caa a22 4500 445840021 CHVBK 20180317145341.0 cr unu---uuuuu 170323e20111001xx s 000 0 eng 10.1007/s00186-011-0362-5 doi (NATIONALLICENCE)springer-10.1007/s00186-011-0362-5 Stability analysis of parallel server systems under longest queue first [Elektronische Daten] [Golshid Baharian, Tolga Tezcan] We consider the stability of parallel server systems under the longest queue first (LQF) rule. We show that when the underlying graph of a parallel server system is a tree, the standard nominal traffic condition is sufficient for the stability of that system under LQF when interarrival and service times have general distributions. Then we consider a special parallel server system, which is known as the X-model, whose underlying graph is not a tree. We provide additional "drift” conditions for the stability and transience of these queueing systems with exponential interarrival and service times. Drift conditions depend in general on the stationary distribution of an induced Markov chain that is derived from the underlying queueing system. We illustrate our results with examples and simulation experiments. We also demonstrate that the stability of the LQF depends on the tie-breaking rule used and that it can be unstable even under arbitrary low loads. Springer-Verlag, 2011 Stability nationallicence Longest queue first nationallicence Parallel server systems nationallicence Fluid model nationallicence Baharian Golshid Industrial and Enterprise Systems Eng., University of Illinois at Urbana-Champaign, Urbana, IL, USA aut Tezcan Tolga Simon Graduate School of Business, University of Rochester, Rochester, NY, USA aut Mathematical Methods of Operations Research Springer-Verlag 74/2(2011-10-01), 257-279 1432-2994 74:2<257 2011 74 186 https://doi.org/10.1007/s00186-011-0362-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-011-0362-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Baharian Golshid Industrial and Enterprise Systems Eng., University of Illinois at Urbana-Champaign, Urbana, IL, USA aut NATIONALLICENCE 700 1- Tezcan Tolga Simon Graduate School of Business, University of Rochester, Rochester, NY, USA aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 74/2(2011-10-01), 257-279 1432-2994 74:2<257 2011 74 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer