Understanding interarrival and interdeparture time statistics from interactions in queuing 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.

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

VESTNIK OF ASTRAKHAN STATE TECHNICAL UNIVERSITY SERIES MANAGEMENT COMPUTER SCIENCE AND INFORMATICS ◽

10.24143/2072-9502-2017-3-7-19 ◽

2017 ◽

pp. 7-19 ◽

Cited By ~ 1

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.

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Optimal Policy in Single-Server Multi-Class Queuing Systems with Abandonment

SSRN Electronic Journal ◽

10.2139/ssrn.3453227 ◽

2019 ◽

Author(s):

Sina Ansari ◽

Laurens Debo ◽

Seyed Iravani

Keyword(s):

Optimal Policy ◽

Single Server ◽

Queuing Systems

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An alternative transient solution for semi-Markov queuing systems

Georgian Mathematical Journal ◽

10.1515/gmj-2020-2050 ◽

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.

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Optimal Control of Time-Varying Queuing Systems

Management Science ◽

10.1287/mnsc.19.11.1249 ◽

1973 ◽

Vol 19 (11) ◽

pp. 1249-1256 ◽

Cited By ~ 7

Author(s):

F. T. Man

Keyword(s):

Optimal Control ◽

Time Varying ◽

Queuing Systems

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

Probability in the Engineering and Informational Sciences ◽

10.1017/s0269964808000077 ◽

2007 ◽

Vol 22 (1) ◽

pp. 107-131 ◽

Cited By ~ 8

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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