Closed two node priority queueing networks
Exact equilibrium distributions are found for a closed Markov queueing system consisting of two nodes and two priority classes having different service time parameters and a preemptive discipline. Writing the matrix form of the global equilibrium equations reveals symmetries that facilitate a solution. This result is then extended to certain state- dependent cases involving non-preemptive as well as preemptive models. A comparison with the approximate solution by \textit{R. J. T. Morris} [Bell. Syst. Tech. J. 60, 1745-1769 (1981; Zbl 0464.90026)] is undertaken. It is noted that the throughput provided by the approximation yields anomalous results in some regions of service rates. Moreover, throughput for the low priority class is not always improved by increasing the relevant service rate. Finally, it is noted that the exact calculation involves little more computation time than the Morris approximation.
scientific article; zbMATH DE number 4092524
scientific article