Mathematical Model of Open Queuing System With Full Set of Memories

Кирпичников, А П; Titovtsev, Anton

doi:10.12732/ijpam.v107i1.11

Cited by 4 publications

(2 citation statements)

References 2 publications

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“…For a specific QS model with full set of memories proposed in work [6], the probabilities of steady states of system upon physical queue calculation take the formP…”

Section: Probabilistic Characteristics and Moments Of Demands Number In A Physical Queuementioning

confidence: 99%

Physical and Mathematical Queues in the Applied Queuing Theory

Кирпичников¹,

Titovtsev²

2016

Int. J. of Pure and Appl. Math.

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“…For a specific QS model with full set of memories proposed in work [6], the probabilities of steady states of system upon physical queue calculation take the formP…”

Section: Probabilistic Characteristics and Moments Of Demands Number In A Physical Queuementioning

confidence: 99%

Physical and Mathematical Queues in the Applied Queuing Theory

Кирпичников¹,

Titovtsev²

2016

Int. J. of Pure and Appl. Math.

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“…The general calculation algorithm of an N-th order queue in case that N<h is convenient to formulate using QS models with a full set of memories proposed in the work [6]. In this case, the normalization condition can be written as…”

Section: Higher Orders Queuesmentioning

confidence: 99%

The Concept of Higher Orders Queues in the Queuing Theory

Titovtsev¹

2016

Int. J. of Pure and Appl. Math.

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The paper considers various types of queues arising in queuing systems. The concept of an N-th order queue is introduced; the calculation algorithm of the first and second moments of main discrete and continuous random variables characterizing behavior of higher orders queues in queuing systems of the mixed type is presented. AMS Subject Classification: 60K25Key Words: physical queue, real queue, quality of service (QoS), queuing system (QS) Main DefinitionsAn N-th order queue will be called the queue calculated in case when there are m+N claims in the system as minimum, and N of them are in the memory. Such a queue exists if a newly arrived claim finds a minimum N claims waiting for service before this one.At N=0 we have a physical queue which is explicitly studied in the work [7]. In the system of GPSS World simulation modeling this characteristic has the name "a queue without zero inputs".At N=1 we have the so-called real queue; at N>1 we have queues of higher orders.

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