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Abstract

In the paper, we investigate queueing system M/G/∞ with non–homogeneous customers. As non–homogenity, 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 volume. The system is unreliable what 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.

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Authors and Affiliations

O. Tikhonenko
M. Ziółkowski
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Abstract

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.

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Authors and Affiliations

O. Tikhonenko
M. Ziółkowski
M. Kurkowski
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Abstract

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.
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Authors and Affiliations

Marcin Ziółkowski
1
ORCID: ORCID

  1. Institute of Information Technology, Warsaw University of Life Sciences – SGGW, Poland

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