Search results for: queueing

Authors: Saulius Minkevicius, Edvinas Greicius

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The paper is devoted to the analysis of queueing systems in the context of the network and communications theory. We investigate the inequality in an open queueing network and its applications to the theorems in heavy traffic conditions (fluid approximation, functional limit theorem, and law of the iterated logarithm) for a queue of customers in an open queueing network.

Keywords: fluid approximation, heavy traffic, models of information systems, open queueing network, queue length of customers, queueing theory

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Authors: Samaneh Rahimirshnani, Hossein Jafari

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In this paper, we consider fluid queueing processes fed by an isonormal Gaussian process. We study the correlation structure of the queueing process and the rate of convergence of the running supremum in the queueing process. The Malliavin calculus techniques are applied to obtain relations that show the workload process inherits the dependence properties of the input process. As examples, we consider two isonormal Gaussian processes, the sub-fractional Brownian motion (SFBM) and the fractional Brownian motion (FBM). For these examples, we obtain upper bounds for the covariance function of the queueing process and its rate of convergence to zero. We also discover that the rate of convergence of the queueing process is related to the structure of the covariance function of the input process.

Keywords: queue length process, Malliavin calculus, covariance function, fractional Brownian motion, sub-fractional Brownian motion

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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In this paper we study that the catastrophic events arrive independently at the service facility according to a Poisson process with rate λ. The nature of a catastrophic event is that upon its arrival at a service station, it destroys all the customers there waiting and in the service. We will derive the net profit associated with queuing system and obtain its probability of the busy period.

Keywords: queueing system, net-profit, busy period, catastrophical events

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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This study analyzed a queueing system with blocking and no waiting line. The customers arrive according to a Poisson process and the service times follow exponential distribution. There are two non-identical servers in the system. The queue discipline is FCFS, and the customers select the servers on fastest server first (FSF) basis. The service times are exponentially distributed with parameters μ1 and μ2 at servers I and II, respectively. Besides, the catastrophes occur in a Poisson manner with rate γ in the system. When server I is busy or blocked, the customer who arrives in the system leaves the system without being served. Such customers are called lost customers. The probability of losing a customer was computed for the system. The explicit time dependent probabilities of system size are obtained and a numerical example is presented in order to show the managerial insights of the model. Finally, the probability that arriving customer finds system busy and average number of server busy in steady state are obtained numerically.

Keywords: queueing system, blocking, poisson process, heterogeneous servers, queue discipline FCFS, busy period

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Authors: Emad Alenany, M. Adel El-Baz

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In this paper, the flow of different classes of patients into a hospital is modelled and analyzed by using the queueing network analyzer (QNA) algorithm and discrete event simulation. Input data for QNA are the rate and variability parameters of the arrival and service times in addition to the number of servers in each facility. Patient flows mostly match real flow for a hospital in Egypt. Based on the analysis of the waiting times, two approaches are suggested for improving performance: Separating patients into service groups, and adopting different service policies for sequencing patients through hospital units. The separation of a specific group of patients, with higher performance target, to be served separately from the rest of patients requiring lower performance target, requires the same capacity while improves performance for the selected group of patients with higher target. Besides, it is shown that adopting the shortest processing time and shortest remaining processing time service policies among other tested policies would results in, respectively, 11.47% and 13.75% reduction in average waiting time relative to first come first served policy.

Keywords: queueing network, discrete-event simulation, health applications, SPT

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Authors: Kailash C. Madan

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We study four models of a three server queueing system with Bernoulli schedule optional server vacations. Customers arriving at the system one by one in a Poisson process are provided identical exponential service by three parallel servers according to a first-come, first served queue discipline. In model A, all three servers may be allowed a vacation at one time, in Model B at the most two of the three servers may be allowed a vacation at one time, in model C at the most one server is allowed a vacation, and in model D no server is allowed a vacation. We study steady the state behavior of the four models and obtain steady state probability generating functions for the queue size at a random point of time for all states of the system. In model D, a known result for a three server queueing system without server vacations is derived.

Keywords: a three server queue, Bernoulli schedule server vacations, queue size distribution at a random epoch, steady state

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Authors: Reni M. Sagayaraj, Anand Gnana S. Selvam, Reynald R. Susainathan

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In this paper, we consider stochastic queueing models for Steady-state behavior of a multi-phase M/M/1 queue in random evolution subject to catastrophe failure. The arrival flow of customers is described by a marked Markovian arrival process. The service times of different type customers have a phase-type distribution with different parameters. To facilitate the investigation of the system we use a generalized phase-type service time distribution. This model contains a repair state, when a catastrophe occurs the system is transferred to the failure state. The paper focuses on the steady-state equation, and observes that, the steady-state behavior of the underlying queueing model along with the average queue size is analyzed.

Keywords: M/G/1 queuing system, multi-phase, random evolution, steady-state equation, catastrophe failure

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Authors: R. Remya

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We consider an M/M/1 multiple variant vacation queueing system and working vacation with waiting server. Here, comparing considering three models. First model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. After completing a working vacation, the server will wait for a random period of time before going on vacation. Then it goes to finite number of vacations same way. After end of J th vacation server waits in busy or served immediately. Second model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. Third model, working vacation is taken after the server has exhaustively served all the customers in the system and waits random amount of time. It is expected that service times and vacation lengths are exponentially distributed . We provide a steady-state solution and cost comparison for the stated models.

Keywords: vacation, working vacation, waiting server, steady state analysis, cost analysis

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Authors: Yutae Lee

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This paper considers a discrete-time bulk-arrival bulkservice queueing system, where service capacity varies depending on the previous service time. By using the generating function technique and the supplementary variable method, we compute the distributions of the queue length at an arbitrary slot boundary and a departure time.

Keywords: discrete-time queue, bulk queue, variable service capacity, queue length distribution

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Authors: Baya Takhedmit, Karim Abbas, Sofiane Ouazine

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The vacations queues are often employed to model many real situations such as computer systems, communication networks, manufacturing and production systems, transportation systems and so forth. These queueing models are solved at fixed parameters values. However, the parameter values themselves are determined from a finite number of observations and hence have uncertainty associated with them (epistemic uncertainty). In this paper, we consider the M/G/1/N queue with server vacation and exhaustive discipline where we assume that the vacation parameter values have uncertainty. We use the Taylor series expansions approach to estimate the expectation and variance of model output, due to epistemic uncertainties in the model input parameters.

Keywords: epistemic uncertainty, M/G/1/N queue with vacations, non-parametric sensitivity analysis, Taylor series expansion

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Authors: Madhu Jain, Rakesh Kumar Meena

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This paper investigates a finite M/G/1 fault tolerant multi-component machining system. The system incorporates the features such as standby support, threshold recovery and imperfect coverage make the study closer to real time systems. The performance prediction of M/G/1 fault tolerant system is carried out using recursive approach by treating remaining service time as a supplementary variable. The numerical results are presented to illustrate the computational tractability of analytical results by taking three different service time distributions viz. exponential, 3-stage Erlang and deterministic. Moreover, the cost function is constructed to determine the optimal choice of system descriptors to upgrading the system.

Keywords: fault tolerant, machine repair, threshold recovery policy, imperfect coverage, supplementary variable technique

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Authors: Fazia Rahmoune, Sofiane Ziani

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Retrial queueing systems have been extensively used to stochastically model many problems arising in computer networks, telecommunication, telephone systems, among others. In this work, we consider a $M/G/1$ retrial queue with an unreliable server with random vacations and two types of primary customers, persistent and impatient. This model involves the unreliability of the server, which can be subject to physical breakdowns and takes into account the correctives maintenances for restoring the service when a failure occurs. On the other hand, we consider random vacations, which can model the preventives maintenances for improving system performances and preventing breakdowns. We give the necessary and sufficient stability condition of the system. Then, we obtain the joint probability distribution of the server state and the number of customers in orbit and derive the more useful performance measures analytically. Moreover, we also analyze the busy period of the system. Finally, we derive the stability condition and the generating function of the stationary distribution of the number of customers in the system when there is no vacations and impatient customers, and when there is no vacations, server failures and impatient customers.

Keywords: modeling, retrial queue, unreliable server, vacation, stochastic analysis

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Authors: Likewin Thomas, M. V. Manoj Kumar, B. Annappa

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Traditional execution process follows the path of execution drawn by the process analyst without observing the behaviour of resource and other real-time constraints. Identifying process model, predicting the behaviour of resource and recommending the optimal path of execution for a real time process is challenging. The proposed AlfyMiner: αyM iner gives a new dimension in process execution with the novel techniques Process Model Analyser: PMAMiner and Resource behaviour Analyser: RBAMiner for recommending the probable path of execution. PMAMiner discovers next probable activity for currently executing activity in an online process using variant matching technique to identify the set of next probable activity, among which the next probable activity is discovered using decision tree model. RBAMiner identifies the resource suitable for performing the discovered next probable activity and observe the behaviour based on; load and performance using polynomial regression model, and waiting time using queueing theory. Based on the observed behaviour αyM iner recommend the probable path of execution with; next probable activity and the best suitable resource for performing it. Experiments were conducted on process logs of CoSeLoG Project1 and 72% of accuracy is obtained in identifying and recommending next probable activity and the efficiency of resource performance was optimised by 59% by decreasing their load.

Keywords: cross-organization process mining, process behaviour, path of execution, polynomial regression model

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Authors: Amirhossein Chambari

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This article proposes a bi-objective model for the facility location problem subject to congestion (overcrowding). Motivated by implementations to locate servers in internet mirror sites, communication networks, one-server-systems, so on. This model consider for situations in which immobile (or fixed) service facilities are congested (or queued) by stochastic demand to behave as M/M/1/K queues. We consider for this problem two simultaneous perspectives; (1) Customers (desire to limit times of accessing and waiting for service) and (2) Service provider (desire to limit average facility idle-time). A bi-objective model is setup for facility location problem with two objective functions; (1) Minimizing sum of expected total traveling and waiting time (customers) and (2) Minimizing the average facility idle-time percentage (service provider). The proposed model belongs to the class of mixed-integer nonlinear programming models and the class of NP-hard problems. In addition, to solve the model, controlled elitist non-dominated sorting genetic algorithms (Controlled NSGA-II) and controlled elitist non-dominated ranking genetic algorithms (NRGA-I) are proposed. Furthermore, the two proposed metaheuristics algorithms are evaluated by establishing standard multiobjective metrics. Finally, the results are analyzed and some conclusions are given.

Keywords: bi-objective, facility location, queueing, controlled NSGA-II, NRGA-I

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Authors: S. Vadivukkarasi, K. Karthi, M. Karthick, C. Dinesh, S. Santhosh, A. Yogaraj

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The appointment system was designed to minimize patient’s idle time overlooking patients waiting time in hospitals. This is no longer valid in today’s consumer oriented society. Long waiting times for treatment in the outpatient department followed by short consultations has long been a complaint. Nowadays, customers use waiting time as a decisive factor in choosing a service provider. Queuing theory constitutes a very powerful tool because queuing models require relatively little data and are simple and fast to use. Because of this simplicity and speed, modelers can be used to quickly evaluate and compare various alternatives for providing service. The application of queuing models in the analysis of health care systems is increasingly accepted by health care decision makers. Timely access to care is a key component of high-quality health care. However, patient delays are prevalent throughout health care systems, resulting in dissatisfaction and adverse clinical consequences for patients as well as potentially higher costs and wasted capacity for providers. Arguably, the most critical delays for health care are the ones associated with health care emergencies. The allocation of resources can be divided into three general areas: bed management, staff management, and room facility management. Effective and efficient patient flow is indicated by high patient throughput, low patient waiting times, a short length of stay at the hospital and overtime, while simultaneously maintaining adequate staff utilization rates and low patient’s idle times.

Keywords: appointment system, patient scheduling, bed management, queueing calculation, system analysis

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Authors: R. Sivasamy, G. Paulraj, S. Kalaimani, N.Thillaigovindan

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For profitable businesses, queues are double-edged swords and hence the pain of long wait times in a queue often frustrates customers. This paper suggests a technical way of reducing the pain of lines through a Poisson M/M1, M2/2 queueing system operated by two heterogeneous servers with an objective of minimising the mean sojourn time of customers served under the queue discipline ‘First Come First Served with an ‘m’ policy, i.e. FCFS-m policy’. Arrivals to the system form a Poisson process of rate λ and are served by two exponential servers. The service times of successive customers at server ‘j’ are independent and identically distributed (i.i.d.) random variables and each of it is exponentially distributed with rate parameter μj (j=1, 2). The primary condition for implementing the queue discipline ‘FCFS-m policy’ on these service rates μj (j=1, 2) is that either (m+1) µ2 > µ1> m µ2 or (m+1) µ1 > µ2> m µ1 must be satisfied. Further waiting customers prefer the server-1 whenever it becomes available for service, and the server-2 should be installed if and only if the queue length exceeds the value ‘m’ as a threshold. Steady-state results on queue length and waiting time distributions have been obtained. A simple way of tracing the optimal service rate μ*2 of the server-2 is illustrated in a specific numerical exercise to equalize the average queue length cost with that of the service cost. Assuming that the server-1 has to dynamically adjust the service rates as μ1 during the system size is strictly less than T=(m+2) while μ2=0, and as μ1 +μ2 where μ2>0 if the system size is more than or equal to T, corresponding steady state results of M/M1+M2/1 queues have been deduced from those of M/M1,M2/2 queues. To conclude this investigation has a viable application, results of M/M1+M2/1 queues have been used in processing of those waiting messages into a single computer node and to measure the power consumption by the node.

Keywords: two heterogeneous servers, M/M1, M2/2 queue, service cost and queue length cost, M/M1+M2/1 queue

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Authors: Cruz Queen Allysa Rose, Bautista Joymeeh Anne, Lantoria Kaye, Barretto Katya Louise

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The study presents the preferences of passengers on the quality of service provided by the two airline check-in methods currently present in airports-traditional counter check-in and common-use self-service kiosks. Since a study has shown that airlines perceive self-service kiosks alone are sufficient enough to ensure adequate services and customer satisfaction, and in contrast, agents and passengers stated that it alone is not enough and that human interaction is essential. In reference with former studies that established opposing ideas about the choice of the more favorable airline check-in method to employ, it is the purpose of this study to present a recommendation that shall somehow fill-in the gap between the conflicting ideas by means of comparing the perceived quality of service through the RATER model. Furthermore, this study discusses the major competencies present in each method which are supported by the theories–FIRO Theory of Needs upholding the importance of inclusion, control and affection, and the Queueing Theory which points out the discipline of passengers and the length of the queue line as important factors affecting quality service. The findings of the study were based on the data gathered by the researchers from selected Thomasian third year and fourth year college students currently enrolled in the first semester of the academic year 2014-2015, who have already experienced both airline check-in methods through the implication of a stratified probability sampling. The statistical treatments applied in order to interpret the data were mean, frequency, standard deviation, t-test, logistic regression and chi-square test. The final point of the study revealed that there is a greater effect in passenger preference concerning the satisfaction experienced in common-use self-service kiosks in comparison with the application of the traditional counter check-in.

Keywords: traditional counter check-in, common-use self-service Kiosks, airline check-in methods

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Authors: Yixin Zhu, Lishengsa Yue, Jian Sun, Lanyue Tang

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Modeling driving distraction in microscopic traffic simulation is crucial for enhancing simulation accuracy. Current driving distraction models are mainly derived from physical motion constraints under distracted states, in which distraction-related error terms are added to existing microscopic driver models. However, the model accuracy is not very satisfying, due to a lack of modeling the cognitive mechanism underlying the distraction. This study models driving distraction based on the Queueing Network Human Processor model (QN-MHP). This study utilizes the queuing structure of the model to perform task invocation and switching for distracted operation and control of the vehicle under driver distraction. Based on the assumption of the QN-MHP model about the cognitive sub-network, server F is a structural bottleneck. The latter information must wait for the previous information to leave server F before it can be processed in server F. Therefore, the waiting time for task switching needs to be calculated. Since the QN-MHP model has different information processing paths for auditory information and visual information, this study divides driving distraction into two types: auditory distraction and visual distraction. For visual distraction, both the visual distraction task and the driving task need to go through the visual perception sub-network, and the stimuli of the two are asynchronous, which is called stimulus on asynchrony (SOA), so when calculating the waiting time for switching tasks, it is necessary to consider it. In the case of auditory distraction, the auditory distraction task and the driving task do not need to compete for the server resources of the perceptual sub-network, and their stimuli can be synchronized without considering the time difference in receiving the stimuli. According to the Theory of Planned Behavior for drivers (TPB), this study uses risk entropy as the decision criterion for driver task switching. A logistic regression model is used with risk entropy as the independent variable to determine whether the driver performs a distraction task, to explain the relationship between perceived risk and distraction. Furthermore, to model a driver’s perception characteristics, a neurophysiological model of visual distraction tasks is incorporated into the QN-MHP, and executes the classical Intelligent Driver Model. The proposed driving distraction model integrates the psychological cognitive process of a driver with the physical motion characteristics, resulting in both high accuracy and interpretability. This paper uses 773 segments of distracted car-following in Shanghai Naturalistic Driving Study data (SH-NDS) to classify the patterns of distracted behavior on different road facilities and obtains three types of distraction patterns: numbness, delay, and aggressiveness. The model was calibrated and verified by simulation. The results indicate that the model can effectively simulate the distracted car-following behavior of different patterns on various roadway facilities, and its performance is better than the traditional IDM model with distraction-related error terms. The proposed model overcomes the limitations of physical-constraints-based models in replicating dangerous driving behaviors, and internal characteristics of an individual. Moreover, the model is demonstrated to effectively generate more dangerous distracted driving scenarios, which can be used to construct high-value automated driving test scenarios.

Keywords: computational cognitive model, driving distraction, microscopic traffic simulation, psychological-physical constraints

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Authors: Yuguang Gao, Mingtao Deng

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The integration of independently operating hospitals into a unified healthcare service system has become a strategic imperative in the pursuit of hospitals’ high-quality development. Central to the concept of group governance over such transformation, exemplified by a collaborative medical alliance, is the delineation of shared value, vision, and goals. Given the inherent disparity in capabilities among hospitals within the alliance, particularly in the treatment of different diseases characterized by Disease Related Groups (DRG) in terms of effectiveness, efficiency and resource utilization, this study aims to address the centralized decision-making of intra-hospital patient referral within the medical alliance to enhance the overall production and quality of service provided. We first introduce the notion of production utility, where a higher production utility for a hospital implies better performance in treating patients diagnosed with that specific DRG group of diseases. Then, a Discrete-Event Simulation (DES) framework is established for patient referral among hospitals, where patient flow modeling incorporates a queueing system with fixed capacities for each hospital. The simulation study begins with a two-member alliance. The pivotal strategy examined is a "whether-to-refer" decision triggered when the bed usage rate surpasses a predefined threshold for either hospital. Then, the decision encompasses referring patients to the other hospital based on DRG groups’ production utility differentials as well as bed availability. The objective is to maximize the total production utility of the alliance while minimizing patients’ average length of stay and turnover rate. Thus the parameter under scrutiny is the bed usage rate threshold, influencing the efficacy of the referral strategy. Extending the study to a three-member alliance, which could readily be generalized to multi-member alliances, we maintain the core setup while introducing an additional “which-to-refer" decision that involves referring patients with specific DRG groups to the member hospital according to their respective production utility rankings. The overarching goal remains consistent, for which the bed usage rate threshold is once again a focal point for analysis. For the two-member alliance scenario, our simulation results indicate that the optimal bed usage rate threshold hinges on the discrepancy in the number of beds between member hospitals, the distribution of DRG groups among incoming patients, and variations in production utilities across hospitals. Transitioning to the three-member alliance, we observe similar dependencies on these parameters. Additionally, it becomes evident that an imbalanced distribution of DRG diagnoses and further disparity in production utilities among member hospitals may lead to an increase in the turnover rate. In general, it was found that the intra-hospital referral mechanism enhances the overall production utility of the medical alliance compared to individual hospitals without partnership. Patients’ average length of stay is also reduced, showcasing the positive impact of the collaborative approach. However, the turnover rate exhibits variability based on parameter setups, particularly when patients are redirected within the alliance. In conclusion, the re-structuring of diagnostic disease groups within the medical alliance proves instrumental in improving overall healthcare service outcomes, providing a compelling rationale for the government's promotion of patient referrals within collaborative medical alliances.

Keywords: collaborative medical alliance, disease related group, patient referral, simulation

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