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
.