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Investigation of G-network with bypasses of queueing systems by positive customers at a non-stationary regime

Naumenko Victor, Kopats Dmitry, Matalytski Mikhail, Pankov Andrey

Journal of Applied Mathematics and Computational Mechanics

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2020

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Vol. 19, nr 3

85--97

EN

An open queuing network (QN) with single-line queuing systems (QS) is considered. QS are characterized by the presence of bypasses and the possibility of coming of negative customers. The network receives two independent elementary streams. The first stream is formed from the ordinary (positive) customers, while the second is composed of negative customers. Arriving of each negative customer to the system destroys exactly one positive customer in the queue, if those are contained. Negative customers do not require maintenance as the service of positive customers in the network systems is carried out in accordance with the FIFO discipline. Positive customers with a probability depending on the state of the node when they are sent to it are added to the queue, and with an additional probability, they immediately bypass it and behave in the future as served. The service in the systems is exponential, the routing of positive customers in the network is Markov, taking into account the possibility of turning the customer into a negative one after sending it to another system.

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Analysis of the queueing network with a random waiting time of negative customers at a non-stationary regime

Naumenko V., Matalytski M., Kopats D.

Journal of Applied Mathematics and Computational Mechanics

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2016

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Vol. 15, nr 3

111--122

EN

In the article a queueing network (QN) with positive customers and a random waiting time of negative customers has been investigated. Negative customers destroy positive customers on the expiration of a random time. Queueing systems (QS) operate under a heavy-traffic regime. The system of difference-differential equations (DDE) for state probabilities of such a network was obtained. The technique of solving this system and finding mean characteristics of the network, which is based on the use of multivariate generating functions was proposed.

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A discrete-time system with service control and repairs

Atencia I.

International Journal of Applied Mathematics and Computer Science

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2014

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Vol. 24, no. 3

471--484

EN

This paper discusses a discrete-time queueing system with starting failures in which an arriving customer follows three different strategies. Two of them correspond to the LCFS (Last Come First Served) discipline, in which displacements or expulsions of customers occur. The third strategy acts as a signal, that is, it becomes a negative customer. Also examined is the possibility of failures at each service commencement epoch. We carry out a thorough study of the model, deriving analytical results for the stationary distribution. We obtain the generating functions of the number of customers in the queue and in the system. The generating functions of the busy period as well as the sojourn times of a customer at the server, in the queue and in the system, are also provided. We present the main performance measures of the model. The versatility of this model allows us to mention several special cases of interest. Finally, we prove the convergence to the continuous-time counterpart and give some numerical results that show the behavior of some performance measures with respect to the most significant parameters of the system.