Mathematical Model of a Queuing System With Arbitrary Quantity of Sources and Size-Limited Queue

Кирпичников, А П; Titovtsev, Anton

doi:10.12732/ijpam.v106i2.27

Cited by 6 publications

(15 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The most general mathematical model of open multi-channel QS having m service facilities of identical efficiency with exponentially distributed time of service was presented in the work of authors [5].The input demand stream in this case is a superposition of the arbitrary number of h components each of which represents a Poisson stream of claims served in the queue. For each type of demands arriving in the system from j-th source limitation for a queue length ε j acts, at the same time ε 0 < ε 1 < ε 2 < · · · < ε h .…”

Section: Real Queuementioning

confidence: 99%

“…To calculate parameters of a physical queue on the basis of a universal mathematical model developed and presented in the work [5], it is necessary to rewrite a normalization condition in such a way as upon totaling in this condition to consider only those states of the system which correspond to a physical queue. As a result, we have…”

Section: Real Queuementioning

confidence: 99%

“…The moments of claims number waiting for service in a real queue are calculated according to the same scheme as for a mathematical queue; however, the probabilities with a tilde obtained with the corresponding normalization condition in view are inserted into corresponding formulas. A detailed conclusion of formulas for the moments of queue length is given in the work [5]. As a result, we have -an average number of claims in a real queuẽ…”

Section: Real Queuementioning

confidence: 99%

“…The algorithm for calculation of claim servicing-waiting moments in a real queue is quite identical to the algorithm for calculation of claim servicingwaiting moments in a general mathematical queue presented in the work [5]. Corresponding probabilities with a tilde obtained with a new normalization condition in view have to be inserted instead of common probability characteristics (1).…”

Section: Real Queuementioning

confidence: 99%

“…Besides, taking into account this circumstance it is necessary to redefine the relative throughout capacity ofq system. In this case, we have the following finite formulas for the claim servicing-waiting moments in the real queue for the QS universal model presented in the work [5]:…”

Section: Real Queuementioning

confidence: 99%

See 4 more Smart Citations

The Concept of Higher Orders Queues in the Queuing Theory

Titovtsev¹

2016

Int. J. of Pure and Appl. Math.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Real Queuementioning

confidence: 99%

Section: Real Queuementioning

confidence: 99%

Section: Real Queuementioning

confidence: 99%

Section: Real Queuementioning

confidence: 99%

Section: Real Queuementioning

confidence: 99%

See 3 more Smart Citations