The probabilistic model of sharing system with collisions, Н-persistence and rejections data processing

Рассматривается математическая модель системы совместного доступа с коллизиями, H-настойчивостью и отказами в виде системы массового обслуживания с повторными вызовами вида M|M|1 и проводится анализ ее вероятностных характеристик. Разработан рекуррентный алгоритм вычисления вероятностей числа заявок на орбите, проведена численная реализация нахождения допредельного распределения вероятностей числа заявок на орбите, технических характеристик функционирования системы

(M/EK/C:C/FCFS) Queue with Two-Class Arrivals,State dependent service, Multi-Servers, and Customers Impatience

This paper deals with the finite Markovian queueing system with multi server facility, customer impatience and two types of arrivalswith heterogeneous arrival ratesalong withphase wise state dependent service. Arrival and departures assumed to be Poisson and exponential distributionsrespectively under first-come-first-serve basis. The service will be rendered in k-phases. Transient state probabilities as well as some performance indices have been calculated.We have presented the results of sensitivity analysis and observed the impact ofvarious parameters on system’s constants

(M/EK/C:C/FCFS) Queue with Two-Class Arrivals, State dependent service, Multi-Servers, and Customers Impatience

This paper deals with the finite Markovian queueing system with multi server facility, customer impatience and two types of arrivals with heterogeneous arrival rates along with phase wise state dependent service. Arrival and departures assumed to be Poisson and exponential distributions respectively under first-come-first-serve basis.  The service will be rendered in k-phases. Transient state probabilities as well as some performance indices have been calculated. We have presented the results of sensitivity analysis and observed the impact of various parameters on system’s constant

A Discrete-Time Unreliable Geo/G/1

This paper deals with the steady-state behavior of a discrete-time unreliable Geo/G/1 retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system

A Discrete-Time Unreliable Geo/G/1 Retrial Queue with Balking Customers, Second Optional Service, and General Retrial Times

This paper deals with the steady-state behavior of a discrete-time unreliable / /1 retrial queueing system with balking customers and second optional service. The server may break down randomly while serving the customers. If the server breaks down, the server is sent to be repaired immediately. We analyze the Markov chain underlying the considered system and its ergodicity condition. Then, we obtain some performance measures based on the generating functions. Moreover, a stochastic decomposition result of the system size is investigated. Finally, some numerical examples are provided to illustrate the effect of some parameters on main performance measures of the system

Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns

The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results

On the impact of customer balking, impatience and retrials in telecommunication systems

This paper deals with a Markovian multiserver model, where the simultaneous effect of customerbalking, impatience and retrials is evaluated. The study of systems incorporating these features is motivated by the observation of real service systems where these queueing phenomena interact. Simple approximations based on truncation and generalized truncation are provided. These approximations are compared according to different criteria for several selected scenarios. Finally, our results are used to evaluate the optimal ratio between the number of available channels and the number of waiting positions in an application to call center management