Search Results (22)

Background: Port congestion contributes significantly to operational inefficiency and environmental impact in maritime logistics. With tightening EU regulations such as the Emissions Trading System (EU ETS) and FuelEU Maritime, understanding and mitigating the economic and environmental effects of vessel delays is increasingly critical. This study focuses on a single bulk cargo pier at Constanta Port (Romania), which has experienced substantial traffic fluctuations since 2021, and examines operational and environmental performance through a queuing-theoretic lens. Methods: The authors have applied an M/G/1/∞/FIFO/∞ queuing model to vessel traffic and service time data from 2021–2023, supplemented by Monte Carlo simulations to capture variability in maneuvering and service durations. Environmental impact was quantified in CO₂ emissions using standard fuel-based emission factors, and a Cold Ironing scenario was modeled to assess potential mitigation benefits. Economic implications were estimated through operational cost modeling and conversion of CO₂ emissions into equivalent EU ETS carbon costs. Results: The analysis revealed high berth utilization rates across all years, with substantial variability in waiting times and queue lengths. Congestion was associated with considerable CO₂ emissions, which, when expressed in monetary terms under prevailing EU ETS prices, represent a significant financial burden. The Cold Ironing scenario demonstrated a substantial reduction in at-berth emissions and corresponding cost savings, underscoring its potential as a viable mitigation strategy. Conclusions: Results confirm that operational congestion at the studied berth imposes substantial environmental and financial burdens. The analysis supports targeted interventions such as Just-In-Time arrivals, optimized berth scheduling, and Cold Ironing adoption. Recommendations are most applicable to single-berth bulk cargo operations; future research should extend the approach to multi-berth configurations and incorporate additional operational constraints for broader generalizability. Full article

This study proposes a Fuzzy-Based Control System (FBCS) for a Bulk Service Queueing Model with Vacation, designed to optimize service performance by dynamically adjusting system parameters. The queueing model is categorized into three service levels: (A) High Bulk Service, where a large number of arrivals are processed simultaneously; (B) Medium Single Service, where individual packets are handled at a moderate rate; and (C) Low Vacation, where the server takes minimal breaks to maintain efficiency. The Mamdani Inference System (MIS) is implemented to regulate key parameters, such as service rate, bulk size, and vacation duration, based on input variables including queue length, arrival rate, and server utilization. The Mamdani-based fuzzy control mechanism utilizes rule-based reasoning to ensure adaptive decision-making, effectively balancing system performance under varying conditions. By integrating bulk service with a controlled vacation policy, the model achieves an optimal trade-off between processing efficiency and resource utilization. This study examines the effects of fuzzy-based control on key performance metrics, including queue stability, waiting time, and system utilization. The results indicate that the proposed approach enhances operational efficiency and service continuity compared to traditional queueing models. Full article

The “carbon neutral power generation” policy of the European Union requires the phasing out of fossil fuel power plants. These plants still play a crucial role in the energy mix in many countries; therefore, efforts are put forward to lower their CO₂ emissions. The available solution for an existing coal plant is the implementation of biomass co-firing, which allows it to reduce twice its carbon footprint in order to achieve the level of natural gas plants, which are preferable on the way to zero-emission power generation. However the side effect is a significant increase in the bulk fuel volumes that are acquired, handled, and finally supplied to the power plant units. A necessary extension of the complex logistic system for unloading, quality tagging, storing, and transporting biomass may increase the plant’s noise emissions beyond the allowed thresholds. For a comprehensive assessment of the concept of expanding the power plant’s biofuel supply system (BSS), a discrete simulation model was built to dimension system elements and verify the overall correctness of the proposed solutions. Then, a dedicated noise emission model was built for the purposes of mandatory environmental impact assessment procedures for the planned expansion of the BSS. The noise model showed the possibility of exceeding the permissible noise levels at night in selected locations. The new simulations of the BSS model were used to analyze various scenarios of biomass supply with regard to alternative switching off the selected branches of the whole BSS. The length of the queue of unloaded freight trains delivering an average quality biomass after a period of 2 weeks is used as a key performance parameter of the BSS. A queue shorter than 1 freight train is accepted. Assuming the rising share of RESS in the Polish energy mix, the thermal plant’s 2-week average power output shall not exceed 70% of its maximum capacity. The results of the simulations indicate that under these constraints, the biofuel supplies can be sufficient regardless of the nighttime stops, if 50% of the supplied biomass volumes are delivered by trucks. If the trucks’ share drops to 25%, the plant’s 2-week average power output is limited to 45% of its maximum power. The use of digital spatial simulation models for a complex, cyclical-continuous transport system to control its operation is an effective method of addressing environmental conflicts at the design stage of the extension of industrial installations in urbanized areas. Full article

Data center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power business intelligence (BI) and cloud load based on the queueing theoretic approach. This model examines a bulk arrival and batch service queueing system, incorporating server overloading and underloading based on the queue length. In a batch service system, customers are served in groups following a general bulk service rule with the server operating between the minimum value $\mathit{‘}\mathit{a}\mathit{’}$ and the maximum value $\mathit{‘}b\mathit{’}$. But in certain situations, maintaining the same extreme values of the server is difficult, and it needs to be changed according to the service request. In this paper, server load balancing is introduced for a batch service queueing model, which is the capacity of the server that can be adjusted, either increased or decreased, based upon the service request by the customer. On service completion, if the service request is not enough to start any of the services, the server will be assigned to perform a secondary job (vacation). After vacation completion based upon the service request, the server will start regular service, overload or underload. Cloud computing using power BI can be analyzed based on server load balancing. The function that determines the probability of the queue size at any given time is derived for the specified queueing model using the supplementary variable technique with the remaining time as the supplementary variable. Additionally, various system characteristics are calculated and illustrated with suitable numerical examples. Full article

This research investigated a single bulk server queuing model where service modes and server vacations are dependent on the number of clients. The server operates in three different service modes: single service, fixed batch service, and variable batch service. Modes will be determined by queue length. The service starts only when the minimum number of customers, say ‘a’, has accumulated in the queue. At this point, the server selects one of three service modes. Transitions between duty modes are permitted only at the beginning of a duty period. At the end of the service, the server can go on vacation if the queue length drops below ‘a’. When returning from vacation, if threshold ‘a’ is not reached, the server will remain inactive until it is reached. A special technique called the Supplementary Variables Technique (SVT) was used to determine the probability-generating function when estimating the queue size at a given time. Appropriate numerical examples exemplify the method developed in the paper. An optimal cost analysis was performed to set the threshold values for different server modes with the intention of minimizing the aggregate average cost. Full article

In this paper, we present research results that extend and supplement our article recently published by MDPI. We derive the closed-form relations among the queue-length probabilities observed in the pre-arrival, random, and post-departure epochs for a complex, bulk-service, multi-server queueing system GI/M^$a,b$/c. Full article

Background: This study addresses optimising fleet size in a system with a heterogeneous truck fleet, aiming to minimise transportation costs in interfacility material transfer operations. Methods: The material transfer process is modelled using a closed queueing network (CQN) that considers heterogeneous nodes and customised service times tailored to the unique characteristics of various truck types and their transported materials. The optimisation problem is formulated as a mixed-integer nonlinear programming (MINLP), falling into the NP-Hard, making exact solution computation challenging. A numerical approximation method, a modified sequential quadratic programming (SQP) method coupled with a mean value analysis (MVA) algorithm, is employed to overcome this challenge. Validation is conducted using a discrete event simulation (DES) model. Results: The proposed analytical model tested within a steel manufacturing plant’s material transfer process. The results showed that the analytical model achieved comparable optimisation of the heterogeneous truck fleet size with significantly reduced response times compared to the simulation method. Furthermore, evaluating performance metrics, encompassing response time, utilisation rate, and cycle time, revealed minimal discrepancies between the analytical and the simulation results, approximately ±8%, ±8%, and ±7%, respectively. Conclusions: These findings affirm the presented analytical approach’s robustness in optimising interfacility material transfer operations with heterogeneous truck fleets, demonstrating real-world applications. Full article

In this paper, a bulk arrival and two-phase bulk service with active Bernoulli feedback, vacation, and breakdown is considered. The server provides service in two phases as mandatory according to the general bulk service rule, with minimum bulk size ${}^{\prime }{a}^{\prime }$ and maximum bulk size ${}^{\prime }{b}^{\prime }$. In the first essential service (FES) completion epoch, if the server fails, with probability ${}^{\prime }{\mathsf{\delta }}^{\prime }$, then the renewal of the service station is considered. On the other hand, if there is no server failure, with a probability ${}^{\prime }1-{\delta }^{\prime }$, then the server switches to a second essential service (SES) in succession. A customer who requires further service as feedback is given priority, and they join the head of the queue with probability $\beta$. On the contrary, a customer who does not require feedback leaves the system with a probability ${}^{\prime }1-{\beta }^{\prime }$. If the queue length is less than ${}^{\prime }{a}^{\prime }$ after SES, the server may leave for a single vacation with probability ${}^{\prime }1-{\beta }^{\prime }$. When the server finds an inadequate number of customers in the queue after vacation completion, the server becomes dormant. After vacation completion, the server requires some time to start service, which is attained by including setup time. The setup time is initiated only when the queue length is at least ${}^{\prime }{a}^{\prime }$. Even after setup time completion, the service process begins only with a queue length ‘N’ (N > b). The novelty of this paper is that it introduces an essential two-phase bulk service, immediate Bernoulli feedback for customers, and renewal service time of the first essential service for the bulk arrival and bulk service queueing model. We aim to develop a model that investigates the probability-generating function of the queue size at any time. Additionally, we analyzed various performance characteristics using numerical examples to demonstrate the model’s effectiveness. An optimum cost analysis was also carried out to minimize the total average cost with appropriate practical applications in existing data transmission and data processing in LTE-A networks using the DRX mechanism. Full article

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. Full article

Background: Studies on prognostic potential and tumor immune microenvironment (TIME) characteristics of cuproptosis-related genes (CRGs) in hepatocellular carcinoma (HCC) are limited. Methods: A multigene signature model was constructed using the least absolute shrinkage and selection operator (LASSO) Cox regression analysis. The cuproptosis-related multivariate cox regression analysis and bulk RNA-seq-based immune infiltration analysis were performed. The results were verified using two cohorts. The enrichment of CRGs in T cells based on single-cell RNA sequencing (scRNA-seq) was performed. Real-time polymerase chain reaction (RT-PCR) and multiplex immunofluorescence staining were performed to verify the reliability of the conclusions. Results: A four-gene risk scoring model was constructed. Kaplan–Meier curve analysis showed that the high-risk group had a worse prognosis (p < 0.001). The time-dependent receiver operating characteristic (ROC) curve showed that the OS risk score prediction performance was good. These results were further confirmed in the validation queue. Meanwhile, the Tregs and macrophages were enriched in the cuproptosis-related TIME of HCC. Conclusions: The CRGs-based signature model could predict the prognosis of HCC. Treg and macrophages were significantly enriched in cuproptosis-related HCC, which was associated with the depletion of proliferating T cells. Full article

Queueing models can be used for making decisions about the resources required to provide high quality service. In this paper, a finite capacity single server queueing model with bulk arrivals is studied in IoT-based edge computing systems. The transient analysis of the model is carried out and the transient analytical solution to the system is derived with a group of recursive coefficients by using the ordinary differential equations (ODEs) technique. From which the steady-state probabilities are solved. Then, some performance metrics of interest are derived along with numerical results. Although the paper is initiated from the IoT based edge computing platform, the proposed system modeling and analysis method can be extended to more general situations such as telecommunication, manufacturing, transportation, and many other areas that are closely related to people’s daily lives. Full article

Bulk-service queueing systems have been widely applied in many areas in real life. While single-server queueing systems work in some cases, multi-servers can efficiently handle most complex applications. Bulk-service, multi-server queueing systems (compared to well-developed single-server queueing systems) are more complex and harder to deal with, especially when the inter-arrival time distributions are arbitrary. This paper deals with analytic and computational analyses of queue-length distributions for a complex bulk-service, multi-server queueing system GI/M^$a,b$/c, wherein inter-arrival times follow an arbitrary distribution, a is the quorum, and b is the capacity of each server; service times follow exponential distributions. The introduction of quorum a further increases the complexity of the model. In view of this, a two-dimensional Markov chain has to be involved. Currently, it appears that this system has not been addressed so far. An elegant analytic closed-form solution and an efficient algorithm to obtain the queue-length distributions at three different epochs, i.e., pre-arrival epoch (p.a.e.), random epoch (r.e.), and post-departure epoch (p.d.e.) are presented, when the servers are in busy and idle states, respectively. Full article

In most of the service systems considered so far in queuing theory, no fresh customer is admitted to a batch undergoing service when the number in the batch is less than a threshold. However, a few researchers considered the case of customers accessing ongoing service batch, irrespective of how long service was provided to that batch. A queuing system with a different kind of accessibility that relates to a real situation is studied in the paper. Consider a single server queuing system in which the service process comprises of k stages. Customers can enter the system for service from a node at the beginning of any of these stages (provided the pre-determined maximum service batch size is not reached) but cannot leave the system after completion of service in any of the intermediate stages. The customer arrivals to the first node occur according to a Markovian Arrival Process $\left(MAP\right)$. An infinite waiting room is provided at this node. At all other nodes, with finite waiting rooms (waiting capacity $c_j,2\le j\le k$), customer arrivals occur according to distinct Poisson processes with rates ${\lambda }_j,2\le j\le k$. The service is provided according to a general bulk service rule, i.e., the service process is initiated only if at least a customers are present in the queue at node 1 and the maximum service batch size is b. Customers can join for service from any of the subsequent nodes, provided the number undergoing service is less than b. The service time distribution in each phase is exponential with service rate ${\mu }_j^m$, which depends on the service stage $j,1\le j\le k$, and the size of the batch $m,a\le m\le b$. The behavior of the system in steady-state is analyzed and some important system characteristics are derived. A numerical example is presented to illustrate the applicability of the results obtained. Full article

The problem considered is the computation of the (limiting) time-dependent performance characteristics of one-dimensional continuous-time Markov chains with discrete state space and time varying intensities. Numerical solution techniques can benefit from methods providing ergodicity bounds because the latter can indicate how to choose the position and the length of the “distant time interval” (in the periodic case) on which the solution has to be computed. They can also be helpful whenever the state space truncation is required. In this paper one such analytic method—the logarithmic norm method—is being reviewed. Its applicability is shown within the queueing theory context with three examples: the classical time-varying $M/M/2$ queue; the time-varying single-server Markovian system with bulk arrivals, queue skipping policy and catastrophes; and the time-varying Markovian bulk-arrival and bulk-service system with state-dependent control. In each case it is shown whether and how the bounds on the rate of convergence can be obtained. Numerical examples are provided. Full article

This paper proposes a real-time chain and a novel embedded Markovian queueing model with variable bulk arrival (VBA) and variable bulk service (VBS) in order to establish and assure a theoretical foundation to design a blockchain-based real-time system with particular interest in Ethereum. Based on the proposed model, various performances are simulated in a numerical manner in order to validate the efficacy of the model by checking good agreements with the results against intuitive and typical expectations as a baseline. A demo of the proposed real-time chain is developed in this work by modifying the open source of Ethereum Geth 1.9.11. The work in this paper will provide both a theoretical foundation to design and optimize the performances of the proposed real-time chain, and ultimately address and resolve the performance bottleneck due to the conventional block-synchrony by employing an asynchrony by the real-time deadline to some extent. Full article