Rapid Technique for the Calculation of Loss Probabilities in Queueing Systems

2018 ◽  
Author(s):  
Vladimir N. Zadorozhnyi ◽  
Tatiana R. Zakharenkova ◽  
Michele Pagano
Keyword(s):  
Queueing Systems ◽  
Rapid Technique ◽  
Loss Probabilities

On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions

1983 ◽  
Vol 20 (04) ◽  
pp. 860-871 ◽  
Author(s):  
Dieter König ◽  
Masakiyo Miyazawa ◽  
Volker Schmidt
Keyword(s):  
Stationary State ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Loss Probabilities ◽  
Poisson Arrivals ◽  
Number Of Customers

For several queueing systems, sufficient conditions are given ensuring that from the coincidence of some time-stationary and customer-stationary characteristics of the number of customers in the system such as idle or loss probabilities it follows that the arrival process is Poisson.

scholarly journals FINITE TWO LAYERED QUEUEING SYSTEMS

2016 ◽  
Vol 30 (3) ◽  
pp. 492-513 ◽  
Author(s):  
Efrat Perel ◽  
Uri Yechiali
Keyword(s):  
Waiting Times ◽  
Queueing Systems ◽  
Service Rate ◽  
Dimensional System ◽  
Single Server ◽  
Matrix Analytic Methods ◽  
Birth And Death Processes ◽  
Operating Modes ◽  
Loss Probabilities ◽  
Steady State Probabilities

We study layered queueing systems comprised two interlacing finite M/M/• type queues, where users of each layer are the servers of the other layer. Examples can be found in file sharing programs, SETI@home project, etc. Let Li denote the number of users in layer i, i=1, 2. We consider the following operating modes: (i) All users present in layer i join forces together to form a single server for the users in layer j (j≠i), with overall service rate μjLi (that changes dynamically as a function of the state of layer i). (ii) Each of the users present in layer i individually acts as a server for the users in layer j, with service rate μj.These operating modes lead to three different models which we analyze by formulating them as finite level-dependent quasi birth-and-death processes. We derive a procedure based on Matrix Analytic methods to derive the steady state probabilities of the two dimensional system state. Numerical examples, including mean queue sizes, mean waiting times, covariances, and loss probabilities, are presented. The models are compared and their differences are discussed.

On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions

1983 ◽  
Vol 20 (4) ◽  
pp. 860-871 ◽  
Author(s):  
Dieter König ◽  
Masakiyo Miyazawa ◽  
Volker Schmidt
Keyword(s):  
Stationary State ◽  
Queueing Systems ◽  
Sufficient Conditions ◽  
Arrival Process ◽  
Loss Probabilities ◽  
Poisson Arrivals ◽  
Number Of Customers

For several queueing systems, sufficient conditions are given ensuring that from the coincidence of some time-stationary and customer-stationary characteristics of the number of customers in the system such as idle or loss probabilities it follows that the arrival process is Poisson.

OPTIMIZATION OF MARKOV SYSTEMS OF QUEUEING WITH WAITING TIME IN THE MATLAB SYSTEM

2017 ◽  
pp. 39-47
Author(s):  
Viktor Afonin ◽  
Vladimir Valer'evich Nikulin
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Random Variable ◽  
Model Systems ◽  
Queuing Systems ◽  
Input Flow ◽  
Continuous Random Variable ◽  
Input Stream ◽  
Time Intervals ◽  
Markov Systems

The article focuses on attempt to optimize two well-known Markov systems of queueing: a multichannel queueing system with finite storage, and a multichannel queueing system with limited queue time. In the Markov queuing systems, the intensity of the input stream of requests (requirements, calls, customers, demands) is subject to the Poisson law of the probability distribution of the number of applications in the stream; the intensity of service, as well as the intensity of leaving the application queue is subject to exponential distribution. In a Poisson flow, the time intervals between requirements are subject to the exponential law of a continuous random variable. In the context of Markov queueing systems, there have been obtained significant results, which are expressed in the form of analytical dependencies. These dependencies are used for setting up and numerical solution of the problem stated. The probability of failure in service is taken as a task function; it should be minimized and depends on the intensity of input flow of requests, on the intensity of service, and on the intensity of requests leaving the queue. This, in turn, allows to calculate the maximum relative throughput of a given queuing system. The mentioned algorithm was realized in MATLAB system. The results obtained in the form of descriptive algorithms can be used for testing queueing model systems during peak (unchanged) loads.

Cooperation in Queueing Systems

2020 ◽  
Author(s):  
Yaroslav Rosokha ◽  
Chen Wei
Keyword(s):  
Queueing Systems
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