Asymptotics for M/G/1 low-priority waiting-time tail probabilities
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
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 preemptive model
Queueing Systems: Theory and Applications
Rare event asymptotics for a random walk in the quarter plane
Queueing Systems: Theory and Applications
Tail asymptotics for a generalized two-demand queueing model--a kernel method
Queueing Systems: Theory and Applications
Queueing Systems: Theory and Applications
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This is a companion paper to Li and Zhao (Queueing Syst. 63:355---381, 2009) recently published in Queueing Systems, in which the classical preemptive priority queueing system was considered. In the current paper we consider the classical non-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. A complete characterization of the regions of system parameters for exact tail asymptotics is obtained through an analysis of generating functions. This is done for the joint stationary distribution of the queue length of the two classes of customers, for the two marginal distributions and also for the distribution of the total number of customers in the system, respectively. This complete characterization is supplemental to the existing literature, which would be useful to researchers.