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Transient analysis of a queue with system disasters and customer impatience. (English) Zbl 1197.60087
Summary: A single server queue with Poisson arrivals and exponential service times is studied. The system suffers disastrous breakdowns at an exponential rate resulting in the loss of all running and waiting customers. When the system is down, it undergoes a repair mechanism where the repair time follows an exponential distribution. During the repair time, any new arrival is allowed to join the system, but the customers become impatient when the server is not available for a long time. In essence, each customer, upon arrival, activates an individual timer, which again follows an exponential distribution with parameter \(\xi \). If the system is not repaired before the customer’s timer expires, the customer abandons the queue and never returns. The time-dependent system size probabilities are presented using generating functions and continued fractions.

60K25 Queueing theory (aspects of probability theory)
30B70 Continued fractions; complex-analytic aspects
90B22 Queues and service in operations research
Full Text: DOI
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