Asymptotic behaviour of the loss probability of the M/G/1/K and G/M/1/K queues
Queueing Systems: Theory and Applications
Modelling extremal events: for insurance and finance
Modelling extremal events: for insurance and finance
Tail Asymptotics for the Busy Period in the GI/G/1 Queue
Mathematics of Operations Research
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Subexponential loss rates in a GI/GI/1 queue with applications
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
Large Deviations of Square Root Insensitive Random Sums
Mathematics of Operations Research
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
Tail behavior of conditional sojourn times in Processor-Sharing queues
Queueing Systems: Theory and Applications
ACM SIGMETRICS Performance Evaluation Review
Processor sharing: A survey of the mathematical theory
Automation and Remote Control
Asymptotic analysis for loss probability of queues with finite GI/M/1 type structure
Queueing Systems: Theory and Applications
Asymptotic expansions for the conditional sojourn time distribution in the M/M/1-PS queue
Queueing Systems: Theory and Applications
Loss Rates for Lévy Processes with Two Reflecting Barriers
Mathematics of Operations Research
Sojourn time tails in the single server queue with heavy-tailed service times
Queueing Systems: Theory and Applications
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We study the asymptotic behavior of the tail probabilities of the waiting time and the busy period for the $$M/G/1/K$$ queues with subexponential service times under three different service disciplines: FCFS, LCFS, and ROS. Under the FCFS discipline, the result on the waiting time is proved for the more general $$GI/G/1/K$$ queue with subexponential service times and lighter interarrival times. Using the well-known Laplace---Stieltjes transform (LST) expressions for the probability distribution of the busy period of the $$M/G/1/K$$ queue, we decompose the busy period into a sum of a random number of independent random variables. The result is used to obtain the tail asymptotics for the waiting time distributions under the LCFS and ROS disciplines.