On a preemptive Markovian queue with multiple servers and two priority classes
Mathematics of Operations Research
Asymptotics for M/G/1 low-priority waiting-time tail probabilities
Queueing Systems: Theory and Applications
Tail Asymptotics for HOL Priority Queues Handling a Large Number of Independent Stationary Sources
Queueing Systems: Theory and Applications
A Markov Renewal Approach to M/G/1 Type Queues with Countably Many Background States
Queueing Systems: Theory and Applications
A matrix-analytic solution for the DBMAP/PH/1 priority queue
Queueing Systems: Theory and Applications
Priority queueing systems: from probability generating functions to tail probabilities
Queueing Systems: Theory and Applications
Processor sharing for two queues with vastly different rates
Queueing Systems: Theory and Applications
Kernel method and linear recurrence system
Journal of Computational and Applied Mathematics
Classifying lattice walks restricted to the quarter plane
Journal of Combinatorial Theory Series A
Asymptotic analysis of Lévy-driven tandem queues
Queueing Systems: Theory and Applications
Tail Decay Rates in Double QBD Processes and Related Reflected Random Walks
Mathematics of Operations Research
Exact tail asymptotics in a priority queue--characterizations of the non-preemptive model
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
Analysis of exact tail asymptotics for singular random walks in the quarter plane
Queueing Systems: Theory and Applications
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In this paper, we consider the classical preemptive priority queueing system with two classes of independent Poisson customers and a single exponential server serving the two classes of customers at possibly different rates. For this system, we carry out a detailed analysis on exact tail asymptotics for the joint stationary distribution of the queue length of the two classes of customers, for the two marginal distributions and for the distribution of the total number of customers in the system, respectively. A complete characterization of the regions of system parameters for exact tail asymptotics is obtained through analysis of generating functions. This characterization has never before been completed. It is interesting to note that the exact tail asymptotics along the high-priority queue direction is of a new form that does not fall within the three types of exact tail asymptotics characterized by various methods for this type of two-dimensional system reported in the literature. We expect that the method employed in this paper can also be applied to the exact tail asymptotic analysis for the non-preemptive priority queueing model, among other possibilities.