Quasi-stationary distributions of single-server phase-type queues
Mathematics of Operations Research
Introduction to matrix analysis (2nd ed.)
Introduction to matrix analysis (2nd ed.)
Queueing analysis of polling models: progress in 1990-1994
Frontiers in queueing
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Analysis and Application of Polling Models
Performance Evaluation: Origins and Directions
Sojourn time distributions in the queue defined by a general QBD process
Queueing Systems: Theory and Applications
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Constructive Computation in Stochastic Models with Applications: The RG-Factorizations
Constructive Computation in Stochastic Models with Applications: The RG-Factorizations
Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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We consider a FIFO queue defined by a QBD process. When the number of phases of the QBD process is finite, it has been proved that the stationary distribution of sojourn times in that queue can be represented as a phase-type distribution. In this paper, we extend this result to the case where the number of phases of the QBD process is countably many and obtain several kinds of asymptotic formula for the steady-state tail probability of sojourn times in the queue when the tail probability decays in exact exponential form.