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Content available Multi–server loss queueing system with random volume customers, non–identical servers and a limited sectorized memory buffer
Ziółkowski Marcin
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2023
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Vol. 71, nr 5
art. no. e146764
EN
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.
2
Content available M/G/n/(0, V) Erlang queueing system with non-homogeneous customers, non-identical servers and limited memory space
Tikhonenko O., Ziółkowski M., Kurkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2019
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Vol. 67, nr 3
489--500
EN
In the present paper, we investigate a?multi-server Erlang queueing system with heterogeneous servers, non-homogeneous customers and limited memory space. The arriving customers appear according to a?stationary Poisson process and are additionally characterized by some random volume. The service time of the customer depends on his volume and the joint distribution function of the customer volume and his service time can be different for different servers. The total customers volume is limited by some constant value. For the analyzed model, steady-state distribution of number of customers present in the system and loss probability are calculated. An analysis of some special cases and some numerical examples are attached as well.
3
Symulator węzłów elastycznych sieci optycznych opartych na strukturze 3-sekcyjnego pola Closa
Głąbowski M., Sobieraj M., Ivanov H.
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
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2018
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nr 8-9
822--825, CD
PL
W artykule przedstawiono opis i zasadę działania symulatora pól komutacyjnych elastycznych sieci optycznych. Symulator umożliwia określenie prawdopodobieństwa strat dla poszczególnych klas zgłoszeń oferowanych węzłom sieci optycznych. Architektura węzła elastycznych sieci optycznych oparta jest na strukturze 3- sekcyjnego pola Closa. W przyszłości program symulacyjny zostanie wykorzystany jako narzędzie weryfikacji modeli analitycznych węzłów elastycznych sieci optycznych.
EN
The article presents a description and operation principle of a simulator of elastic optical networks switching networks. The simulator allows to determine the loss probability for individual traffic classes offered to optical network nodes. The node architecture of elastic optical networks is based on the structure of the 3-stage Clos switching network. In the future, the simulation software will be used as a verification tool for analytical models of elastic network nodes.
4
Content available Single-server queueing system with external and internal customers
Tikhonenko O., Ziółkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
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2018
|
Vol. 66, nr 4
539--551
EN
In the paper, we investigate a single-server queueing system with unlimited memory space and non-homogeneous customers (calls) of the two following types: 1) external customers that are served by the system under consideration, 2) internal customers that arrive and interrupt the service process only when an external customer is being served. The external customers appear according to a stationary Poisson process. Customers of each of the above-mentioned types are characterized by some random volume. The customer service time depends arbitrarily on its volume. Two schemes of customer service organization are analyzed. The non-stationary and stationary distributions of the total volume of customers present in the system are determined in terms of Laplace and Laplace-Stieltjes transforms. The stationary first and second moments of total customers volume are also calculated. The obtained results are used to approximate loss characteristics in analogous systems with limited buffer space. Numerical examples illustrating theoretical results are attached as well.
5
Content available Performance evaluation of an M/G/n-type queue with bounded capacity and packet dropping
Tikhonenko O., Kempa W. M.
International Journal of Applied Mathematics and Computer Science
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2016
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Vol. 26, no. 4
841--854
EN
A queueing system of the M/G/n-type, n ≥ 1, with a bounded total volume is considered. It is assumed that the volumes of the arriving packets are generally distributed random variables. Moreover, the AQM-type mechanism is used to control the actual buffer state: each of the arriving packets is dropped with a probability depending on its volume and the occupied volume of the system at the pre-arrival epoch. The explicit formulae for the stationary queue-size distribution and the loss probability are found. Numerical examples illustrating theoretical formulae are given as well.
6
Content available Queueing system M/M/n/(m, V ) with non-identical servers
Małek J., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2013
|
Vol. 18
29--39
EN
We investigate multi-server queueing systems with Poisson arrivals, non-identical servers and customers of random volume, under assumption that customer’s service time having an exponential distribution doesn’t depend on his volume, but service time parameters can be different for different servers. We also assume that the total volume of customers present in the system at arbitrary time instant is bounded by some constant value V > 0. For such systems the stationary customers number distribution and loss probability are determined.
7
Systemy obsługi zgłoszeń objętości z ograniczoną pojemnością pamięci
Tikhonenko O., Kawecka M.
Studia Informatica
|
2012
|
Vol. 33, nr 3A
19-28
PL
W artykule są analizowane wieloliniowe systemy obsługi zgłoszeń o losowej objętości z najprostszym strumieniem wejściowym, w których czas obsługi nie zależy od objętości zgłoszenia, a objętość sumaryczna jest ograniczona. Dowodzi się twierdzenie, pozwalające na wyznaczenie charakterystyk takich systemów przy warunku, że wyznaczone są charakterystyki odpowiedniego systemu klasycznego.
EN
Multi-server queueing systems with Poisson entry and customers having some random space reauireinent are considered for the case of service time independent of the space requirement and lirnited buffer space. It's shown that all characteristics of siieh systenis can be obtained, if eharacteristics of proper classical systems are known.
8
Content available remote Queueing Systems with Common Memory Space
Tikhonenko O., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
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2005
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Vol. 10
131--149
EN
In the present paper we investigate queueing systems of different types with customers having some random space requirements connected via common memory space. For such systems combinations we determine the stationary loss probability and the distribution of customers present in each system.
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