Processor-sharing queues: some progress in analysis
Queueing Systems: Theory and Applications
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Waiting Time Distributions for Processor-Sharing Systems
Journal of the ACM (JACM)
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Tails of waiting times and their bounds
Queueing Systems: Theory and Applications
Sojourn time asymptotics in the M/G/1 processor sharing queue
Queueing Systems: Theory and Applications
Large Deviation Analysis of Subexponential Waiting Times in a Processor-Sharing Queue
Mathematics of Operations Research
Sojourn Times In The M/G/1 FB Queue With Light-Tailed Service Times
Probability in the Engineering and Informational Sciences
Large deviations of sojourn times in processor sharing queues
Queueing Systems: Theory and Applications
Sojourn time asymptotics in processor-sharing queues
Queueing Systems: Theory and Applications
A large-deviations analysis of the GI/GI/1 SRPT queue
Queueing Systems: Theory and Applications
Sojourn Time Tails In The M/D/1 Processor Sharing Queue
Probability in the Engineering and Informational Sciences
The equivalence between processor sharing and service in random order
Operations Research Letters
ACM SIGMETRICS Performance Evaluation Review
Queueing Systems: Theory and Applications
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We investigate the tail behavior of the sojourn-time distribution for a request of a given length in an M/G/1 Processor-Sharing (PS) queue. An exponential asymptote is proven for general service times in two special cases: when the traffic load is sufficiently high and when the request length is sufficiently small. Furthermore, using the branching process technique we derive exact asymptotics of exponential type for the sojourn time in the M/M/1 queue. We obtain an equation for the asymptotic decay rate and an exact expression for the asymptotic constant. The decay rate is studied in detail and is compared to other service disciplines. Finally, using numerical methods, we investigate the accuracy of the exponential asymptote.