We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload $$a\in (0,1)$$ . The result is...

We derive the stationary distribution of the regenerative process W(t), t ≥ 0, whose cycles behave like an M / G / 1 workload process terminating at the end of its first busy period or when it reaches or exceeds level 1, and restarting with some fixed workload <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$a\in (0,1)$$</EquationSource> </InlineEquation>. The result is...</equationsource></inlineequation>

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...

Let (X0,j)j [greater-or-equal, slanted] 1 and (X1,j)j [greater-or-equal, slanted] 1 be two independent sequences of independent nonnegative random variables and let (S0,n)n [greater-or-equal, slanted] 1 and (S1,n)n [greater-or-equal, slanted] 1 be the corresponding renewal processes. For any...

It is a well-known result (which can be traced back to Gauss) that the only translation family of probability densities on for which the arithmetic mean is a maximum likelihood estimate of the translation parameter originates from the normal density. We generalize this characterization of the...

A classic result in probability theory states that two independent real-valued random variables having independent sum and difference are either constant or normally distributed with the same variance. In this article conditions are round on independent random variables X and Y taking values in...