Transient analysis of a two-heterogeneous servers queue with system disaster, server repair and customers’ impatience

R. Sudhesh (), P. Savitha () and S. Dharmaraja ()
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R. Sudhesh: Bharathidasan Institute of Technology (BIT) Campus, Anna University
P. Savitha: Bharathidasan Institute of Technology (BIT) Campus, Anna University
S. Dharmaraja: Indian Institute of Technology Delhi

TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, 2017, vol. 25, issue 1, No 12, 179-205

Abstract: Abstract A two-heterogeneous servers queue with system disaster, server failure and repair is considered. In addition, the customers become impatient when the system is down. The customers arrive according to a Poisson process and service time follows exponential distribution. Each customer requires exactly one server for its service and the customers select the servers on fastest server first basis. Explicit expressions are derived for the time-dependent system size probabilities in terms of the modified Bessel function, by employing the generating function along with continued fraction and the identity of the confluent hypergeometric function. Further, the steady-state probabilities of the number of customers in the system are deduced and finally some important performance measures are obtained.

Keywords: Heterogeneous servers; System disaster; Server repair; Customers’ impatience; Confluent hypergeometric function; Moments; Steady-state probabilities; Performance measures; 60K25 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s11750-016-0428-x

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