A BIRTH AND DEATH PROCESS-RELATED TO THE ROGERS-RAMANUJANCONTINUED FRACTION

Time-dependent system size probabilities of a birth and death process related to the Rogers-Ramanujan continued fraction are obtained. The r ange for the parameter in this continued fraction is obtained to ensur e the positivity of the recursively defined birth and death rates. The general behavior of the birth and death rates is described and the as ymptotic behavior of the transition probabilities and the (quasi)-stat ionary distribution is determined. For the transient case the birth an d death process can be seen as a model in queuing theory where the len gth of the queue encourages customers to join the queue (the more the merrier). (C) 1998 Academic Press.