Analysis of a Resource-Based Queue with the Parallel Service and Renewal Arrivals

Lisovskaya, Ekaterina; Pankratova, Ekaterina; Moiseeva, Svetlana; Pagano, Michele

doi:10.1007/978-3-030-66471-8_26

Cited by 2 publications

(2 citation statements)

References 23 publications

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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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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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“…Identifying these aspects and analyzing their influence on the systems allow to optimize networks for loss reduction. Such mathematical models are called queuing systems with a random volume of the customers or resource queuing systems [20][21][22][23][24][25][26][27][28]. Resource queuing systems are applied in modern wireless communication networks, cloud computing systems, technical devices, or next-generation data transmission networks.…”

Section: Introductionmentioning

confidence: 99%

Resource Retrial Queue with Two Orbits and Negative Customers

et al. 2022

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In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measures.

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Analysis of a Resource-Based Queue with the Parallel Service and Renewal Arrivals

Cited by 2 publications

References 23 publications

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

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

Resource Retrial Queue with Two Orbits and Negative Customers

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