Multiple Server Queues Research Articles

Strength and Limitation of Biological Paradigm during Pandemic of Covid-19: An Application of Queueing Theory

The coronavirus disorder is an epidemic induced by the SARS-CoV-2 germ. The health region is recognized as one of the most important areas in the service sector due to its direct connection to human well-being, particularly in context of the pandemic COVID-19. The overcrowding of patients in the patient registration department, outpatient department, and pharmacy department is the most important issue facing hospitals these days. The investigation of the patient registration, outpatient, and pharmacy departments of PIMS hospital in Islamabad and Benazir Bhutto hospital in Rawalpindi served as the foundation for this study. Queuing Theory is an extension of operation research and is concerned with the aspect of queues. Additionally, the multiple-server queueing model is used to calculate the performance parameters. The approach of queuing simulation used in this research deals with multiple queues and multiple server models. Poisson distribution is used to estimate the arrival rate and exponential distribution is used to calculate the service rate. The satisfaction level of patients with hospital services during the pandemic (Omicron duration) is measured through the questionnaire. As compared to other departments, the utilization factor is higher in the pharmacy department in both hospitals. From PIMS hospital 44% of patients are satisfied with the service system while from BBH 40% of patients are satisfied with the service system.

Computing and Analysis of Multi Server Queueing Model Using Pentagonal Fuzzy Numbers

In the present study, analysed the multiple server queue miniature using Pentagonal Fuzzy number. To cope with a real-world scenario, the input parameters are converted from crisp to fuzzy type by taking into account. The system parameters, rate of arrival and rate of service are taken fuzzy. The system characteristics like expected number of clients waiting in queue and expected number of clients waiting in system are calculated using DSW algorithm and using alpha-cut at various levels, in interval [0,1]. Using pentagonal number arithmetic, the performance measures are calculated directly as PFNs. Different numerical examples with arrival rate and service rate as PFN are demonstrated to show the authenticity implementation of the performance measures. Finally effect of different parameters are shown for validation purpose.

Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times

We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs. In contrast to the regularly varying case, we observe several subtle features such as a non-trivial trade-off between the number of big jobs and their sizes and a surprising asymmetric structure in asymptotic job sizes leading to congestion.

Machine diagnostic service centre design under imperfect diagnosis with uncertain error cost consideration

As modern machines are always highly customised, it is important to diagnose the specific maintenance requirement of each machine before performing regular maintenance tasks. However, the diagnosis cannot always be accurate. In this study, we focus on a diagnostic service design problem considering imperfect diagnosis with uncertain error cost, which increases in the inaccuracy of the diagnosis. The service system is modelled as a multiple server queue, with servers performing a sequential diagnosis and customers deciding whether or not to use the service. We consider the case where the expert skill level is exogenous, uncertain and endogenous, respectively. The results suggests that (1) when the expert skill level is exogenous, the congestion of the system increases in expert skill level. In addition, the error costs for the two major stakeholders-the service centre and the customer-may affect the optimal service time and number of experts in different ways; (2) when expert skill level becomes more uncertain, the service centre should improve the optimal service time further and will see a further erosion of the profit; and (3) different from the exogenous expert skill level, high skill level experts always accompany with long service time when expert skill level is endogenous.

A simulation-based heuristic that promotes business profit while increasing the perceived quality of service industries

This paper tackles the problem of minimising the direct server costs of complex multiple-server queueing systems while improving the quality perceived by customers. The problem is solved by finding the server roster, defined as the allocation of active individual servers in each time interval of the working day. As no closed solution is available at this time, it was obtained by simulation modelling. The complex queueing system was solved by a simulation-based heuristic that includes the dynamic arrivals, entity reneging and/or balking, multi-servicing, and the individual service-time distributions of servers. The distributions of the random variables of single or multiple-branch businesses were identified by sampling procedures for multiple company-branch deployment. The beneficial financial impact of the proposed solution is confirmed in numerical real-life banking scenarios. The quality perceived by customers (evaluated through the expected queueing time) was also improved. Finally, additional insights that might improve the system performance are highlighted.

Pricing policy for a cloud registration service with a novel cloud architecture

In order to attract more users, cloud vendors always provide free service in many cloud applications. If a Non-VIP (Non-Very Important Person) user is satisfied with the free cloud service, the user may well register as a VIP (Very Important Person) user. In this paper, we focus on the registration process. In order to provide a timely registration service, we propose a novel cloud architecture where free service and registration service are deployed on the same VM (Virtual Machine). We present a multiple-server queueing model with a second optional service for analyzing the stochastic behavior of cloud users. By establishing a two-dimensional Markov chain, we derive the steady-state distribution of the queueing model. We construct an individual benefit function to investigate the Nash equilibrium arrival rate of anonymous users, and propose a new intelligent searching algorithm to obtain the socially optimal arrival rate of anonymous users. For coinciding these two arrival rates of anonymous users, we impose an appropriate registration fee with a pricing policy.

A pathwise comparison of parallel queues

By conducting a pathwise comparison of multiple server queues, we show in what sense it is better to have more servers in ‘First Come, First Served’ or equivalently, more queues in parallel under the policy ‘Join the Shortest Workload’. This comparison result is based on the recursive representation of Kiefer and Wolfowitz, and on a non-mass conservative generalization of the Schur-Convex semi-ordering, showing in what sense it is better to send jobs to the server of least load. We also show that this pathwise result does not hold true in general for the semi-cyclic policies introduced by Scheller-Wolf, and propose a weaker ordering that suits this larger class of models.

English

One of the greatest challenges facing every society today is crime control and management. It could be as little as pick–pocketing, or human trafficking, or even as deadly as terrorism. As criminal’s perfect ways of avoiding being detected, Law Enforcement Agencies (LEAs) must adopt innovative ways on crime prevention and control. This research applies Queuing Network (QN) model to evaluation the performance of LEAs on crime information management. The QN comprise two queuing theory models; single server (M/M/1) and multiple server (M/M/m) queuing models. To implement this model, crime data was collected from Eleme (2012) and Nsukka (2013) police stations with a table format to capture the timing such as case arrival time, service time (investigation and handling time) and termination time. The model was implemented using PHP programming language Excel application was used to plot some graphs to observe the system’s behaviour. The case timing captured (input data) were used to calculate the queuing theory performance measures (model parameters). Results from the analysis shows how many cases were handled by how many staff members in a specified period of time. This model will make LEA’s crime management system visible at different levels (local, state and federal) to both government, LEA’s admins and general public. Government can assess the LEA’s performance at any time. Use of this model will improve LEA’s productivity and public security as well. Key words: Crime management, information system, law enforcement agency, performance evaluation, queueing network, single server queuing model, multiple server queueing model.

Solving multiple-server queues in rough environment

In this paper, a multiple-server queue in rough environment is considered in which the arrival rate and service rate are rough interval numbers. A new method namely, multi-level method is proposed to determine the performance measures in the given queueing system as rough interval numbers. The solution procedure for the proposed method is demonstrated with the help of numerical example. The performance measures of the multiple-server queue in rough environment provided by the proposed method are rough interval numbers which are very much useful for decision makers for taking the managerial decision-making.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μ i , where μ i decreases in i. Arrivals have associated vectors (X 1, …, X n ) of binary variables, with X i = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting I j be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I 1, …, I r ) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(X i = 1) increases in i.

Optimal Server Selection in a Queueing Loss Model with Heterogeneous Exponential Servers, Discriminating Arrivals, and Arbitrary Arrival Times

We consider a multiple server queueing loss system where the service times of server i are exponential with rate μi, where μi decreases in i. Arrivals have associated vectors (X1, …, Xn) of binary variables, with Xi = 1 indicating that server i is eligible to serve that arrival. Arrivals finding no idle eligible servers are lost. Letting Ij be the indicator variable for the event that the jth arrival enters service, we show that, for any arrival process, the policy that assigns arrivals to the smallest numbered idle eligible server stochastically maximizes the vector (I1, …, Ir) for every r if the eligibility vector of arrivals is either (a) exchangeable, or (b) a vector of independent variables for which P(Xi = 1) increases in i.

Unfair Consequence of Fair Competition in Service Systems—An Agent-Based and Queueing Approach

This paper considers the competition of service centers within a service system. Each service center is modeled as a multiple-server queue. Service centers compete with each other in a fair manner and adjust their service resources (number of servers) to accommodate the demand obtained from the competition. An agent-based approach is used to model the competition and adjustment processes. Our objective is to study the size distribution of service centers under a fair competition, i.e., to answer the question, will the size distribution be uniform, normal, or skewed? It turns out that a skewed distribution (e.g., power law distribution) is obtained. Two data sets of hospital sizes are analyzed and are found to have a skewed distribution. An analytical argument is provided to explain how a fair competition could give rise to a skewed (i.e., unfair) size distribution.

A hybrid method for performance analysis of G/G/m queueing networks

Open queueing networks are useful for the performance analysis of numerous real systems. Since exact results exist only for a limited class of networks, decomposition methods have been extensively used for approximate analysis of general networks. This procedure is based on several approximation steps. Successive approximations made in this approach can lead to a considerable error in the output. In particular, there are no general accurate formulas for computing the mean waiting time and the inter-departure variance in general multiple-server queues. This causes the results from decomposition methods when applied to G/G/m queueing networks to be very approximative and to significantly deviate from actual performance values. We suggest substituting some approximate formulae by low-cost simulation estimates in order to obtain more accurate results when benefiting from the speed of an analytical method. Numerical experiments are presented to show that the proposed approach provides improved performance.

ON M(M,m)/M/C/N: Interdependent Queueing Model

This paper deals with a multiple server Queueing system in which arrivals and services are intredependent and follow a bivariate Poisson process and having startup delay. Using the Supplementary Varible Techniue these models are analyzed. The expected length of the Dorment period, the busy period, expected number of units in the queue are derived and analyzed in the light of the dependence paramater.

Estimating the loss probability under heavy traffic conditions

This paper studies a multiple-server queueing model under the assumptions of renewal arrival processes and limited buffer size. An approximation for the loss probability and the asymptotic behavior are studied under the heavy traffic conditions. We present an asymptotic analysis of the loss probability when both the arrival rate and number of servers approach infinity. In illustrative examples, the loss probabilities are estimated with heavy traffic under three common distributions of inter-arrival times: exponential, deterministic and Erlang-r distributions, respectively.

Incentive Effects of Multiple-Server Queueing Networks: The Principal-Agent Perspective

AbstractA two-server service network has been studied from the principal-agent perspective. In the model, services are rendered by two independent facilities coordinated by an agency, which seeks to devise a strategy to suitably allocate customers to the facilities and to simultaneously determine compensation levels. Two possible allocation schemes were compared — viz. the common queue and separate queue schemes. The separate queue allocation scheme was shown to give more competition incentives to the independent facilities and to also induce higher service capacity. In this paper, we investigate the general case of a multiple-server queueing model, and again find that the separate queue allocation scheme creates more competition incentives for servers and induces higher service capacities. In particular, if there are no severe diseconomies associated with increasing service capacity, it gives a lower expected sojourn time in equilibrium when the compensation level is sufficiently high.

Applying multidisciplinary logistic techniques to improve operations productivity at a mine

This case study uses a surface mine to investigate multidisciplinary logistics analysis methods for improving refinery operations. Existing resource scheduling, inventory forecasting, and economic production quantity procedures have not been able to identify how to improve productivity. The objective was to locate and demonstrate proven techniques from operations research (and other related disciplines) which could be applied to solve logistics problems. Historical operations data along with a new sample (n = 140) were utilized for the analysis. Preliminary parametric tests failed, but later a multiple server queue model was developed by integrating nonparametric techniques, waiting line theory, stochastic probabilities, and break-even scenario analysis. Quantitative and qualitative data were analyzed, resulting in a solution to increase truck arrival rates by 10% which was projected to increase refinery utilization by 7–77%, thereby generating a potential productivity savings of $161,223.31 per year.

Design and Analysis of Diagnostic Service Centers

In the health-care domain, diagnostic service centers provide advice to patients over the phone about what the most appropriate course of action is based on their symptoms. Managers of such centers must strike a balance between accuracy of advice, callers' waiting time, and staffing costs by setting the appropriate capacity (staffing) and service depth. We model this problem as a multiple-server queueing system, with the servers performing a sequential testing process and the customers deciding whether or not to use the service, based on their expectation of accuracy and congestion. We find the dual concerns of accuracy and congestion lead to a counterintuitive impact of capacity: Increasing capacity might increase congestion. In addition, (i) patient population size is an important driver in management decisions, not only in staffing but also in accuracy of advice; (ii) increasing asymmetry in error costs may not increase asymmetry in the corresponding error rates; and (iii) the error costs for the two major stakeholders—the service manager and the patient—may impact the optimal staffing level in different ways. Finally, we highlight the relevance of our model and results to challenges in practice elicited during interviews with current clinical researchers and practitioners.

Novel Approach to Improve QoS of a Multiple Server Queue

The existing models of servers work on the M/G/1 model which is in some ways predictable and offers us an opportunity to compare the various other server queuing models. Mathematical analysis on the M/G/1 model is available in detail. This paper presents some mathematical analysis which aims at reducing the mean service time of a multiple server model. The distribution of the Mean Service Time has been derived using Little’s Law and a C++ simulation code has been provided to enable a test run so that the QoS of a multi-server system can be improved by reducing the Mean Service Time.

Optimal service capacity in a multiple-server queueing system: A game theory approach

The economic behavior of service providers in a competitiveenvironment is a very important and interesting research topic.A two-server service network has been proposed byKalai et al. [14] for this purpose.Their model actually aims at studying both the role and impact ofservice capacity in capturing larger market share.The market share is important in maximizing individual'slong-run expected profit.A Markovian queueing system of two servers wasemployed in their model for the captured problem.The obvious advantage of such a model is that it is mathematically tractable.They then further formulated the problem as a two-personstrategic game and analyzed the equilibrium solutions.The main aim of this paper is to extend the results of theirtwo-server queueing model to the case of a general multiple-server queueing model.Here we will focus on the case when the queueing system is stable.It is found that when the marginal cost of service capacityis low relatively to the revenue per customer, a unique Nash equilibrium exists,in which all servers choose the same service capacity and the expected waiting times are finite.