scholarly journals Stationary Blocking Probability in Multi-server Finite Queuing System with Ordered Entry and Poisson Arrivals

2016 ◽  
pp. 344-357
Author(s):  
Rostislav Razumchik ◽  
Ivan Zaryadov
Keyword(s):  
Blocking Probability ◽  
Queuing System ◽  
Poisson Arrivals ◽  
Multi Server

scholarly journals On the analysis of the limited resources queuing system under MAP arrivals

2018 ◽  
Vol 16 ◽  
pp. 01008
Author(s):  
Eduard Sopin ◽  
Konstantin Samouylov
Keyword(s):  
Blocking Probability ◽  
Queuing System ◽  
Limited Resources ◽  
System Of Equations ◽  
Stationary Probability ◽  
Equilibrium System ◽  
Vector Form ◽  
Stationary Probability Distribution ◽  
Resource Requirements ◽  
Resource Allocation Schemes

In the paper, we analyse a multiserver queuing system with discrete limited resources and random resource requirements under MAP arrivals, which can adequately model resource allocation schemes in the contemporary wireless networks. The equilibrium system of equations is derived in the vector form and is solved numerically. With stationary probability distribution, we provide formulas for the average and the variance of the occupied resources, as well as for the blocking probability. The results are illustrated by a numerical example.

scholarly journals Performance Evaluation of Cloud Data Centers with Batch Task Arrivals

2013 ◽  
pp. 199-223 ◽  
Author(s):  
Hamzeh Khazaei ◽  
Jelena Mišić ◽  
Vojislav B. Mišić
Keyword(s):  
Performance Evaluation ◽  
Queue Length ◽  
Blocking Probability ◽  
General Distribution ◽  
Cloud Data ◽  
Wide Range ◽  
Accurate Performance ◽  
Cloud Data Centers ◽  
Poisson Arrivals

Accurate performance evaluation of cloud computing resources is a necessary prerequisite for ensuring that Quality of Service (QoS) parameters remain within agreed limits. In this chapter, the authors consider cloud centers with Poisson arrivals of batch task requests under total rejection policy; task service times are assumed to follow a general distribution. They describe a new approximate analytical model for performance evaluation of such systems and show that important performance indicators such as mean request response time, waiting time in the queue, queue length, blocking probability, probability of immediate service, and probability distribution of the number of tasks in the system can be obtained in a wide range of input parameters.

scholarly journals Queuing System with Unreliable Servers and Inhomogeneous Intensities for Analyzing the Impact of Non-Stationarity to Performance Measures of Wireless Network under Licensed Shared Access

Mathematics ◽  
2020 ◽  
Vol 8 (5) ◽  
pp. 800 ◽  
Author(s):  
Ekaterina Markova ◽  
Yacov Satin ◽  
Irina Kochetkova ◽  
Alexander Zeifman ◽  
Anna Sinitcina
Keyword(s):  
Performance Measures ◽  
Blocking Probability ◽  
Radio Resource Management ◽  
Queuing System ◽  
Finite Buffer ◽  
Data Traffic ◽  
Multiservice Networks ◽  
Limited Frequency ◽  
The Impact

Given the limited frequency band resources and increasing volume of data traffic in modern multiservice networks, finding new and more efficient radio resource management (RRM) mechanisms is becoming indispensable. One of the implemented technologies to solve this problem is the licensed shared access (LSA) technology. LSA allows the spectrum that has been licensed to an owner, who has absolute priority on its utilization, to be used by other participants (i.e., tenants). Owner priority impacts negatively on the quality of service (QoS) by reducing the data bit rate and interrupting user services. In this paper, we propose a wireless multiservice network scheme model described as a queuing system with unreliable servers and a finite buffer within the LSA framework. The aim of this work is to analyze main system performance measures: blocking probability, average number of requests in queue, and average queue length depending on LSA frequencies’ availability.

Throughput maximization in a loss queueing system with heterogeneous servers

1990 ◽  
Vol 27 (03) ◽  
pp. 693-700 ◽  
Author(s):  
Matthew J. Sobel
Keyword(s):  
Queueing System ◽  
Blocking Probability ◽  
Cost Structure ◽  
Throughput Maximization ◽  
Queueing Model ◽  
Heterogeneous Servers ◽  
Waiting Room ◽  
Discounted Cost ◽  
Long Run ◽  
Poisson Arrivals

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

scholarly journals On optimal stochastic jumps in multi server queue with impatient customers via stochastic control

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ali Delavarkhalafi
Keyword(s):  
Optimal Control ◽  
Complete Information ◽  
Queuing System ◽  
Arrival Process ◽  
Impatient Customers ◽  
Time Intervals ◽  
Poisson Arrival ◽  
Server Queue ◽  
Multi Server ◽  
Request Service

<p style='text-indent:20px;'>In this paper, a queuing system as multi server queue, in which customers have a deadline and they request service from a random number of identical severs, is considered. Indeed there are stochastic jumps, in which the time intervals between successive jumps are independent and exponentially distributed. These jumps will be occurred due to a new arrival or situation change of servers. Therefore the queuing system can be controlled by restricting arrivals as well as rate of service for obtaining optimal stochastic jumps. Our model consists of a single queue with infinity capacity and multi server for a Poisson arrival process. This processes contains deterministic rate <inline-formula><tex-math id="M1">\begin{document}$ \lambda(t) $\end{document}</tex-math></inline-formula> and exponential service processes with <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> rate. In this case relevant customers have exponential deadlines until beginning of their service. Our contribution is to extend the Ittimakin and Kao's results to queueing system with impatient customers. We also formulate the aforementioned problem with complete information as a stochastic optimal control. This optimal control law is found through dynamic programming.</p>

Multi server queuing system with crashes and alternative repair strategies

2021 ◽  
pp. 1-13
Author(s):  
Mamatha Elliriki ◽  
C. S. Reddy ◽  
Krishna Anand ◽  
S. Saritha
Keyword(s):  
Queuing System ◽  
Multi Server
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