The aim of this paper is to solve the basic stochastic shortest-path problem (SSPP) for Markov chains (MCs) with countable state space and then apply the results to a class of nearest-neighbor MCs on the lattice state space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\mathbb Z \times \mathbb Z $$</EquationSource> </InlineEquation> whose only moves are one step up,...</equationsource></inlineequation>

The aim of this paper is to solve the basic stochastic shortest-path problem (SSPP) for Markov chains (MCs) with countable state space and then apply the results to a class of nearest-neighbor MCs on the lattice state space $$\mathbb Z \times \mathbb Z $$ whose only moves are one step up, down,...

We consider the group testing problem for a finite population of possibly defective items with the objective of sampling a prespecified demanded number of nondefective items at minimum cost.Group testing means that items can be pooled and tested together; if the group comes out clean, all items...

We study several group testing models with and without processing times.The objective is to choose an optimal group size for pooled screening of a contaminated population so as to collect a prespeciffied number of good items from it with minimumtesting expenditures.The tested groups that are...

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...