par Lefèvre, Claude 
;Picard, Philippe
Editeur scientifique Charalambides, C.;Koutras, Markos V.;Balakrishnan, Narayanaswamy
Référence Probability and statistical models with applications, a volume dedicated to C. Cacoullos, Chapman, page (169-183)
Publication Publié, 2000
;Picard, Philippe Editeur scientifique Charalambides, C.;Koutras, Markos V.;Balakrishnan, Narayanaswamy
Référence Probability and statistical models with applications, a volume dedicated to C. Cacoullos, Chapman, page (169-183)
Publication Publié, 2000
Partie d'ouvrage collectif
| Résumé : | The queueing systems considered in this paper are the D g /M (Q) /1 queue with deterministic, not necessarily equidistant, interarrival times, and with exponential service times where customers are served in batches of random size, and its dual the M (Q) /D g /1 queue with Poisson arrival process where customers arrive in batches of random size, and with deterministic, not necessarily equidistant, service times. Our purpose is to determine the exaej: distribution of the statistic N r that represents the number of customers served during some busy period initiated by r customers. The problem is analyzed as the first crossing of a compound Poisson trajectory with a fixed non-linear boundary, upper or lower respectively. For the D g /M (Q) /1 queue, a simple explicit formula is derived for the law of N r that is expressed in terms of a generalization of Appell polynomials. For the M (Q) /D g /1 queue, the law of N r is now written using a generalization of Abel-Gontcharoff polynomials. |
