Analysis of N-policy queues with disastrous breakdown

R. Sudhesh (), R. Sebasthi Priya () and R. B. Lenin ()
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R. Sudhesh: Bharathidasan Institute of Technology (BIT) Campus, Anna University
R. Sebasthi Priya: Bharathidasan Institute of Technology (BIT) Campus, Anna University
R. B. Lenin: University of Central Arkansas

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2016, vol. 24, issue 3, No 5, 612-634

Abstract: Abstract In the area of optimal design and control of queues, the N-policy has received great attention. A single server queueing system with system disaster is considered where the server waits till N customers accumulate in the queue and upon the arrival of Nth customer the server begins to serve the customers until the system becomes idle or the occurrence of disaster whichever happens earlier. The system size probabilities in transient state are obtained in closed form using generating functions and steady-state system size probabilities are derived in closed form using generating functions and continued fractions. Further, the mean and variance for the number of customers in the system are derived for both transient and steady states and these results are deduced for the specific models. Time-dependent busy period distribution is also obtained. Numerical illustrations are also shown to visualize the system effect.

Keywords: System size probabilities; Transient and steady state; Generating functions; Modified Bessel functions; Chebyshev polynomials; Disaster; Mean and variance; Busy period; 60K25 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11750-016-0411-6

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