2018/06/06 by Ioannis Dimitriou, Dimitriou, Ioannis
Business, Management and Accounting · Engineering · #30B10 #60G50 #60K25 #Advanced Queuing Theory Analysis #Advanced Wireless Network Optimization #FOS: Mathematics #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1806.02033
openalex publication_date 2018/06/06 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
We provide power series approximations for a structured batch arrival single\nserver retrial system with two infinite capacity weighted fair orbit queues,\ni.e., the re-transmission rate of an orbit depends on the state of the other\norbit queue. We consider both exponential and arbitrary distributed service\ntimes. In both cases we obtain power series expansions of the generating\nfunctions of the stationary joint orbit queue-length distributions, and provide\na recursive approach to calculate their coefficients. We also show how to\nobtain the generating function of the stationary joint orbit queue-length\ndistribution with the aid of a Riemann boundary value problem. Power series\napproximations are also provided for the model with two independent Poisson\nstreams of jobs with single arrivals. Numerical illustrations are performed and\nshow the accuracy of our approach.\n