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2 Bulletin of the Polish Academy of Sciences. Technical Sciences

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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

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.

M/G→ /n/0 Erlang queueing system with heterogeneous servers and non-homogeneous customers

Ziółkowski M.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2018

Vol. 66, nr 1

59--66

In the present paper, we investigate a multi-server queueing system with heterogeneous servers, unlimited memory space, and non-homogeneous customers. The arriving customers appear according to a stationary Poisson process. Service time distribution functions may be different for every server. Customers are additionally characterized by some random volume. On every server, the service time of the customer depends on their volume. The number of customers distribution function is obtained in the classical model of the system. In the model with non-homogeneous customers, the stationary total volume distribution function is determined in the term of Laplace–Stieltjes transform. The stationary first and second moments of a total customers volume are calculated. An analysis of some special cases of the model and some numerical examples are also included.