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

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...

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Bibliographic Details
Published in:TOP 2017-04, Vol.25 (1), p.179-205
Main Authors: Sudhesh, R., Savitha, P., Dharmaraja, S.
Format: Article
Language:English
Subjects:
Business and Management
Economic Theory/Quantitative Economics/Mathematical Methods
Economics
Finance
Hypergeometric functions
Industrial and Production Engineering
Insurance
Management
Operations Research/Decision Theory
Optimization
Original Paper
Statistics for Business
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Summary: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.
ISSN:1134-5764
1863-8279
DOI:10.1007/s11750-016-0428-x