Limit theorems for multiphase queueing systems

1987 ◽  
Vol 38 (5) ◽  
pp. 2288-2298
Author(s):  
F. I. Karpelevich ◽  
A. Ya. Kreinin
Keyword(s):  
Limit Theorems ◽  
Queueing Systems ◽  
Multiphase Queueing Systems

scholarly journals On the law of the iterated logarithm in hybrid multiphase queueing systems

2020 ◽  
Vol 30 (4) ◽  
Author(s):  
Saulius Minkevičius
Keyword(s):  
Queue Length ◽  
Limit Theorems ◽  
Queueing System ◽  
Heavy Traffic ◽  
Queueing Systems ◽  
Probability Limit ◽  
Iterated Logarithm ◽  
Multiphase Queueing Systems ◽  
Multi Phase ◽  
Complex Computer

The model of a Hybrid Multi-phase Queueing System (HMQS) under conditions of heavy traffic is developed in this paper. This is a mathematical model to measure the performance of complex computer networks working under conditions of heavy traffic. Two probability limit theorems (Laws of the iterated logarithm, LIL) are presented for a queue length of jobs in HMQS.

scholarly journals Application of methods of the theory of multiphase queueing systems to the problems of optimizing the resources of service companies in the field of housing sector

2018 ◽  
Vol 196 ◽  
pp. 04040
Author(s):  
Rustam Khayrullin ◽  
Alexey Myasnikov
Keyword(s):  
Customer Service ◽  
Queuing Theory ◽  
Methodological Approach ◽  
Queueing Systems ◽  
Housing Sector ◽  
Fair Price ◽  
Service Companies ◽  
Multiphase Queueing Systems ◽  
The Individual ◽  
To Receive

The scientific - methodological approach to calculation of duration and estimation of complexity of the expertise of technical and operational documentation for measuring equipment and technical devices used in the field of construction and housing sector is suggested. The approach is based on both the theory of queueing systems and probabilistic and statistical methods. The developed approach is implemented in the form of package of applied programs. The software based on complex using the principle of decomposition of object into constituent parts, the queuing theory and the method of expert estimations. The software allows on the basis of the results of statistical data processing for the past periods of work to receive both estimates of the average time of the expertise as a whole, and the estimates of the individual expertise stages. The algorithm for calculating the required number of employees for quality customer service is developed, taking into account the restriction on the waiting time of the request in the queue. The obtained results make it possible to make optimal use of working personnel at various work sites, taking into account their qualifications and training. The developed approach can be used to form a “fair price list” for private clients and enterprises - customers of expertise.

On the waiting-time process in a single-line queue with repeated calls

1986 ◽  
Vol 23 (1) ◽  
pp. 185-192 ◽  
Author(s):  
G. I. Falin
Keyword(s):  
Waiting Time ◽  
Limit Theorems ◽  
Queueing System ◽  
Queueing Systems ◽  
Retrial Queue ◽  
Time Process ◽  
Light Traffic ◽  
Repeated Calls ◽  
Waiting Time Process ◽  
Mean Variance

Waiting time in a queueing system is usually measured by a period from the epoch when a subscriber enters the system until the service starting epoch. For repeated orders queueing systems it is natural to measure the waiting time by the number of repeated attempts, R, which have to be made by a blocked primary call customer before the call enters service. We study this problem for the M/M/1/1 retrial queue and derive expressions for mean, variance and generating function of R. Limit theorems are stated for heavy- and light-traffic cases.

scholarly journals Python for Scientific Computing Education: Modeling of Queueing Systems

2014 ◽  
Vol 22 (1) ◽  
pp. 37-51 ◽  
Author(s):  
Vladimiras Dolgopolovas ◽  
Valentina Dagienė ◽  
Saulius Minkevičius ◽  
Leonidas Sakalauskas
Keyword(s):  
Parallel Programming ◽  
Scientific Computing ◽  
Queueing Systems ◽  
Computer Code ◽  
Learning Objects ◽  
Stochastic Simulations ◽  
Computing Education ◽  
Multiphase Queueing Systems

In this paper, we present the methodology for the introduction to scientific computing based on model-centered learning. We propose multiphase queueing systems as a basis for learning objects. We use Python and parallel programming for implementing the models and present the computer code and results of stochastic simulations.

scholarly journals Randomized longest-queue-first scheduling for large-scale buffered systems

2015 ◽  
Vol 47 (04) ◽  
pp. 1015-1038 ◽  
Author(s):  
A. B. Dieker ◽  
T. Suk
Keyword(s):  
Limit Theorems ◽  
Large Scale ◽  
Scheduling Algorithm ◽  
Queueing Systems ◽  
Mean Field ◽  
Diffusion Approximations ◽  
Mean Field Limit ◽  
Multi Scale ◽  
Noteworthy Feature ◽  
Longest Queue First

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling (LQF) algorithm by establishing new mean-field limit theorems as the number of buffers n → ∞. We achieve this by allowing the number of sampled buffers d = d(n) to depend on the number of buffers n, which yields an asymptotic 'decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of n and d(n). To the best of the authors' knowledge, this is the first derivation of diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized LQF algorithm emulates the LQF algorithm, yet is computationally more attractive. The analysis of the system performance as a function of d(n) is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized LQF scheduling algorithm.

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