Asymptotic Analysis of an Retrial Queueing System M|M|1 with Collisions and Impatient Calls

Danilyuk, Elena; Fedorova, Ekaterina; Moiseeva, Svetlana

doi:10.1134/s0005117918120044

Cited by 13 publications

(4 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The present paper generalizes the results obtained in [4,5]. We find the asymptotic stationary distribution of the number of calls in the orbit for the system under consideration.…”

supporting

confidence: 81%

“…Equation 19has at least one root R 1 ∈ [0; 1], and the proof of existence of R 1 is similar to that in [4].…”

Section: Stage 1 Finding the First-order Asymptoticmentioning

confidence: 92%

“…Such messages collide. They are considered distorted and both go into the orbit from where they ask the device for servicing again after a random delay time, see for example [4][5][6][7][8].…”

mentioning

confidence: 99%

“…Impatience of calls in the orbit is understood as the case when a customer in the orbit can leave the orbit after a random time without service [4,5,7,[9][10][11]. But there is another way to specify impatience, for example, non-persistence, balking and reneging are used [8,[12][13][14][15].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Asymptotic Analysis of Retrial Queueing System M/M/1 with Impatient Customers, Collisions and Unreliable Server

Danilyuk

Moiseeva

Sztrik

et al. 2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

View full text Add to dashboard Cite

The retrial queueing system of M=M=1 type with Poisson flow of arrivals, impatient cus- tomers, collisions and unreliable service device is considered in the paper. The novelty of our contribution is the inclusion of breakdowns and repairs of the service into our previous study to make the problem more realistic and hence more complicated. Retrial time of customers in the orbit, service time, impa- tience time of customers in the orbit, server lifetime (depending on whether it is idle or busy) and server recovery time are supposed to be exponentially distributed. An asymptotic analysis method is used to find the stationary distribution of the number of customers in the orbit. The heavy load of the system and long time patience of customers in the orbit are proposed as asymptotic conditions. Theorem about the Gaussian form of the asymptotic probability distribution of the number of customers in the orbit is formulated and proved. Numerical examples are given to show the accuracy and the area of feasibility of the proposed method

show abstract

“…The present paper generalizes the results obtained in [4,5]. We find the asymptotic stationary distribution of the number of calls in the orbit for the system under consideration.…”

supporting

confidence: 81%

“…Equation 19has at least one root R 1 ∈ [0; 1], and the proof of existence of R 1 is similar to that in [4].…”

Section: Stage 1 Finding the First-order Asymptoticmentioning

confidence: 92%

mentioning

confidence: 99%