Queuing Model

The Session Initiation Protocol (SIP) retransmission mechanism can cause SIP network collapse with short-term overload. In this paper, we investigate with a fluid modelling approach the chaotic behaviour of the SIP retransmission mechanism in SIP networks. We capture the complex correlation structure in SIP systems through a detailed and novel queuing analysis. To dimension a buffer size which can avoid

The spreading of coronavirus (COVID-19) has increased exponentially throughout the world, and still, no vaccine is available for the treatment of patients. The load has increased tremendously in the hospitals where the resources are minimal. The queuing theory is applied for the multi-server system, to identify the queue time of the patients in hospitals for the identification and confirmation of disease. This paper presents a sequential queuing model for estimating the time of the detection and identification of infections in severe loading conditions. The goal is to present a simplified probabilistic model to determine the general behaviour to predict how long the treatment cycle takes to diagnose and classify people already infected. For this type of method, the law of the isolated logarithm is proved, showing that the general process of recognition is in line with the right of iterated logarithm. There are some graphical representations of the various measurement criteria. The results of the modelling showed that the patient’s waiting period in the course of inquiries, detections, detecting or treating coronaviruses in the event of imbalances in the system as a whole rise following the logarithm rule

In this paper, we apply both agent-based models and queuing models to investigate patient access and patient flow through emergency departments. The objective of this work is to gain insights into the comparative contributions and limitations of these complementary techniques, in their ability to contribute empirical input into healthcare policy and practice guidelines. The models were developed independently, with a view to compare their suitability to emergency department simulation. The current models implement relatively simple general scenarios, and rely on a combination of simulated and real data to simulate patient flow in a single emergency department or in multiple interacting emergency departments. In addition, several concepts from telecommunications engineering are translated into this modeling context. The framework of multiple-priority queue systems and the genetic programming paradigm of evolutionary machine learning are applied as a means of forecasting patient wait ...

As customer’s wait longer in line they become more dissatisfied. Because a wait time of zero is not economical, a balance must be obtained between the cost of waiting and the cost of service. Classic queuing theory does not generally provide cost figures. Therefore, in order to quantify the cost of waiting, this article utilizes the Taguchi loss function, which was developed for physical products, to determine the cost of customer dissatisfaction. Specifically, this article combines the M/M/1 queuing model with the Taguchi loss function to establish the cost of customer dissatisfaction.

Abstract—Virtual machine technology enables highly agile system deployments in which components can be cheaply moved, cloned, and allocated controlled hardware resources. In this paper, we examine in the context of multitier Enterprise applications, how these facilities can be used to provide enhanced solutions to the classic problem of ensuring high availability without a loss in performance on a fixed amount of resources. By using virtual machine clones to restore the redundancy of a system whenever component failures occur, we achieve improved availability compared to a system with a fixed redundancy level. By smartly controlling component placement and colocation using information about the multitier system’s flows and predictions made by queuing models, we ensure that the resulting performance degradation is minimized. Simulation results show that our proposed approach provides better availability and significantly lower degradation of system response times compared to traditio...

The spreading of coronavirus (COVID-19) has increased exponentially throughout the world, and still, no vaccine is available for the treatment of patients. The load has increased tremendously in the hospitals where the resources are minimal. The queuing theory is applied for the multi-server system, to identify the queue time of the patients in hospitals for the identification and confirmation of disease. This paper presents a sequential queuing model for estimating the time of the detection and identification of infections in severe loading conditions. The goal is to present a simplified probabilistic model to determine the general behaviour to predict how long the treatment cycle takes to diagnose and classify people already infected. For this type of method, the law of the isolated logarithm is proved, showing that the general process of recognition is in line with the right of iterated logarithm. There are some graphical representations of the various measurement criteria. The results of the modelling showed that the patient’s waiting period in the course of inquiries, detections, detecting or treating corona viruses in the event of imbalances in the system as a whole rise following the logarithm rule.

This paper analyses an alternative traffic queuing model for the quality of service (QoS) optimization in mobile communications systems. According to the proposed model, the queue of handover attempts is separated to each of the used transceivers of a base transceiver station that covers a particular area. Fixed channel assignment and TDMA are considered, while the proposed technique is compared to the classic queuing model. The comparison results show that the QoS of the proposed model is fully optimized, especially if large queue sizes are chosen.

Converged network seamlessly integrates different communications media such as data, voice and multimedia on a single platform. It refers to convergence both types of network and technologies as well as convergence between the different layers of network architecture. In this paper, we examine a priority-based queuing model and perform the mathematical analysis of different media calls processing in converged network environment. We use for this purpose a queuing system model M3/G3/1/NPRP in order to process effectively input jobs/requests (or packets). Tasks within this queuing system get a higher priority if they are handling a real-time event. We present in our paper mathematical results of the expected response and waiting time, and build hypothetical diagrams for the further practical usage in real-time system. A modeling method developed in this paper will be used for the fast configuration and testing of new converged network applications and services.

An analytical model is employed to solve a cross-layer optimization problem in IEEE 802.11 wireless local area networks (WLANs). Closed-form expressions for the optimum retry limit, packet overflow drop rate and overall loss rate are derived using M/M/l queuing model, and subsequently an adaptive MAC retry limit scheme is studied. Furthermore simulation results (network simulator-2) will verify the accuracy of our analytical model.

A queue is a line of people or things to be handled in a sequential order. It is a sequence of objects that are waiting to be processed. Queuing theory is the study of queues for managing process and objects. Simulation has been applied successfully for modelling small and large complex systems and understanding queuing behaviour. Analysis of the models helps to increases the performance of the system. In this paper we analyze various models of the Single server queuing system with necessary implementation using Microsoft Excel and Matlab Software. For better understanding we have considered a Virtual Telecommunication System, is presented with help of Microsoft Excel. Empirical distribution of Service Time and Inter-arrival Time of call has an impact on the performance of Queuing models. Examples include: A Telecommunication System staffing a call centre and measuring system parameters like average time that a call spend in the system ,average waiting time for those calls which are waiting. Numerous problems and more motivate the development of a queuing theory. Queuing theory as discussed in this paper is organized and a simulation of queuing system and the necessary mathematical tools are developed to analyze them. Finally, we illustrate the use of these models through various communication applications.

Emergency response services are critical for modern societies. This paper presents a model and a heuristic solution for the optimal deployment of many emergency response units in an urban transportation network and an application for transit mobile repair units (TMRU) in the city of Athens, Greece. The model considers the stochastic nature of such services, suggesting that a unit may be already engaged, when an incident occurs. The proposed model integrates a queuing model (the hypercube model), a location model and a metaheuristic optimization algorithm (genetic algorithm) for obtaining appropriate unit locations in a two-step approach. In the first step, the service area is partitioned into sub-areas (called superdistricts) while, in parallel, necessary number of units is determined for each superdistrict. An approximate solution to the symmetric hypercube model with spatially homogeneous demand is developed. A Genetic Algorithm is combined with the approximate hypercube model for obtaining best superdistricts and associated unit numbers. With both of the above requirements defined in step one, the second step proceeds in the optimal deployment of units within each superdistrict.