RT Journal Article
T1 Maximum queue lengths during a fixed time interval in the M/M/c retrial queue
A1 Gómez-Corral, Antonio
A1 López-García, M.
AB 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.
PB Elsevier
SN 0096-3003
YR 2014
FD 2014
LK https://hdl.handle.net/20.500.14352/33603
UL https://hdl.handle.net/20.500.14352/33603
LA eng
NO Government of Spain (Ministry of Economy and Competitiveness)
NO European Commission
DS Docta Complutense
RD 7 dic 2023