capacity buffers and the Bernoulli reliability machines and use a control-theoretic approach to formulate the bottleneck identification and mitigation problem as a state-based feedback control problem with the objective being the maximization of steady-state throughput. Computation formulas and procedures are developed to calculate the performance metrics of such systems with dynamic bottleneck control. Properties of the optimal control policies are investigated, and a computationally efficient algorithm is developed to obtain an effective real-time bottleneck indicator. Numerical experiments are used to demonstrate the efficacy of the proposed method, and a case study is presented to illustrate its application. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —It is very common in manufacturing practice that operators, engineers, and managers need to make decisions on-the-fly to ensure efficient production operations. One of the key tasks involved is to identify real-time bottleneck (RTBN). This is typically carried out based on the practitioners’ intuition and experience. With the advances in sensing, computing, and communication technologies emerging in the Industry 4.0 era, manufacturers now have the capability to collect, process, and visualize an enormous amount of data in real time. This provides a foundation for more rigorous real-time production management and control. The research described in this article is intended to provide such a tool for RTBN identification in production lines and, thus, guide timely decision-making on the factory floor for smarter production activities.

Numerical Study on Transient Behaviour of Finite Bulk Arrival or Service Queues with Multiple Working Vacations

The transient behaviour of single server bulk queues with finite-buffer capacity is discussed numerically under the assumption that the server may take multiple working vacations after completing a busy period. It is considered that the inter-arrival and the service times are exponentially distributed and independent of each other. The buffer space is limited, therefore partial and full batch rejection policies are studied for the bulk arrival queueing model. However, for the batch service, the general bulk service rule is considered. Using probabilistic arguments and relating the state of the systems at two consecutive time epochs, differential equations are obtained to model such phenomena. Further, these equations are solved numerically by Runge-Kutta method and the time dependent numerical solutions are compared with the exact stationary solutions. The blocking probability and the mean waiting time of the first, last and an arbitrary customer are also reviewed mathematically and computed numerically.

Stability and phase transitions of dynamical flow networks with finite capacities

We study deterministic continuous-time lossy dynamical flow networks with constant exogenous demands, fixed routing, and finite flow and buffer capacities. In the considered model, when the total net flow in a cell —consisting of the difference between the total flow directed towards it minus the outflow from it— exceeds a certain capacity constraint, then the exceeding part of it leaks out of the system. The ensuing network flow dynamics is a linear saturated system with compact state space that we analyse using tools from monotone systems and contraction theory. Specifically, we prove that there exists a set of equilibrium points that is globally asymptotically stable. Such set of equilibrium points reduces to a single globally asymptotically stable equilibrium point for generic exogenous demand vectors. Moreover, we show that the critical exogenous demand vectors giving rise to non-unique equilibrium points correspond to phase transitions in the asymptotic behavior of the dynamical flow network.

Multipath Delay Analysis Using Queuing Theory for Gateway Selection in Hybrid MANET

Hybrid Mobile ad hoc network (H-MANET) is a network in which MANET is connected to the Internet using some special nodes called Internet Gateways (IGs). Previous work in this field considered the infinite buffer scenario and therefore buffer overflow would never occur. But in realistic MANET, the buffer size of each node is strictly bounded that incurs packet loss and intensifies delay. In this paper, a mathematical model has been proposed for modeling of multipath delay analysis for IG selection in H-MANET. The proposed work is used to estimate end to end delay of each individual path amongst Source Node (SN) and IGs. The M/M/m/R network model has been employed for modeling the network in which packets arrive in Poisson distribution in a bounded queue with finite buffer capacity. Burke theorem has been used to calculate queuing delay of each individual path as well as the complete path from the SN to an IG. Furthermore, best IG is selected for data transmission based on delay analysis of multiple paths. The Opnet modeler 18.0 has been used to perform the simulation work. The numerical results represent the effectiveness of proposed model.