2026-06-29T07:22:58Zhttps://docta.ucm.es/rest/oai/request

oai:docta.ucm.es:20.500.14352/336032023-07-14T03:30:19Zcom_20.500.14352_14col_20.500.14352_15

Maximum queue lengths during a fixed time interval in the M/M/c retrial queue Gómez-Corral, Antonio López-García, M. 519.2 Absorbing Markov chain Eigenvalues/eigenvectors Maximum queue length Retrial queue Splitting method Estadística matemática (Matemáticas) 1209 Estadística We are concerned with the problem of characterizing the distribution of the maximum number Z(t(0)) of customers during a fixed time interval [0, t(0)] in the M/M/c retrial queue, which is shown to have a matrix exponential form. We present a simple condition on the service and retrial rates for the matrix exponential solution to be explicit or algorithmically tractable. Our methodology is based on splitting methods and the use of eigen-values and eigenvectors. A particularly appealing feature of our solution is that it allows us to obtain global error control. Specifically, we derive an approximating solution p(x; t(0)) = p(x; t(0); epsilon) verifying [P(Z(t(0)) <= x vertical bar X(0) = (i,j)) - p(x; t(0))] < epsilon uniformly in x >= i + j, for any epsilon > 0 and initial numbers i of busy servers and j of customers in orbit. Government of Spain (Ministry of Economy and Competitiveness) European Commission Depto. de Estadística e Investigación Operativa Fac. de Ciencias Matemáticas TRUE pub 2023-06-19T13:24:53Z 2023-06-19T13:24:53Z 2014 journal article https://hdl.handle.net/20.500.14352/33603 0096-3003 10.1016/j.amc.2014.02.074 eng MTM-2011-23864 BES-2009-018747 restricted access application/pdf Elsevier