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1

The system M2θ/G/1/m with threshold control of the arrival rate and service time

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2014

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tom Vol. 13, nr 2

149--163

EN

We consider a M2θ/G/1/m queueing system with arrival of customer batches, which uses a threshold control mechanism of the service time and arrival rate. The system receives two independent flows of customers, one of which is blocked in an overload mode (under the condition that the number of customers in the system exceeds a given threshold value h). Full blocking of the input flow is carried out from the moment when the queue length reaches the number m until the beginning of the service of the first customer, for which the number of customers in the system does not exceed h. From the beginning of the service of the first customer during the excess of number of customers in the system of h until the completion of full blocking the time of service of customer is distributed under the law of F(x) (an increased service rate is used). Rest of the time the system applies the normal service rate with the distribution function F(x) of service time. Laplace transforms for the distributions of the number of customers in the system during the busy period and for the distribution function of the busy period are found. The average duration of the busy period is obtained. Formulas for the stationary distribution of the number of customers in the system, for the probability of service and for the stationary characteristics of the system are established. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

2

Recurrence relations for two-channel queueing systems with Erlangian service times and hysteretic strategy of random dropping of customers

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2018

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tom Vol. 17, nr 2

93--103

EN

This article proposes a method of study the M/Es/2/m and M/Es/2/∞ queueing systems with a hysteretic strategy of random dropping of customers. Recurrence relations are obtained to compute the stationary distribution of the number of customers and steadystate characteristics. The constructed algorithms were tested on examples with the use of simulation models constructed with the help of GPSS World.

3

Recurrence relations for a multi-channel closed queueing system with Erlangian service times of second order

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2017

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tom Vol. 16, nr 3

123--128

EN

We propose a method for determining the steady-state characteristics of a multichannel closed queueing system with exponential distribution of the time generation of service requests and the second order Erlang distributions of the service times. Recurrence relations to compute the steady-state distribution of the number of customers are obtained. The developed algorithms are tested on examples using simulation models constructed with the assistance of the GPSS World tools.

4

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

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2015

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tom 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.

5

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

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2016

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tom 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.

6

The queueing system M2X/M/n with hysteretic control of the input flow intensity

100%

Zhernovyi Y. , Kopytko B.

Journal of Applied Mathematics and Computational Mechanics

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2014

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tom Vol. 13, nr 1

149--161

EN

We consider a multi-channel queueing system with unlimited queue and with exponentially distributed service time and the intervals between the arrival of customers batches, which uses a hysteretic control mechanism of the input flow intensity. The system receives two independent flows of customers, one of which is blocked in an overload mode. An algorithm for finding the stationary distribution of the number of customers and stationary characteristics (the mean queue length, the mean waiting time in the queue, the probability of customers loss) is proposed. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

7

On characteristics of the Mθ/G/1/m and Mθ/G/1 queues with queue-size based packet dropping

80%

Zhernovyi Y. , Kopytko B. , Zhernovyi K.

Journal of Applied Mathematics and Computational Mechanics

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2014

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tom Vol. 13, nr 4

163--175

EN

We study the Mθ/G/1/m and Mθ/G/1 queuing systems with the function of the random dropping of customers used to ensure the required characteristics of the system. Each arriving packet of customers can be rejected with a probability defined depending on the queue length at the service beginning of each customer. The Laplace transform for the distribution of the number of customers in the system on the busy period is found, the mean duration of the busy period is determined, and formulas for the stationary distribution of the number of customers in the system are derived via the approach based on the idea of Korolyuk’s potential method. The obtained results are verified with the help of a simulation model constructed with the assistance of GPSS World tools.

8

The busy period for the Mθ /G/1/m system with service time dependent of the queue length

80%

Zhernovyi Y. , Kopytko B. , Zhernovyi K.

Journal of Applied Mathematics and Computational Mechanics

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2013

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tom Vol. 12, nr 4

127--133

EN

We consider the Mθ/G/1/m system wherein the service time depends on the queuelength and it is determined at the beginning of customer service. Using an approach basedon the potential method proposed by V. Korolyuk, the Laplace transforms for the distribution f the number of customers in the system on the busy period and for the distribution function of the busy period are found.