Analysis of input control based on discrete monitoring in mixed input queueing model

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Abstract

This paper analyzes input control with discrete monitoring in a queueing system involving two input systems. One stream with Poisson arrivals (Poisson stream) can enter the system when waiting room is not full. For the other stream with arrival of general distribution (GI stream), entry into the system is controlled as follows. The system is monitored at Poisson epoch, and when the number of calls in the system at the beginning of each interval is beyond the threshold, the arriving calls are regulated and lost during that interval. The holding time for both of the streams obeys an identical exponential distribution. The model is analyzed using piecewise Markov process theory and the stationary state probabilities at GI call arrival speech and Poisson call arrival epoch are obtained. Next, using these probabilities, regulation probability, regulation action frequency, individual loss probability, and mean waiting time are evaluated. By some numerical examples, this input control is compared with no control and input control with continuous monitoring. As a result, the following are revealed: (i) Under this control, the loss probability for Poisson stream and its mean waiting time are reduced compared with no control case; (ii) Regulation action frequency of this control is far smaller than that of the continuous monitoring control and is little affected by the Inter‐arrival time distribution of GI call.

Original languageEnglish
Pages (from-to)57-65
Number of pages9
JournalElectronics and Communications in Japan (Part I: Communications)
Volume68
Issue number12
DOIs
Publication statusPublished - Jan 1 1985

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Monitoring
Markov processes

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Electrical and Electronic Engineering

Cite this

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title = "Analysis of input control based on discrete monitoring in mixed input queueing model",
abstract = "This paper analyzes input control with discrete monitoring in a queueing system involving two input systems. One stream with Poisson arrivals (Poisson stream) can enter the system when waiting room is not full. For the other stream with arrival of general distribution (GI stream), entry into the system is controlled as follows. The system is monitored at Poisson epoch, and when the number of calls in the system at the beginning of each interval is beyond the threshold, the arriving calls are regulated and lost during that interval. The holding time for both of the streams obeys an identical exponential distribution. The model is analyzed using piecewise Markov process theory and the stationary state probabilities at GI call arrival speech and Poisson call arrival epoch are obtained. Next, using these probabilities, regulation probability, regulation action frequency, individual loss probability, and mean waiting time are evaluated. By some numerical examples, this input control is compared with no control and input control with continuous monitoring. As a result, the following are revealed: (i) Under this control, the loss probability for Poisson stream and its mean waiting time are reduced compared with no control case; (ii) Regulation action frequency of this control is far smaller than that of the continuous monitoring control and is little affected by the Inter‐arrival time distribution of GI call.",
author = "Akira Fukuda",
year = "1985",
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language = "English",
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journal = "Electronics and Communications in Japan, Part I: Communications (English translation of Denshi Tsushin Gakkai Ronbunshi)",
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N2 - This paper analyzes input control with discrete monitoring in a queueing system involving two input systems. One stream with Poisson arrivals (Poisson stream) can enter the system when waiting room is not full. For the other stream with arrival of general distribution (GI stream), entry into the system is controlled as follows. The system is monitored at Poisson epoch, and when the number of calls in the system at the beginning of each interval is beyond the threshold, the arriving calls are regulated and lost during that interval. The holding time for both of the streams obeys an identical exponential distribution. The model is analyzed using piecewise Markov process theory and the stationary state probabilities at GI call arrival speech and Poisson call arrival epoch are obtained. Next, using these probabilities, regulation probability, regulation action frequency, individual loss probability, and mean waiting time are evaluated. By some numerical examples, this input control is compared with no control and input control with continuous monitoring. As a result, the following are revealed: (i) Under this control, the loss probability for Poisson stream and its mean waiting time are reduced compared with no control case; (ii) Regulation action frequency of this control is far smaller than that of the continuous monitoring control and is little affected by the Inter‐arrival time distribution of GI call.

AB - This paper analyzes input control with discrete monitoring in a queueing system involving two input systems. One stream with Poisson arrivals (Poisson stream) can enter the system when waiting room is not full. For the other stream with arrival of general distribution (GI stream), entry into the system is controlled as follows. The system is monitored at Poisson epoch, and when the number of calls in the system at the beginning of each interval is beyond the threshold, the arriving calls are regulated and lost during that interval. The holding time for both of the streams obeys an identical exponential distribution. The model is analyzed using piecewise Markov process theory and the stationary state probabilities at GI call arrival speech and Poisson call arrival epoch are obtained. Next, using these probabilities, regulation probability, regulation action frequency, individual loss probability, and mean waiting time are evaluated. By some numerical examples, this input control is compared with no control and input control with continuous monitoring. As a result, the following are revealed: (i) Under this control, the loss probability for Poisson stream and its mean waiting time are reduced compared with no control case; (ii) Regulation action frequency of this control is far smaller than that of the continuous monitoring control and is little affected by the Inter‐arrival time distribution of GI call.

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