For the queue with deterministic, not necessarily equidistant arrival times and exponential service times and for the dual queue with Poisson arrivals and deterministic but unequal service times we derive some explicit formulas for the distribution of the number of customers served during a busy...

Let (Sn)n[greater-or-equal, slanted]0 be a renewal process with interarrival times X1,X2,... Several results on the behavior of the renewal process up to a given time t0 or up to a given Sn=s are proved. For example, X1 is stochastically dominated by XN(t)+1, and X0=0, X1,...,XN(t)+1 is a...

The problem of selling a commodity optimally at one of n successive time instants leads to the optimal stopping problem for the finite sequence ((n-j)lSj)1[less-than-or-equals, slant]j[less-than-or-equals, slant]n, where Sj=U1 + ... + Uj, U1, U2,... are i.i.d., E(U1) = 0 and E(U21) = 1. The...

For Wald's SPRT of a simple hypothesis against a simple alternative an upper bound for the differences of the error probabilities and their Wiener process approximations is derived. This upper bound only depends on the first three moments of the log-likelihood ratio and is seen to be especially...