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Tytuł:
M/M/n/m queueing systems with non-identical servers
Autorzy:
Ziółkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/121808.pdf
Data publikacji:
2011
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
queueing theory
queueing systems
teoria kolejkowania
system kolejkowania
Opis:
M/M/n/m queueing systems with identical servers are well known in queueing theory and its applications. The analysis of these systems is very simple thanks to the fact that the number of customers ɳ(t) in the system at arbitrary time instant t forms a Markov chain. The main purpose of this paper is to analyse the M/M/n/m system under assumption that its servers are different, i.e. they have different parameters of service time.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2011, 16; 163-168
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Optimization of an M/M/1/N feedback queue with retention of reneged customers
Autorzy:
Kumar, R.
Jain, N. K.
Som, B. K.
Powiązania:
https://bibliotekanauki.pl/articles/969064.pdf
Data publikacji:
2014
Wydawca:
Politechnika Wrocławska. Oficyna Wydawnicza Politechniki Wrocławskiej
Tematy:
reneging
retention of reneged customers
revenue
queuing system
optimization
dochód
system kolejkowania
optymalizacja
Opis:
Customer impatience has become a threat to the business world. Firms employ various customer retention strategies to retain their impatient (or reneged) customers. Customer retention mechanisms may help to retain some or all impatient customers. Further, due to unsatisfactory service, customers may rejoin a queue immediately after departure. Such cases are referred to as feedback customers. Kumar and Sharma take this situation into account and study an M/M/1/N feedback queuing system with retention of reneged customers. They obtain only a steady-state solution for this model. In this paper, we extend the work of Kumar and Sharma by performing an economic analysis of the model. We develop a model for the costs incurred and perform the appropriate optimization. The optimum system capacity and optimum service rate are obtained.
Źródło:
Operations Research and Decisions; 2014, 24, 3; 45-58
2081-8858
2391-6060
Pojawia się w:
Operations Research and Decisions
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation
Autorzy:
Zhernovyi, Yuriy
Kopytko, Bohdan
Powiązania:
https://bibliotekanauki.pl/articles/1839796.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
single-channel closed queueing system
arbitrary distributions
hyperexponential approximation
system kolejkowania
rozkład prawdopodobieństwa
aproksymacja wykładnicza
Opis:
In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 113-120
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculating steady-state probabilities of single-channel closed queueing systems using hyperexponential approximation
Autorzy:
Zhernovyi, Yuriy
Kopytko, Bohdan
Powiązania:
https://bibliotekanauki.pl/articles/122348.pdf
Data publikacji:
2020
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
single-channel closed queueing system
arbitrary distributions
hyperexponential approximation
system kolejkowania
rozkład prawdopodobieństwa
aproksymacja wykładnicza
Opis:
In this paper we propose a method for calculating steady-state probability distributions of the single-channel closed queueing systems with arbitrary distributions of customer generation times and service times. The approach based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type by the method of moments. We defined conditions for the variation coefficients of the gamma distributions and Weibull distributions, for which the best accuracy of calculating the steady-state probabilities is achieved in comparison with the results of simulation modeling.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2020, 19, 1; 113-120
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Passenger level of service estimation model for queuing systems at the airport
Autorzy:
Kierzkowski, A.
Kisiel, T.
Pawlak, M.
Powiązania:
https://bibliotekanauki.pl/articles/223601.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
airport
passenger service
level of service
queuing system
lotnisko
obsługa pasażerów
poziom usług
system kolejkowania
Opis:
This paper presents a model for the management of passenger service operations at airports by the estimation of a global index of the level of service. This paper presents a new approach to the scheduling of resources required to perform passenger service operations at airports. The approach takes into account the index of level of service as a quantitative indicator that can be associated with airport revenues. Taking this index into account makes it possible to create an operating schedule of desks, adapted to the intensity of checking-in passengers, and, as such, to apply dynamic process management. This offers positive aspects, particularly the possibility of improvement of service quality that directly translates into profits generated by the non-aeronautical activity of airports. When talking about level of service, there can be distinguish other important indicators that are considered very often (eg maximum queuing time, space in square meters). In this model, however, they are considered as secondary. Of course, space in square meters is important when designing a system. Here this system is already built and functioning. The concept of the model is the use of a hybrid method: computer simulation (Monte Carlo simulation) with multiple regression. This paper focuses on the presentation of a mathematical model used to determine the level of service index that provides new functionality in the current simulation model, as presented in the authors’ previous scientific publications. The mathematical model is based on a multiple regression function, taking into account the significance of individual elementary operations of passenger service at an air terminal.
Źródło:
Archives of Transport; 2018, 47, 3; 29-38
0866-9546
2300-8830
Pojawia się w:
Archives of Transport
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Classical and non-classical processor sharing systems with non-homogeneous customers
Autorzy:
Tikhonenko, O.
Powiązania:
https://bibliotekanauki.pl/articles/121683.pdf
Data publikacji:
2009
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
kolejkowanie
system kolejkowania
egalitarne współdzielenie procesora
transformata Laplace'a
queuing
queuing system
egalitarian processor sharing
Laplace transform
Opis:
We discuss a processor sharing system with non-homogeneous customers. There are resources of two types for their service: 1) resource of the first type is discrete, there are N units (servers) of the resource; 2) resource of the second type (capacity) is not-necessary discrete. The type of a customer is defined by the amount of first type resource units which is used for the customer service. Each customer is also characterized by some random capacity or some amount of the second type resource which is also used for his service. The total capacity of customers present in the system is limited by some value V >0, which is called the memory volume of the system. The customer capacity and length (the work necessary for service) are generally dependent. The joint distribution of these random variables also depends on the customer type. For such systems we determine the stationary distribution of the number of customers of each type present in the system and stationary loss probabilities for each type of customers.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2009, 14; 133-150
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recurrence relations for two-channel closed queueing systems with Erlangian service times
Autorzy:
Kopytko, B.
Zhernovyi, K.
Powiązania:
https://bibliotekanauki.pl/articles/122421.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
two-channel closed queueing system
Erlangian service times
fictitious phase method
recurrence relations
system kolejkowania dwukanałowy
czas obsługi Erlanga
rozkład Erlanga
Opis:
This paper proposes a method for determining the steady-state characteristics of two-channel closed queueing systems with an exponential distribution of the time generation of service requests and the Erlang distributions of the service times. Recurrence relations for computing the steady-state distribution of the number of customers in the system are deduced. The obtained algorithms are tested on examples using simulation models in the GPSS World environment.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 1; 37-48
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recurrence relations for a multi-channel closed queueing system with Erlangian service times of second order
Autorzy:
Zhernovyi, Y.
Kopytko, B.
Powiązania:
https://bibliotekanauki.pl/articles/122441.pdf
Data publikacji:
2017
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
multi-channel closed queueing system
Erlangian service times of second order
fictitious phase method
recurrence relations
system kolejkowania
zależności rekurencyjne
Opis:
We propose a method for determining the steady-state characteristics of a multichannel closed queueing system with exponential distribution of the time generation of service requests and the second order Erlang distributions of the service times. Recurrence relations to compute the steady-state distribution of the number of customers are obtained. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2017, 16, 3; 123-128
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculating steady-state probabilities of single-channel queueing systems with changes of service times depending on the queue length
Autorzy:
Zhernovyi, Yuriy
Kopytko, Bohdan
Powiązania:
https://bibliotekanauki.pl/articles/122726.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
single-channel queueing system
service times changes depending of the queue length
hyperexponential approximation
rozkład hiperesponencjalny
czas obsługi
system kolejkowania jednokanałowy
długość kolejki
Opis:
In this paper, we propose a method for calculating steady-state probabilities of the G/G/1/m and M/G/1/m queueing systems with service times changes depending of the number of customers in the system. The method is based on the use of fictitious phases and hyperexponential approximations with parameters of the paradoxical and complex type. A change in the service mode can only occur at the moment the service is started. We verified the obtained numerical results using the potential method and simulation models, constructed by means of GPSS World.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 3; 107-117
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Steady-state characteristics of three-channel queueing systems with Erlangian service times
Autorzy:
Kopytko, B.
Zhernovyi, K.
Powiązania:
https://bibliotekanauki.pl/articles/122266.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
three-channel queueing system
Poisson input
Erlangian service times
random dropping of customers
fictitious phase method
recurrence relations
trójkanałowy system kolejkowania
metoda fazy fikcyjnej
równanie rekurencyjne
Opis:
We propose a method of study the M/E2/3/∞ queueing systems: standard system and systems with the threshold and hysteretic strategies of the random dropping of customers in order to control the input flow. Recurrence relations to compute the stationary distribution of the number of customers and the steady-state characteristics are obtained. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 3; 75-87
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change
Autorzy:
Zhernovyi, Y.
Kopytko, B.
Powiązania:
https://bibliotekanauki.pl/articles/122350.pdf
Data publikacji:
2016
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
single-channel queueing system
random dropping of customers
hysteretic strategy for service time
potentials method
stationary characteristics
system kolejkowania jednokanałowy
metoda potencjałów
charakterystyka stacjonarna
czas obsługi
Opis:
We propose a method for determining the probabilistic characteristics of the M/G/1/m queueing system with the random dropping of arrivals and distribution of the service time depending on the queue length. Two sets of service modes, with the service time distribution functions Fn (x) and Fn (x) respectively, are used according to the twothreshold hysteretic strategy. The Laplace transforms for the distribution of the number of customers in the system during the busy period and for the distribution function of the length of the busy period are found. The developed algorithm for calculating the stationary characteristics of the system is tested with the help of a simulation model constructed with the assistance of GPSS World tools.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2016, 15, 1; 197-210
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Recurrence relations for two-channel queueing systems with Erlangian service times and hysteretic strategy of random dropping of customers
Autorzy:
Zhernovyi, Y.
Kopytko, B.
Powiązania:
https://bibliotekanauki.pl/articles/122986.pdf
Data publikacji:
2018
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
two-channel queueing system
Erlangian service times
random dropping of customers
fictitious phase method
hysteretic strategy
recurrence relations
steady-state characteristics
czas obsługi Erlanga
strategia histeretyczna
system kolejkowania dwukanałowy
Opis:
This article proposes a method of study the M/Es/2/m and M/Es/2/∞ queueing systems with a hysteretic strategy of random dropping of customers. Recurrence relations are obtained to compute the stationary distribution of the number of customers and steadystate characteristics. The constructed algorithms were tested on examples with the use of simulation models constructed with the help of GPSS World.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2018, 17, 2; 93-103
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Queueing systems with random volume customers and a sectorized unlimited memory buffer
Autorzy:
Tikhonenko, Oleg
Ziółkowski, Marcin
Kempa, Wojciech M.
Powiązania:
https://bibliotekanauki.pl/articles/2055163.pdf
Data publikacji:
2021
Wydawca:
Uniwersytet Zielonogórski. Oficyna Wydawnicza
Tematy:
queueing system
random volume customers
sectorized memory buffer
total volume vector
Laplace transform
Laplace–Stieltjes transform
multivariate L’Hospital rule
system kolejkowania
wektor objętości
transformata Laplace'a
transformata Laplace'a-Stieltjesa
Opis:
In the present paper, we concentrate on basic concepts connected with the theory of queueing systems with random volume customers and a sectorized unlimited memory buffer. In such systems, the arriving customers are additionally characterized by a non-negative random volume vector. The vector’s indications can be understood as the sizes of portions of information of a different type that are located in the sectors of memory space of the system during customers’ sojourn in it. This information does not change while a customer is present in the system. After service termination, information immediately leaves the buffer, releasing its resources. In analyzed models, the service time of a customer is assumed to be dependent on his volume vector characteristics, which has influence on the total volume vector distribution. We investigate three types of such queueing systems: the Erlang queueing system, the single-server queueing system with unlimited queue and the egalitarian processor sharing system. For these models, we obtain a joint distribution function of the total volume vector in terms of Laplace (or Laplace-Stieltjes) transforms and formulae for steady-state initial mixed moments of the analyzed random vector, in the case when the memory buffer is composed of two sectors. We also calculate these characteristics for some practical case in which the service time of a customer is proportional to the customer’s length (understood as the sum of the volume vector’s indications). Moreover, we present some numerical computations illustrating theoretical results.
Źródło:
International Journal of Applied Mathematics and Computer Science; 2021, 31, 3; 471--486
1641-876X
2083-8492
Pojawia się w:
International Journal of Applied Mathematics and Computer Science
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers
Autorzy:
Ziółkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/199840.pdf
Data publikacji:
2018
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
multi-server queueing systems
queueing systems with non-homogeneous customers
queueing systems with heterogeneous servers
total volume distribution
Laplace–Stieltjes transform
system kolejkowania
transformata Laplace'a-Stieltjesa
dystrybucja
Opis:
In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2018, 66, 1; 59-66
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping
Autorzy:
Zhernovyi, Y.
Kopytko, B.
Zhernovyi, K.
Powiązania:
https://bibliotekanauki.pl/articles/122429.pdf
Data publikacji:
2014
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
queuing systems
packet arrival of customers
active queue management
random dropping of customers
busy period
distribution of the number of customersdistribution of the number of customers
system kolejkowania
aktywne zarządzanie kolejką
przedział zajętości
Opis:
We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk’s potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2014, 13, 4; 163-175
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł

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