Queueing systems with correlated arrival flows and their applications to modeling telecommunication networks

Dudina

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

2021

A novel flexible discipline for providing priority in a singleserver queue is applied to the system where the service can be unreliable what results in the loss of a customer or repetition of its service. According to this discipline, arriving customers are stored in the finite buffers dedicated to the customers of the corresponding type if the buffer is not full. After the staying in the corresponding buffer during the exponentially distributed time, the customers try to enter the main buffer of a finite capacity which is common for both types of customers. If this main buffer is full, the customer returns to the dedicated buffer and repeats the attempts to enter the main buffer later. Customers staying in the dedicated buffers are impatient and can go away from the system after a certain patience period duration of which has an exponential distribution. Customers of both types, which succeed to enter the main buffer, are picked up for the service in the order of their admission to this buffer. Providing the preference to priority customers is managed via the corresponding choice of capacities of the dedicated buffers and the rate of trials to transfer to the main buffer. Performance measures of this system are obtained under the assumption that the arrival flows of two types of customers are defined by the Markov arrival processes and the service time has the distribution of phase-type with failures type. Some aspects relating to an optimal choice of the parameters of the system are discussed via numerical experiments.

Section: Mathematical Modelmentioning

confidence: 99%

Improved Priority Scheme for Unreliable Queueing System

Dudina

Information Technologies and Mathematical Modelling. Queueing Theory and Applications

2021

“…BMAP и результаты исследования систем с таким потоком даны в [5,6]. В настоящей статье предполагается, что процесс поступления -это марковский процесс прибытия MAP , который является частным случаем , BMAP когда не допускается групповое поступление.…”

Section: дополнительная информация оunclassified

Analysis of retrial queue with heterogeneous servers and Markovian arrival process

Лю

2020

Informatika (Minsk)

Multi-server retrial queueing system with heterogeneous servers is analyzed. Requests arrive to the system according to the Markovian arrival process. Arriving primary requests and requests retrying from orbit occupy an available server with the highest service rate, if there is any available server. Otherwise, the requests move to the orbit having an infinite capacity. The total retrial rate infinitely increases when the number of requests in orbit increases. Service periods have exponential distribution. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary probabilities distribution of chain states. Presented numerical results illustrate the dynamics of some system effectiveness indicators and the importance of considering of correlation in the requests arrival process.

“…Hereinafter, e denotes a column vector consisting of 1's, and 0 is a zero row vector. For more information about the MAP and its properties, see [10][11][12].…”

Section: Description Of the Modelmentioning

confidence: 99%

Optimization of Queueing Model with Server Heating and Cooling

Dudina

2019

Mathematics

The operation of many real-world systems, e.g., servers of data centers, is accompanied by the heating of a server. Correspondingly, certain cooling mechanisms are used. If the server becomes overheated, it interrupts processing of customers and needs to be cooled. A customer is lost when its service is interrupted. To prevent overheating and reduce the customer loss probability, we suggest temporal termination of service of new customers when the temperature of the server reaches the predefined threshold value. Service is resumed after the temperature drops below another threshold value. The problem of optimal choice of the thresholds (with respect to the chosen economical criterion) is numerically solved under quite general assumptions about the parameters of the system (Markovian arrival process, phase-type distribution of service time, and accounting for customers impatience). Numerical examples are presented.