Queueing System MAP/M/ ∞ with n Types of Customers

Pankratova, Ekaterina; Moiseeva, Svetlana

doi:10.1007/978-3-319-13671-4_41

Cited by 10 publications

(5 citation statements)

References 15 publications

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“…The single-server queueing systems for random-capacity customers with Poisson input flow were considered [15] where the servicing time is distributed exponentially and arbitrarily under the assumption that the customer capacity and the servicing time are independent, and the AQM mechanism is realized in them. Similar results were established for the infinite-server system with exponentially and arbitrary distributed servicing time [2,[9][10][11]. We note that the queueing system with random-capacity customers, processor sharing, and limited capacity of memory using specific algorithm was discussed in detail [1].…”

supporting

confidence: 66%

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Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities

V.¹,

P.²,

P.³

et al. 2019

J. Sib. Fed. Univ., Math. phys.

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A heterogeneous queuing system with an infinite number of servers is considered in this paper. Customers arrive in the system according to a Markov Modulated Poisson Process. The type of incoming customer is defined as i-type with probability pi (i = 1, 2). Each customer carries a random quantity of work (capacity of the customer). In this study service time does not depend on the customers capacities. It is shown that the joint probability distribution of the customers number and total capacities in the system is multidimensional Gaussian distribution under the asymptotic condition of an infinitely growing service time. Simulation results allow us to determine an applicability area of the asymptotic result.

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supporting

confidence: 66%

“…Let us consider the queueing system with unlimited number of servers of two different types [10,11]. Each customer carries a random quantity of work (capacity of the customer) [2] (Fig.1).…”

Section: Matematical Modelmentioning

confidence: 99%

Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities

V.¹,

P.²,

P.³

et al. 2019

J. Sib. Fed. Univ., Math. phys.

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“…As a rule, when studying multi-server systems, it is usually assumed that the servers are identical and that arriving requests can occupy an arbitrary server to be serviced. QSs with heterogeneous servers are much less frequently studied, which makes them a more interesting object of research [28][29][30][31][32][33][34]. Nontrivial optimization problems often arise related to the assignment of servers to arriving orders depending on the ratio of the service rates of the facilities and the costs of their use.…”

Section: Introductionmentioning

confidence: 99%

Infinite-Server Resource Queueing Systems with Different Types of Markov-Modulated Poisson Process and Renewal Arrivals

2022

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In this paper, we propose models that significantly expand the scope of practical applications, namely, queueing systems with various nodes for processing heterogeneous data that require arbitrary resource capacities for their service. When a customer arrives in the system, the customer typeis randomly selected according to a set of probabilities. Then the customer goes to the server of the corresponding device type, where its service is performed during a random time period with a distribution function depending on the type of customer. Moreover, each customer requires a random amount of resources, of which the distribution function also depends on the customer type, but is independent of its service time. The aim of this research was to develop a heterogeneous queueing resource system with an unlimited number of servers and an arrival process in the form of a Markov-modulated Poisson process or stationary renewal process, and with requests for a random number of heterogeneous resources. We have performed analysis under conditions of growing intensity of the arrival process. Here we formulate the theorems and prove that under high-load conditions, the joint asymptotic probability distribution of the n-dimensional process of the total amounts of the occupied resources in the system is a multidimensional Gaussian distribution with parameters that are dependent on the type of arrival process. As a result of numerical and simulation experiments, conclusions are drawn on the limits of the applicability of the obtained asymptotic results. The dependence of the convergence of experimental results on the type of distribution of the system parameters (including the distributions of the service time and of the customer capacity) are also studied. The results of the approximations may be applied to estimating the optimal total number of resources for a system with a limited amount of resources.

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“…In other terms, it can be called a paperless ticketing system, which was developed in a study [3,13,14]. Several studies conducted simulations based on queuing theory analysis, as reported in [1,[15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of a Registration System with Mobile Application at Public Health Center Based on IoT Using a RESTful API

Hadiyoso

Alfaruq

Hariyani

et al. 2021

Proceedings of the 1st International Conference on Electronics, Biomedical Engineering, and Health Informatics

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In the health service center, many people often meet in a queue and tend to be chaotic, causing uncomfortable conditions and time inefficiency. From these problems, it was thought that technology was needed to make it easier for users to register and monitor queues. In previous studies, we have successfully implemented a digital queue system using a mini PC as the main control. This system has been implemented at the public health center "Puskesmas" Bojong Soang, Bandung. However, the mechanism of queuing, registration, or ticketing and monitoring could not be done online in an application. Therefore, in this study, an Android-based application was developed to register and monitor queues online and in real-time. The main purpose of this study is to build an integrated system between existing queuing machines and mobile applications so that the queuing mechanism can be done online. The proposed system consisted of three main components, namely the digital queue machine, server-cloud, and client application in the user's smartphone. All modules were connected via the cloud with the developed protocol. This application was called "Q-Puskesmas", which could run on the Android mobile platform with a minimum version of 5.0. The proposed system is able to display location identity, the latest queue number, and a menu for registering. From the test results, the application can update the queue number in real-time according to the existing conditions with a delay of <150 ms and also print a virtual registration number. This developed application was expected to facilitate the public in using health facilities/services.

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Queueing System MAP/M/ ∞ with n Types of Customers

Cited by 10 publications

References 15 publications

Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities

Heterogeneous System MMPP/GI(2)/∞ with Random Customers Capacities

Infinite-Server Resource Queueing Systems with Different Types of Markov-Modulated Poisson Process and Renewal Arrivals

Design and Implementation of a Registration System with Mobile Application at Public Health Center Based on IoT Using a RESTful API

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