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

*(English)*Zbl 1364.60124Summary: 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.

##### MSC:

60K25 | Queueing theory (aspects of probability theory) |

90B22 | Queues and service in operations research |

##### Keywords:

queueing system; heterogeneous servers; system disaster; confluent hypergeometric function; steady-state probabilities; performance measures
Full Text:
DOI

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