Computing Laplace Transforms for Numerical Inversion Via Continued Fractions
INFORMS Journal on Computing
Analysis of customers' impatience in queues with server vacations
Queueing Systems: Theory and Applications
Queues with system disasters and impatient customers when system is down
Queueing Systems: Theory and Applications
Time-dependent analysis of a single-server retrial queue with state-dependent rates
Operations Research Letters
Time dependent analysis of M/M/1 queue with server vacations and a waiting server
Proceedings of the 6th International Conference on Queueing Theory and Network Applications
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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 驴. 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.