Queueing Analysis Research Articles

Cost Analysis of a Finite Capacity Queue with Server Failures, Balking, and Threshold-Driven Recovery Policy

The study is on the cost dynamics which is concerned with finite queues in particular to susceptibility to server outages, threshold-driven recovery and Catastrophic events, but main focus is on balking behaviour of the customers. A thorough investigation of the financial implications of interruptions and efficacy to recovery strategies is done and to alleviate the impact of breakdowns, disasters and customer refusals the queue system designs through empirical research is conducted. Various recovery policies have been compared with the existing thresholds, and the study further endeavors to categorize the cost-effective approach to mitigate the economic concerns of server failures and catastrophic incidents. The study brings discernments on the expected development in the management of the queuing system along with the assistance in complete decision-making in cost efficiency and enhancement of the complete system performance.

Analysis of Bulk Arrival Recurrent Queue with Active and Passive Breakdowns

Analysis of Bulk Arrival Recurrent Queue with Active and Passive Breakdowns

Performance analysis of a versatile bulk-service queue with group-arrival, batch-size-dependent service time and queue-length-dependent vacation

ABSTRACT Queueing systems with bulk-service and vacation policy have become one of the pivotal interest for the researchers due to their widespread application in food processing technology, manufacturing systems, power consumption in small cell base stations etc. This article analyzes a single server versatile bulk-service queueing system wherein the customers arrive according to a compound Poisson process and the service time is dependent on the batch size of undergoing service. Moreover, single and multiple vacation policies have been incorporated along with queue-length-dependent vacation. After providing the steady-state system equations, the bivariate probability generating function of queue and server content distribution together has been derived at departure epoch. After the evaluation of the unknown probabilities, complete joint distributions have been extracted in terms of roots of the denominator of the bivariate probability generating function. The discussed procedure and the reported results have been depicted through some numerical examples for different service and vacation time distributions. Some significant observation about the model has been sketched graphically.

Exploring non-Markovian dynamics: Stochastic analysis of a single-server retrial queue with recurrent clients and balking behavior under extended Bernoulli vacations

The present study delves into the dynamics of a specific form of queueing system described as an M/G/1 retrial queue. Here, the queue comprises two distinct categories of clients: transit clients and recurrent clients. Transit clients are those who appear at the queue following a Poisson process, reflecting a random arrival pattern commonly seen in queueing scenarios. On the other hand, recurrent clients are predefined entities who immediately rejoin the queue once they've been served, demonstrating repetitive behavior in their interactions with the system. Once the server completes servicing a client, it initiates a vacation period. Moreover, in this approach, an optional extended vacation is also taken into account, i.e., the server may opt to indulge in an extended vacation following the initial essential Bernoulli vacation. Also, the consumers are allowed to balk. Further, the ergodicity requirement for the system's stability and then analytical findings for the stationary distribution are obtained. Additionally, various performance metrics for the system are also established. Furthermore, a comprehensive cost function is formulated and further optimized by incorporating a particle swarm optimization (PSO) approach. The convergence analysis is conducted as well, which is supported by illustrative figures. As a result, this work provides a beneficial understanding of enhancing the efficiency of such intricate queueing systems.

Transient analysis of a bulk stream queue with arbitrarily distributed arrival intervals

We study the classical infinite buffer single server queueing model with renewal input of customers in batches of random size, having arbitrarily distributed arrival intervals and exponentially distributed service times. Using the technique of supplementary variable and shift operator we derive closed form expression of the time dependent system content distribution in terms of its Laplace transform. The analysis is mainly based on the root-finding technique of the non-linear characteristic equation in terms of the Laplace transform variable. Additionally, using asymptotic properties of Laplace transform, we deduce the corresponding steady-state distribution. We discuss some special cases of the model, thus providing an alternative approach in deriving the transient distribution. We further evaluate certain performance measures and present extensive numerical examples in tabular and graphical form to illustrate the applicability of our theoretical work. The effect of system parameters, interarrival time distribution and traffic intensity on the system behavior is also demonstrated.

M/M/1/FCFS/~ /~ QUEUE MODEL SIMULATION WITH EXCEL

Queuing Theory is a conceptual framework used to analyze and optimize the queuing or waiting process in the context of a service system. In queuing theory, customers arrive at the service server from a source, where they can immediately start service or wait in a queue if the server is busy. Once service is complete, the server automatically serves the next customer in the queue. In queuing analysis, customer arrival time is represented by the inter-arrival interval while service is measured by service time per customer. Even though queuing theory is a simple method, it can become complex if done manually because it requires high accuracy. Using Microsoft Excel is the right tool because it makes it easier to carry out calculations accurately. Excel displays the calculation results in spreadsheet form so that the calculation stages can be more easily understood..

Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment

Analysis of Renewal Batch Arrival Queues with Multiple Vacations and Geometric Abandonment

Modeling and optimizing an AMS with DV policy, waiting servers, impatient customers, and failures: A queueing analysis

In this paper, we analyze an automated manufacturing system modeled as a queueing system with multiple servers, differentiated vacation (DV) policy, customer impatience, and server failures. We consider the waiting servers policy, where the servers wait for a random duration before leaving for a vacation once the system gets empty. Upon their return, if no customers are waiting, the servers may leave for a second type-2 vacation of shorter duration. The system may experience breakdowns and require immediate repair. During the repair period, customers are served at a lower rate, and they become impatient during busy, vacation, and repair periods, abandoning the queue if their timer expires. Further, based on the queue length, arriving customers may either join the system or balk with some probability. We use the matrix analytic method to derive the steady-state probability of the system and several performance measures. Moreover, we illustrate the effect of different system parameters on various performance measures. Additionally, we develop a cost model and optimize the system capacity, number of servers, and service rates such that cost per unit time is minimized. Finally, we analyze the impact of system parameters on the cost through numerical examples.

Queue Analysis at Sari Mulia Campus ATM

Queue Analysis at Sari Mulia Campus ATM

Analysis of Tandem Queue with Multi-Server Stages and Group Service at the Second Stage

In this paper, we consider a tandem dual queuing system consisting of multi-server stages. Stage 1 is characterized by an infinite buffer, one-by-one service of customers, and an exponential distribution of service times. Stage 2 is characterized by a finite buffer and a phase-type distribution of service times. Service at Stage 2 is provided to groups of customers. The service time of a group depends on the size of the group. The size is restricted by two thresholds. The waiting time of a customer at each stage is limited by a random variable with an exponential distribution, with the parameter depending on the stage. After service at Stage 1, a customer can depart from the system or try to enter Stage 2. If the buffer at this stage is full, the customer is either lost or returns for service at Stage 1. Customer arrivals are described by the versatile Markov arrival process. The system is studied via consideration of a multi-dimensional continuous-time Markov chain. Numerical examples, which highlight the influence of the thresholds on the system performance measures, are presented. The possibility of solving optimization problems is illustrated.

Elaborated Analysis of a Nonreplenishable Queue with Erlang Distribution of the Service Time

Elaborated Analysis of a Nonreplenishable Queue with Erlang Distribution of the Service Time

Progressions of the correlation between lipid metabolism and immune infiltration characteristics in gastric cancer and identification of BCHE as a potential biomarker.

Globally, gastric cancer (GC) is a category of prevalent malignant tumors. Its high occurrence and fatality rates represent a severe threat to public health. According to recent research, lipid metabolism (LM) reprogramming impacts immune cells' ordinary function and is critical for the onset and development of cancer. Consequently, the article conducted a sophisticated bioinformatics analysis to explore the potential connection between LM and GC. We first undertook a differential analysis of the TCGA queue to recognize lipid metabolism-related genes (LRGs) that are differentially expressed. Subsequently, we utilized the LASSO and Cox regression analyses to create a predictive signature and validated it with the GSE15459 cohort. Furthermore, we examined somatic mutations, immune checkpoints, tumor immune dysfunction and exclusion (TIDE), and drug sensitivity analyses to forecast the signature's immunotherapy responses. Kaplan-Meier (K-M) curves exhibited considerably longer OS and PFS (p<0.001) of the low-risk (LR) group. PCA analysis and ROC curves evaluated the model's predictive efficacy. Additionally, GSEA analysis demonstrated that a multitude of carcinogenic and matrix-related pathways were much in the high-risk (HR) group. We then developed a nomogram to enhance its clinical practicality, and we quantitatively analyzed tumor-infiltrating immune cells (TIICs) using the CIBERSORT and ssGSEA algorithms. The low-risk group has a lower likelihood of immune escape and more effective in chemotherapy and immunotherapy. Eventually, we selected BCHE as a potential biomarker for further research and validated its expression. Next, we conducted a series of cell experiments (including CCK-8 assay, Colony formation assay, wound healing assay and Transwell assays) to prove the impact of BCHE on gastric cancer biological behavior. Our research illustrated the possible consequences of lipid metabolism in GC, and we identified BCHE as a potential therapeutic target for GC. The LRG-based signature could independently forecast the outcome of GC patients and guide personalized therapy.

Transient analysis of energy-saving strategy for cognitive radio networks using G-queue with heterogeneity

Energy efficiency, high data speeds, and effective spectrum utilization stand as the primary factors governing 5G and beyond networks. A base station (BS) in a cognitive radio network (CRN) that conserves energy during sleep periods is a promising contender for achieving more effective spectrum allocation. An efficient energy-saving strategy is offered in this study to achieve greener communication in wireless cellular networks. This study aims to propose and analyze an energy-saving scheme for the BS, taking into account the heterogeneity and reliability of networks. The entire system is modeled as a three-dimensional Markov chain by establishing a discrete-time preemptive priority queueing model with single vacation, heterogeneous packets, and negative packets such as viruses. Then, the transient analysis of the Markov chain is performed using the recursive method. Utilizing the transient probability distribution, we present numerical results derived from reliability analysis and queueing analysis to substantiate the validity of the proposed model. Furthermore, results based on the energy-saving degree are showcased to affirm the effectiveness of the proposed scheme. Finally, a reward cost function is obtained depending on the successful transmission of secondary packets, and the Quasi-Newton method is used to determine the optimal reward cost.

Sensitivity analysis of a non-Markovian feedback retrial queue, reneging, delayed repair with working vacation subject to server breakdown

This study investigated the steady-state characteristics of a non-Markovian feedback retrial queue with reneging, delayed repair, and working vacation. In this scenario, we assumed that consumers arrive through Poisson processes and the server provides service to consumers during both regular and working vacation periods. However, it is subject to breakdowns at any moment, resulting in a service interruption for a random duration. Additionally, the concept of delay time was also presented. The consumer that is dissatisfied with the service may re-enter the orbit to receive another service; this individual is considered a feedback consumer. The server will go on a working vacation if the orbit is empty after successfully serving a satisfied consumer. By utilizing the supplementary variable technique (SVT), we examined the steady-state probability generating function of the system and orbit sizes. Finally, numerical outcomes and a sensitivity analysis were given to verify the analytical findings of important performance indicators.

Performance approximations of Markov Modulated Poisson Process arrival queue with Markovian Service using matrix geometric approach

Queue analysis of correlated work of the arrival and the service process are not available much in literature. This research paper applies matrix geometric approach to study the MMPP/MSP/1 queuing model under the quasi-birth death(QBD) process. Customers admitted in the system are having two different intensity of arrival followed by Markov Modulated Poisson Process(MMPP). MMPP is a versatile class of MAP and it is necessary to adapt the first characterization of the queuing model. In service mechanism Markov Service Process(MSP) is adopted. As like MMPP, MSP is also a versatile and can capture the correlation of the modulated arrivals. The methodology presented in this research work calculates the metric performances not depending on the series of infinite state of the system. The assumed model is formulated as QBD process to obtain the steady state probability of the system. The complexity model formulated involves structures matrices with appropriate dimension. Neut?s pioneered the matrix geometric approach to such complex models which involves the rate computation of rate matrix R. The rate matrix R is approximated to derive the performance metrics of the system and then compute the cost for the underlying Markov chain. To attain this approximation the sensitivity analysis is done with numerical results.

Comparative Analysis of Different Binary Tree and Priority Queue (Heap) Algorithms

Comparative Analysis of Different Binary Tree and Priority Queue (Heap) Algorithms

Analysis of two-station polling queues with setups

Analysis of two-station polling queues with setups

Transient Analysis of a Single Server Queue with Working Vacation Operating in a Multi-Level Environment Controlled by a Random Switch

A single server queueing system with working vacation operating in a multi-level environment controlled by a random switch is considered. The environment has [Formula: see text] levels and the random switch puts the server in one of the [Formula: see text] levels to perform a service. The server resides in a level and reports to the random switch immediately after completing the service of the last customer in the queue. The random switch initiates an assignment process immediately at the arrival of a customer. The assignment process takes a random time and immediately at the end of the assignment interval, the server is put to operate in any one of the [Formula: see text] levels with a positive probability. In each level [Formula: see text] of the environment, the queueing system behaves like an [Formula: see text] queue and switches to a working vacation at a random time and serves with a lesser rate [Formula: see text] During the working vacation, all newly arriving customers are lost. When the server is with the control switch, customers are permitted to join in the queue. For this model, time-dependent state probabilities are explicitly found and the corresponding steady-state probabilities are deduced. Some key performance measures are also obtained. A numerical study is also made.

Exact and asymptotic analysis of infinite server batch service queues with random batch sizes

Exact and asymptotic analysis of infinite server batch service queues with random batch sizes

Analysis of Queues Fed by Lognormal Distributed Arrivals for IoT Network Traffic

Analysis of Queues Fed by Lognormal Distributed Arrivals for IoT Network Traffic