2021/04/16 by Ioannis Dimitriou, Dimitriou, Ioannis
Business, Management and Accounting · Social Sciences · #60K25 #68M20 #90B22 #Advanced Queuing Theory Analysis #FOS: Computer and information sciences #FOS: Mathematics #Performance (cs.PF) #Probability (math.PR) #Transportation Planning and Optimization
paper · pdf · doi:10.48550/arxiv.2104.08037
openalex publication_date 2021/04/16 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
We introduce the \generalized join the shortest queue model with\nretrials and two infinite capacity orbit queues. Three independent Poisson\nstreams of jobs, namely a \smart, and two \dedicated streams,\nflow into a single server system, which can hold at most one job. Arriving jobs\nthat find the server occupied are routed to the orbits as follows: Blocked jobs\nfrom the \smart stream are routed to the shortest orbit queue, and in\ncase of a tie, they choose an orbit randomly. Blocked jobs from the\n\dedicated streams are routed directly to their orbits. Orbiting jobs\nretry to connect with the server at different retrial rates, i.e.,\nheterogeneous orbit queues. Applications of such a system are found in the\nmodelling of wireless cooperative networks. We are interested in the asymptotic\nbehaviour of the stationary distribution of this model, provided that the\nsystem is stable. More precisely, we investigate the conditions under which the\ntail asymptotic of the minimum orbit queue length is exactly geometric.\nMoreover, we apply a heuristic asymptotic approach to obtain approximations of\nthe steady-state joint orbit queue-length distribution. Useful numerical\nexamples are presented, and shown that the results obtained through the\nasymptotic analysis and the heuristic approach agreed.\n