ANALYSIS OF M/G/1 QUEUEING MODEL WITH STATE DEPENDENT ARRIVAL AND VACATION

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SINGH CHARAN JEET; JAIN MADHU; KUMAR BINAY

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Journal Paper

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Journal: JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL Year:2012 | Volume:8 | Issue:8 Page(s): 1-8

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Information Journal Paper

Title

ANALYSIS OF M/G/1 QUEUEING MODEL WITH STATE DEPENDENT ARRIVAL AND VACATION

Author(s)

SINGH CHARAN JEET | JAIN MADHU | KUMAR BINAY | Issue Writer Certificate

Keywords

STATE DEPENDENT

QUEUE

ARBITRARY SERVICE TIME

VACATION

SUPPLEMENTARY VARIABLE

AVERAGE QUEUE LENGTH

Abstract

This investigation deals with single server QUEUEing system wherein the arrival of the units follow Poisson process with varying arrival rates in different states and the service time of the units is arbitrary (general) distributed. The server may take a VACATION of a fixed duration or may continue to be available in the system for next service. Using the probability argument, we construct the set of steady state equations by introducing the SUPPLEMENTARY VARIABLE corresponding to elapsed service time. Then, we obtain the probability generating function of the units present in the system. Various performance indices, such as expected number of units in the QUEUE and in the system, average waiting time, etc., are obtained explicitly.Some special cases are also deduced by setting the appropriate parameter values. The numerical illustrations are provided to carry out the sensitivity analysis in order to explore the effect of different parameters on the system performance measures.

Cites

COMPARATIVE ANALYSIS OF PROFIT BETWEEN THREE DISSIMILAR REPAIRABLE REDUNDANT SYSTEMS USING SUPPORTING EXTERNAL DEVICE FOR OPERATION

References

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APA: Copy

SINGH, CHARAN JEET, JAIN, MADHU, & KUMAR, BINAY. (2012). ANALYSIS OF M/G/1 QUEUEING MODEL WITH STATE DEPENDENT ARRIVAL AND VACATION. JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL, 8(8), 1-8. SID. https://sid.ir/paper/309931/en

Vancouver: Copy

SINGH CHARAN JEET, JAIN MADHU, KUMAR BINAY. ANALYSIS OF M/G/1 QUEUEING MODEL WITH STATE DEPENDENT ARRIVAL AND VACATION. JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL[Internet]. 2012;8(8):1-8. Available from: https://sid.ir/paper/309931/en

IEEE: Copy

CHARAN JEET SINGH, MADHU JAIN, and BINAY KUMAR, “ANALYSIS OF M/G/1 QUEUEING MODEL WITH STATE DEPENDENT ARRIVAL AND VACATION,” JOURNAL OF INDUSTRIAL ENGINEERING INTERNATIONAL, vol. 8, no. 8, pp. 1–8, 2012, [Online]. Available: https://sid.ir/paper/309931/en

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