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1

The potentials method for the M/G/1/m queue with customer dropping and hysteretic strategy of the service time change

Zhernovyi Y., Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 1

197--210

EN

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.

2

Optymalizacja kosztów transportu w sferze logistyki zaopatrzenia

Szkutnik J., Ziółkowski J.

Logistyka

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2015

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nr 4

6015--6024, CD 2

PL

W artykule opisano przykład rozwiązania problemu transportowego różnymi metodami. W oparciu o dane liczbowe przedstawiono sposób postępowania prowadzący do uzyskania rozwiązania i optymalizacji kosztów transportu w sferze logistyki zaopatrzenia. Cel pracy, jakim było zaprezentowanie efektywności metod: kąta północno – zachodniego, najmniejszego elementu oraz VAM z ekonomicznego punku widzenia został osiągnięty.

EN

Examples of soluting the transportation problems by using several methods were presented in the article. In accordance to collected datas, some algorithms enabling the user to reach the solutions were described. These were the solutions that performed costs connected with transport of inbound logistics sphere. The aim of this article was to present effectiveness of such methods as: north – west angle, the least element and VAM, solutions made by all of them were examined and finally the aim was accomplished.

3

The potentials method for a closed queueing system with hysteretic strategy of the service time change

Zhernovyi Y., Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2015

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Vol. 14, nr 2

131--143

EN

We propose a method for determining the characteristics of a single-channel closed queueing system with an exponential distribution of the time generation of service requests and arbitrary distributions of the service times. In order to increase the system capacity, two service modes (the main mode and overload mode), with the service time distribution functions F ( x ) and F ( x ) respectively, are used. The overload mode starts functioning if at the beginning of service of the next customer the number of customers in the system ξ(t ) satisfies the condition ξ (t ) > h2. The return to the main mode carried out at the beginning of service of the customer, for which ξ (t ) = h1, where 1 ≤ h1 < h2. 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.

4

Modelowanie obsługi zadań w serwerach z oscylacjami

Oniszczuk W., Podobińska M.

Zeszyty Naukowe Politechniki Białostockiej. Informatyka

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2008

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Z. 3

83-95

PL

Idea przedstawianego systemu kolejek z oscylacjami jest oparta na dwóch progowych wartościach. Obsługa procesu w tym systemie jest zorganizowana, w przybliżeniu, w ten sposób, że długość kolejki utrzymuje się pomiędzy tymi wartościami. System kolejki z oscylacjami pozwala lepiej wykorzystywać dostępne zasoby i jest stosowany w wielu urządzeniach, które korzystają z obsługi pojedynczej kolejki. Jest to również uogólnianie niektórych procedur zaproponowanych dla sieci ATM (ang. Asynchronous Transfer Mode). W tej pracy rozważać będziemy systemy kolejkowe z oscylacjami w wersji ze skończonym buforem. Charakterystyki stanów systemów z procesem Poissona na wejściu (M/G-G/1/N) otrzymuje sie metodą potencjałów. To podejście daje przejrzyste i łatwe do implementacji formuły matematyczne.

EN

In this paper a finite buffer version of the oscillating queuing system is studied. The idea of the lately introduced oscillating queuing system is based on two threshold values. The service process in this system is planned in such a way that the queue length is kept between these values. The oscillating queuing system has the advantage of making improved use of the available resources and is applicable in many devices which use a single server queuing scheme. It is also a simplification of some cell disposal procedures projected for ATM networks.