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1
Content available Advanced Considerations Concerning Impact of Applied Call Admission Control Mechanisms on Traffic Characteristics in Elastic Optical Network Nodes
Głąbowski Mariusz, Sobieraj Maciej
Journal of Telecommunications and Information Technology
|
2023
|
nr 4
68--75
EN
Over the past few years, a significant increase in network traffic volumes has been observed. The ever growing bandwidth demands mean that a reliable and optimum service level needs to be ensured in communication systems for specific traffic categories. Optimal allocation and use of resources may be achieved through the use of call admission control (CAC) mechanisms implemented in network systems. The resource reservation mechanism and the threshold mechanism are two of the most popular CAC methods. In the reservation mechanisms, a certain number of resources is reserved for selected (predefined) services only. In the case of threshold mechanisms, the number of resources allocated to individual traffic classes depends on the network load. This article discusses the results of simulations verifying the impact of applied CAC mechanisms on the traffic characteristics in elastic optical network (EON) nodes with a Clos structure. Loss probability results obtained with the use of the simulator are presented as well.
2
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
|
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.
3
Content available Performance evaluation of unreliable system with infinite number of servers
Tikhonenko O., Ziółkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
2020
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Vol. 68, nr 2
289--297
EN
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.
4
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
|
2019
|
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.
5
Symulator węzłów elastycznych sieci optycznych opartych na strukturze 3-sekcyjnego pola Closa
Głąbowski M., Sobieraj M., Ivanov H.
Przegląd Telekomunikacyjny + Wiadomości Telekomunikacyjne
|
2018
|
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.
6
Content available Multiline queueing system with random time limitations and limited buffer space
Tikhonenko O., Zając P.
Journal of Applied Mathematics and Computational Mechanics
|
2018
|
Vol. 17, nr 4
99--106
EN
In the paper, we investigate multi-server queueing systems with demands of random space requirements (volumes), in which buffer space is limited by constant value and queueing ore (and) service time are limited by exponentially distributed random variables. For such systems, stationary demands number distribution and loss probability are determined. Some numerical results are attached as well.
7
Content available Single-server queueing system with external and internal customers
Tikhonenko O., Ziółkowski M.
Bulletin of the Polish Academy of Sciences. Technical Sciences
|
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.
8
Content available Multi-server closed queueing system with limited buffer space
Tikhonenko A., Tikhonenko-Kędziak A.
Journal of Applied Mathematics and Computational Mechanics
|
2017
|
Vol. 16, nr 1
117--125
EN
In the paper, we investigate multi-server closed queueing systems with identical servers and a finite number of terminals. Requests from each terminal are characterized by a random space requirement (volume), the request service time doesn’t depend on its volume and has an exponential distribution. The total requests capacity in the system is limited by a positive value (buffer space memory volume) V. For such systems, stationary requests number distribution and loss probability are determined. The analogous results for open multi-server systems are obtained as a limit case. Some numerical results are attached as well.
9
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
|
2016
|
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.
10
Content available remote Determination of loss characteristicsfor queueing systems with bounded buffer space
Tikhonenko O., Tikhonenko-Kędziak A.
Studia i Materiały / Europejska Uczelnia Informatyczno-Ekonomiczna w Warszawie
|
2013
|
Nr 2(6)
29--38
EN
We investigate non-classical queueing systems with demands characterized by some random capacity under assumption that demand service time generally depends on its capacity. This dependency can be defined by the joint distribution function. The total demands capacity (i.e. the sum of capacities of demands present in the system at arbitrary time instant) is bounded by some constant value V that is named buffer space volume of the system. Such systems have been used to model and solve various problems occurring in the design of computer and communicating systems. The main steady-state performance characteristics of such systems are loss probability (the relative part of demands that was lost in the system during infinite time interval) and probability of capacity unit losing (the relative part of total demands capacity that was lost during infinite time interval). In the paper we determine these characteristics for some systems with bounded buffer space and compare the results of our calculations with the results of calculations of loss probability in classical regenerative queueing systems using the relation obtained in [3]. Numerical examples and results of simulation are attached as well.
PL
W artykule zbadano nieklasyczne systemy kolejkowe, w których zgłoszenia są charakteryzowane losową objętością przy założeniu, że czas obsługi zgłoszenia ogólnie zależy od jego objętości. Wskazana zależność może być określona za pomocą wspólnej dystrybuanty. Objętość sumaryczna (tj. suma objętości zgłoszeń obecnych w systemie w dowolnej chwili czasu) jest ograniczona wielkością stałą V, którą nazywamy pojemnością pamięci systemu. Systemy podobnego typu są wykorzystywane do rozwiązywania rożnych zagadnień w trakcie projektowania systemów komputerowych i sieci komunikacyjnych. Podstawowymi charakterystykami wydajności takich systemów w trybie stacjonarnym są prawdopodobieństwo utraty (część względna utraconych zgłoszeń w ciągu nieskończonego przedziału czasowego działania systemu) oraz prawdopodobieństwo utraty jednostki objętości (część względna utraconej sumarycznej objętości zgłoszeń w ciągu nieskończonego przedziału czasowego działania systemu). W artykule przedstawiono sposób obliczania wskazanych charakterystyk dla pewnych systemów kolejkowych z ograniczoną pojemnością pamięci oraz porównanie otrzymanych wielkości prawdopodobieństwa utraty z wynikami podobnych obliczeń otrzymanych w [3] dla klasycznych systemów kolejkowych o zachowaniu opisywanym procesem regenerującym się. Podano także wyniki obliczeń numerycznych i symulacji komputerowej.
11
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.
12
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.
13
Content available remote Queueing Systems with Common Memory Space
Tikhonenko O., Ziółkowski M.
Scientific Issues of Jan Długosz University in Częstochowa. Mathematics
|
2005
|
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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