Simple spectral representations for the M/M/1 queue
Queueing Systems: Theory and Applications
Decompositions of the M/M/1 transition function
Queueing Systems: Theory and Applications
The Fourier-series method for inverting transforms of probability distributions
Queueing Systems: Theory and Applications - Numerical computations in queues
Computing distributions and moments in polling models by numerical transform inversion
Performance Evaluation
Numerical inversion of multidimensional Laplace transforms by the Laguerre method
Performance Evaluation
Exponents for the tails of distributions in some polling models
Queueing Systems: Theory and Applications
Limits and approximations for the M/G/1 LIFO waiting-time distribution
Operations Research Letters
Resource management in wide-area ATM networks using effective bandwidths
IEEE Journal on Selected Areas in Communications
Effective bandwidth in high-speed digital networks
IEEE Journal on Selected Areas in Communications
Tails of waiting times and their bounds
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Tail probabilities of low-priority waiting times and queue lengths in {MAP}/{GI}/1 queues
Queueing Systems: Theory and Applications
The impact of a heavy-tailed service-time distribution upon the M/GI/s waiting-time distribution
Queueing Systems: Theory and Applications
Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers
Queueing Systems: Theory and Applications
Heavy Tails: The Effect of the Service Discipline
TOOLS '02 Proceedings of the 12th International Conference on Computer Performance Evaluation, Modelling Techniques and Tools
The impact of the service discipline on delay asymptotics
Performance Evaluation - Modelling techniques and tools for computer performance evaluation
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
A Tandem Queue With LÉVY Input: A New Representation Of The Downstream Queue Length
Probability in the Engineering and Informational Sciences
Priority queueing systems: from probability generating functions to tail probabilities
Queueing Systems: Theory and Applications
Tail behavior of conditional sojourn times in Processor-Sharing queues
Queueing Systems: Theory and Applications
A Unified Framework for Numerically Inverting Laplace Transforms
INFORMS Journal on Computing
The last departure time from an Mt/G/∞ queue with a terminating arrival process
Queueing Systems: Theory and Applications
On asymptotics of the emptiness probability in the M/GI/1 queue
Automation and Remote Control
Asymptotic analysis of Lévy-driven tandem queues
Queueing Systems: Theory and Applications
On a generic class of two-node queueing systems
Queueing Systems: Theory and Applications
Tail asymptotics for a Lévy-driven tandem queue with an intermediate input
Queueing Systems: Theory and Applications
Exact tail asymptotics in a priority queue--characterizations of the preemptive model
Queueing Systems: Theory and Applications
Simulation-based computation of the workload correlation function in a Lévy-driven queue
Winter Simulation Conference
Performance analysis of priority queueing systems in discrete time
Network performance engineering
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Geometric tail of queue length of low-priority customers in a nonpreemptive priority MAP/PH/1 queue
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
The impact of buffer finiteness on the loss rate in a priority queueing system
EPEW'06 Proceedings of the Third European conference on Formal Methods and Stochastic Models for Performance Evaluation
Analysis and control of correlated web server queues
Computer Communications
Analysis of exact tail asymptotics for singular random walks in the quarter plane
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
Hi-index | 0.00 |
We consider the classical M/G/1 queue with two priority classes and the nonpreemptive and preemptive-resume disciplines. We show that the low-priority steady-state waiting-time can be expressed as a geometric random sum of i.i.d. random variables, just like the M/G/1 FIFO waiting-time distribution. We exploit this structures to determine the asymptotic behavior of the tail probabilities. Unlike the FIFO case, there is routinely a region of the parameters such that the tail probabilities have non-exponential asymptotics. This phenomenon even occurs when both service-time distributions are exponential. When non-exponential asymptotics holds, the asymptotic form tends to be determined by the non-exponential asymptotics for the high-priority busy-period distribution. We obtain asymptotic expansions for the low-priority waiting-time distribution by obtaining an asymptotic expansion for the busy-period transform from Kendall’s functional equation. We identify the boundary between the exponential and non-exponential asymptotic regions. For the special cases of an exponential high-priority service-time distribution and of common general service-time distributions, we obtain convenient explicit forms for the low-priority waiting-time transform. We also establish asymptotic results for cases with long-tail service-time distributions. As with FIFO, the exponential asymptotics tend to provide excellent approximations, while the non-exponential asymptotics do not, but the asymptotic relations indicate the general form. In all cases, exact results can be obtained by numerically inverting the waiting-time transform.