ABSTRACT
Keywords and phrases Singlc server queue, busy period, dctcrrninistic interarrival or service times, bulk queuc, first crossing problem, compound Poisson process, generalized Appell polynomials, generalizctl Abel-GontcharoR polynorrlials
10.1 Introduction 111 queueing tllcwry, the analysis of busy periods is an important problem, from s Ihcoretical point of view and for practical applications. The literature on this subject, however, is relatively little ;tE)untlant, cspccially in view of tllc largc r~lurlbcr of papers on the a~ymptot~ic behmior
of various queueirig systems. A nurnl)er of results can be found in the books by T a k k s (1962)) Rhat (1968) and Prabhu (1998), for instar~ce.
