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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

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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

2023

Vol. 71, nr 5

art. no. e146764

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.

Single–server queueing system with limited queue, random volume customers and unlimited sectorized memory buffer

Ziółkowski Marcin, Tikhonenko Oleg

Bulletin of the Polish Academy of Sciences. Technical Sciences

2022

Vol. 70, nr 6

art. no. e143647

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.