Estimating the Parameters of Queuing Systems with Channel Switching

2021 ◽  
Vol 82 (11) ◽  
pp. 1886-1891
Author(s):  
Yu. A. Dorofeyuk ◽  
V. A. Laptin ◽  
A. S. Mandel
Keyword(s):  
Queuing Systems ◽  
Channel Switching

Optimal Control of Queuing Systems with Channel Switching

2021 ◽  
Vol 82 (10) ◽  
pp. 1720-1729
Author(s):  
A. S. Mandel ◽  
V. A. Laptin
Keyword(s):  
Optimal Control ◽  
Queuing Systems ◽  
Channel Switching

scholarly journals DELAYS IN QUEUES OF QUEUING SYSTEMS WITH STATIONARY REQUESTS FLOWS

T-Comm ◽  
2021 ◽  
Vol 15 (2) ◽  
pp. 54-58
Author(s):  
Boris Ya. Likhttsinder ◽  
◽  
Yulia O. Bakai ◽  
Keyword(s):  
Flow Model ◽  
Resource Constraints ◽  
Interval Methods ◽  
Queuing Systems ◽  
Channel Switching ◽  
Time Intervals ◽  
Flow Models ◽  
Average Value ◽  
Multiservice Networks ◽  
Stationary Flows

During all periods of the study of telecommunications systems traffic, the analysis was based on mass service theory. The subjects of the study here are request flows to be processed by some limited performance resources. Resource constraints and the random nature of requests’ receipt lead to refusals in processing or queues. The first works devoted to the analysis of teletraffic belong to A. K. Erlang. Request flows represented flows of requests for connections in networks with channel switching. Since requests were received from a large number of independent users, the flows of such requests could be defined as stationary, ordinary with no effect, or as recurring requests, with an exponential distribution of time intervals between neighboring requests. Connection request flows to a telephone exchange node are a superposition of a large number of low-intensity flows from independent users. Therefore, the fixed Poisson flow model describes the real flows in telephone exchanges with channel switching quite well. Therefore, the stationary Poisson flow model describes real flows in telephone exchanges with channel switching rather well. The emergence of telecommunications networks with packet switching, especially multiservice networks, showed the impossibility of using Poisson flow models for their analysis. The article is devoted to the analysis of delays in queues of queuing systems with correlated stationary flows of general type requests. The traffic of packets in multiservice networks is typically characterized by a high degree of correlation. On the basis of interval methods of analysis, the relations generalizing the Khinchin-Pollaczek formula for the average value of waiting time in queuing systems with flows of the general kind of requests are obtained. The main parameters to be analyzed when outputting the above formulas are time intervals between neighboring requests. It is shown that the values of time delays in queues depend on the dispersion and dispersion index of a random value characterizing the degree of additional maintenance of processed requests.

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.

COMMUNICATION OF COMMON AND MARGINAL CHARACTERISTICS OF CONDITIONS IN A TWO-CHANNEL SYSTEM WITH SIMPLE STREAMLINES OF APPLICATIONS

2017 ◽  
pp. 7-19 ◽  
Author(s):  
Georgiy Aleksandrovich Popov
Keyword(s):  
Operating Systems ◽  
Queue Length ◽  
Recurrence Relations ◽  
Queuing Systems ◽  
Channel System ◽  
Current Period ◽  
Multichannel Systems ◽  
Incoming Call ◽  
Marginal Values ◽  
Time Required

The article deals with a two-channel queuing system with a Poisson incoming call flow, in which the application processing time on each of the devices is different. Such models are used, in particular, when describing the operation of the system for selecting service requests in a number of operating systems. A complex system characteristic was introduced at the time of service endings on at least one of the devices, including the queue length, the remaining service time on the occupied device, and the time since the beginning of the current period of employment. This characteristic determines the state of the system at any time. Recurrence relations are obtained that connect this characteristic with its marginal values when there is no queue in the system. The method of introducing additional events was chosen as one of the main methods for analyzing the model. The relationships presented in this article can be used for analysis of the average characteristics of this system, as well as in the process of its simulation. Summarizing the results of work on multichannel systems with an arbitrary number of servicing devices will significantly reduce the time required for simulating complex systems described by sets of multichannel queuing systems.

scholarly journals Fashion Consumers’ Channel Switching Behavior During the COVID-19: Protection Motivation Theory in the Extended Planned Behavior Framework

2021 ◽  
pp. 0887302X2098652
Author(s):  
Song-yi Youn ◽  
Jung Eun Lee ◽  
Jung Ha-Brookshire
Keyword(s):  
Planned Behavior ◽  
Subjective Norm ◽  
Protection Motivation Theory ◽  
Switching Behavior ◽  
Behavior Control ◽  
Channel Switching ◽  
Perceived Severity ◽  
Response Efficacy ◽  
Perceived Behavior Control ◽  
Perceived Behavior

The purpose of this study is to understand fashion consumers’ channel switching to online stores during the COVID-19. We proposed an extended theory of planned behavior by incorporating protection motivation theory. The results showed that consumer assessments of perceived severity and altruistic fear of COVID-19 and response efficacy and self-efficacy of channel switching increased their beliefs (i.e., attitude, perceived behavior control, subjective norm) and intentions to switch shopping channels to online. We also found that the age (young vs. old) moderated the effects of response efficacy and self-efficacy on perceived behavior control, perceived severity on subjective norm, perceived behavior control on channel switching intentions, and channel switching intention on actual switching behavior. The findings provide fashion retailers and the society with a better understanding about fashion consumers’ shopping channel switching under the pandemic.

An alternative transient solution for semi-Markov queuing systems

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Revaz Kakubava
Keyword(s):  
Queuing System ◽  
Queuing Systems ◽  
Transient Solution ◽  
Methods Of Analysis ◽  
Supplementary Variables ◽  
Probabilistic Argumentation

AbstractBy using a purely probabilistic argumentation, two theorems are proved. They simplify the existing methods of analysis for the {M/G/1} queuing system by means of the supplementary variables method.

Optimal Control of Time-Varying Queuing Systems

1973 ◽  
Vol 19 (11) ◽  
pp. 1249-1256 ◽  
Author(s):  
F. T. Man
Keyword(s):  
Optimal Control ◽  
Time Varying ◽  
Queuing Systems

OPTIMAL CONTROL OF FLEXIBLE SERVERS IN TWO TANDEM QUEUES WITH OPERATING COSTS

2007 ◽  
Vol 22 (1) ◽  
pp. 107-131 ◽  
Author(s):  
Dimitrios G. Pandelis
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Optimal Allocation ◽  
Operating Costs ◽  
Queuing Systems ◽  
Tandem Queues ◽  
Holding Costs ◽  
Flexible Servers ◽  
Tandem Queuing ◽  
Dedicated Servers

We consider two-stage tandem queuing systems with dedicated servers in each station and flexible servers that can serve in both stations. We assume exponential service times, linear holding costs, and operating costs incurred by the servers at rates proportional to their speeds. Under conditions that ensure the optimality of nonidling policies, we show that the optimal allocation of flexible servers is determined by a transition-monotone policy. Moreover, we present conditions under which the optimal policy can be explicitly determined.

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