Customers arrive at a single-server queue in accordance witha
poisson process having rate
. however, an arrival that finds n customers already in the system
willonly join the system with probability 1 / (n + 1). that is, withprobability
n / ( n +1) such an arrival
will not join the system. show that thelimiting distributioni of
the number of customers in the system ispoisson with mean
.