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Wyświetlanie 1-15 z 41
Tytuł:
Multi–server loss queueing system with random volume customers, non–identical servers and a limited sectorized memory buffer
Autorzy:
Ziółkowski, Marcin
Powiązania:
https://bibliotekanauki.pl/articles/27311432.pdf
Data publikacji:
2023
Wydawca:
Polska Akademia Nauk. Czasopisma i Monografie PAN
Tematy:
multi–server queueing system with heterogeneous servers
queueing systems with random volume customers
sectorized memory buffer
loss probability
Stieltjes convolution
wieloserwerowy system kolejkowy z serwerami heterogenicznymi
prawdopodobieństwo straty
splot Stieltjesa
bufor pamięci sektorowany
system kolejkowy z losowymi klientami
Opis:
In the present paper, the model of multi–server queueing system with random volume customers, non–identical (heterogeneous) servers and a sectorized memory buffer has been investigated. In such system, the arriving customers deliver some portions of information of a different type which means that they are additionally characterized by some random volume vector. This multidimensional information is stored in some specific sectors of a limited memory buffer until customer ends his service. In analyzed model, the arrival flow is assumed to be Poissonian, customers’ service times are independent of their volume vectors and exponentially distributed but the service parameters may be different for every server. Obtained results include general formulae for the steady–state number of customers distribution and loss probability. Special cases analysis and some numerical computations are attached as well.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 5; art. no. e146764
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Single–server queueing system with limited queue, random volume customers and unlimited sectorized memory buffer
Autorzy:
Ziółkowski, Marcin
Tikhonenko, Oleg
Powiązania:
https://bibliotekanauki.pl/articles/2173725.pdf
Data publikacji:
2022
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
single-server queueing system
queueing systems with random volume customers
sectorized memory buffer
total volume vector
Laplace-Stieltjes transform
system kolejkowy z jednym serwerem
system kolejkowy z losowymi klientami
bufor pamięci sektorowany
wektor objętości całkowity
transformata Laplace'a-Stieltjesa
Opis:
In the present paper, we analyze the model of a single–server queueing system with limited number of waiting positions, random volume customers and unlimited sectorized memory buffer. In such a system, the arriving customer is additionally characterized by a non– negative random volume vector whose indications usually represent the portions of unchanged information of a different type that are located in sectors of unlimited memory space dedicated for them during customer presence in the system. When the server ends the service of a customer, information immediately leaves the buffer, releasing resources of the proper sectors. We assume that in the investigated model, the service time of a customer is dependent on his volume vector characteristics. For such defined model, we obtain a general formula for steady–state joint distribution function of the total volume vector in terms of Laplace-Stieltjes transforms. We also present practical results for some special cases of the model together with formulae for steady–state initial moments of the analyzed random vector, in cases where the memory buffer is composed of at most two sectors. Some numerical computations illustrating obtained theoretical results are attached as well.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2022, 70, 6; art. no. e143647
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
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:
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:
M/M/n/(m,V) queueing systems with a rejection mechanism based on AQM
Autorzy:
Ziółkowski, M.
Małek, J.
Powiązania:
https://bibliotekanauki.pl/articles/122605.pdf
Data publikacji:
2013
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
Markovian process
queueing systems with non-homogeneous customers
active queue management introduction
Opis:
M/M/n/(m,V) queueing systems with service time independent of customer volume are well known models used in computer science. In real computer systems (computer networks etc.) we often deal with the overload problem. In computer networks we solve the problem using AQM techniques, which are connected with introducing some accepting function that lets us reject in random way some part of the arriving customers. It causes reduction of each customer's mean waiting time and let us avoid jams in consequence. Unfortunately, in this way the loss probability increases. In this paper we investigate the analogous model based on some generalization of M/M/n/(m,V) queueing system. We obtain formulas for a stationary number of customers distribution function and loss probability and we do some computations in special cases.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2013, 12, 1; 121-130
2299-9965
Pojawia się w:
Journal of Applied Mathematics and Computational Mechanics
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Calculating steady-state probabilities of queueing systems using hyperexponential approximation
Autorzy:
Zhernovyi, Yuriy
Kopytko, Bohdan
Powiązania:
https://bibliotekanauki.pl/articles/122829.pdf
Data publikacji:
2019
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
non-Markovian queueing system
hyperexponential approximation
complex and paradoxical parameters of distribution
system kolejkowy
aproksymacja
rozkład hiperesponencjalny
Opis:
This article proposes an analysis of the results of the application of hyperexponential approximations with parameters of the paradoxical and complex type for calculating the steady-state probabilities of the G/G/n/m queueing systems with the number of channels n = 1, 2 and 3. The steady-state probabilities are solutions of a system of linear algebraic equations obtained by the method of fictitious phases. Approximation of arbitrary distributions is carried out using the method of moments. We verified the obtained numerical results using potential method and simulation models, constructed by means of GPSS World.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2019, 18, 2; 111-122
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/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:
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:
Formulas for average transition times between states of the Markov birth-death process
Autorzy:
Zhernovyi, Yuriy
Kopytko, Bohdan
Powiązania:
https://bibliotekanauki.pl/articles/2175497.pdf
Data publikacji:
2021
Wydawca:
Politechnika Częstochowska. Wydawnictwo Politechniki Częstochowskiej
Tematy:
birth-death process
Markov models
mean transition time
mean time spent in the group of states
queueing systems
reliability model
proces narodzin i śmierci
modele Markova
średni czas przejścia
średni czas spędzony w grupie stanów
systemy kolejkowe
model niezawodności
Opis:
In this paper, we consider Markov birth-death processes with constant intensities of transitions between neighboring states that have an ergodic property. Using the exponential distributions properties, we obtain formulas for the mean time of transition from the state i to the state j and transitions back, from the state j to the state i. We found expressions for the mean time spent outside the given state i, the mean time spent in the group of states (0,...,i-1) to the left from state i, and the mean time spent in the group of states (i+1,i+2,...) to the right. We derive the formulas for some special cases of the Markov birth-death processes, namely, for the Erlang loss system, the queueing systems with finite and with infinite waiting room and the reliability model for a recoverable system.
Źródło:
Journal of Applied Mathematics and Computational Mechanics; 2021, 20, 4; 99--110
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:
Expected volumes of requests in systems of the queueing network with a limited number of waiting places
Autorzy:
Zając, P.
Matalytski, M.
Powiązania:
https://bibliotekanauki.pl/articles/121834.pdf
Data publikacji:
2017
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
sieci HM
sieci kolejkowe
system kolejkowy
bezprzewodowy punkt dostępu
HM-networks
queueing network
single-line queueing system
queueing system
queuing time
limited queue
demands total volume
wireless access point
volume of requests
Opis:
We present a method of finding the expected volume of requests in HM-network with homogeneous requests and bypass of the queueing systems of requests. The case was considered when the volume changes associated with the transitions between the states of the network are deterministic functions, depending on the state of the network and time, and the systems are single line. It is assumed that the probability of the states of the network systems, the parameters of the entrance flow of the requests and the service depend on the time.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2017, 22; 141-160
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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:
Performance evaluation of unreliable system with infinite number of servers
Autorzy:
Tikhonenko, O.
Ziółkowski, M.
Powiązania:
https://bibliotekanauki.pl/articles/201519.pdf
Data publikacji:
2020
Wydawca:
Polska Akademia Nauk. Czytelnia Czasopism PAN
Tematy:
queueing systems with non-homogeneous customers
unreliable queueing systems
total volume
loss probability
Laplace–Stieltjes transform
Opis:
In the paper, we investigate queueing system M/G/∞ with non-homogeneous customers. By non-homogeneity we mean that each customer is characterized by some arbitrarily distributed random volume. The arriving customers appear according to a stationary Poisson process. Service time of a customer is proportional to his its volume. The system is unreliable, which means that all its servers can break simultaneously and then the repair period goes on for random time having an arbitrary distribution. During this period, customers present in the system and arriving to it are not served. Their service continues immediately after repair period termination. Time intervals of the system in good repair mode have an exponential distribution. For such system, we determine steady-state sojourn time and total volume of customers present in it distributions. We also estimate the loss probability for the similar system with limited total volume. An analysis of some special cases and some numerical examples are attached as well.
Źródło:
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2020, 68, 2; 289-297
0239-7528
Pojawia się w:
Bulletin of the Polish Academy of Sciences. Technical Sciences
Dostawca treści:
Biblioteka Nauki
Artykuł
Tytuł:
Processor sharing queueing systems with non-homogeneous customers
Autorzy:
Tikhonenko, O.
Powiązania:
https://bibliotekanauki.pl/articles/121919.pdf
Data publikacji:
2010
Wydawca:
Uniwersytet Humanistyczno-Przyrodniczy im. Jana Długosza w Częstochowie. Wydawnictwo Uczelniane
Tematy:
egalitarian processor sharing
EPS
queueing models
egalitarne współdzielenie procesora
modele kolejkowe
Opis:
We investigate processor sharing queueing systems with non-homogeneous customers having some random space requirements. Such systems have been used to model and solve various practical problems occurring in the design of computer or communicating systems. The above non-homogenity means that each customer (independently of others) has some random space requirement and his length (or amount of work for his service) generally depends on the space requirement. In real systems, a total sum of space requirements of customers presenting in the system is limited by some constant value (memory capacity) V > 0. We estimate loss characteristcs for such a system using queueing models with unlimited memory space.
Źródło:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics; 2010, 15; 149-162
2450-9302
Pojawia się w:
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
Dostawca treści:
Biblioteka Nauki
Artykuł
Wyświetlanie 1-15 z 41

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