Communication: Reply to Fox and Schruben
In the recent issue of Management Science Fox Fox, B. 1978. Estimation and simulation. Management Sci.24 8, April 860--861. expressed doubts about the relevance of steady-state behavior. In a reply Schruben Schruben, L. W. 1978. Reply to Fox. Management Sci.24 8, April 862. disagreed on this point. With Fox he was in favor of publishing failures of variance reduction techniques VRT's. I would like to add the following remarks.
Approximate Transient Analysis of Some Queuing Systems
We propose approximations for the time-dependent queue size distribution Pnt and the mean queue size E[Xt] of an M/M/1 queue. With a Laplace transform-generating function technique, the exact analysis involves the complex root u* inside the unit circle of a certain quadratic. The exact value of u* leads to transforms that, when inverted, yield rather complicated expressions for Pnt and E[Xt]. We discuss three iterative procedures that give successive rational approximations for u*. These approximations yield, for the queue size distribution and the mean queue size, approximate transforms that are rational and easier to invert. We obtain sharp bounds for Pnt and E[Xt] for a wide range of parameter values by performing the second iteration and combining the approximate results given by the iterative procedures. 
 
The methods can be applied to approximate the behavior of more complicated queues. Applications to the M/M/2 queue and the M/Ep/1 queue are discussed briefly.
Cross talk between redox signalling and metabolic activity of osteoblasts and fibroblasts in the presence of hydroxyapatite-based biomaterials influences bone regeneration
Regeneration of bone tissue defects that result from metabolic disorders, including periodontal diseases, can be supported by biomaterials based on hydroxyapatite. Despite of good biocompatibility of biomaterials they can cause oxidative stress and inflammatory processes as a result of mechanical interaction with surrounding tissues. Because osteoblasts are responsible for bone regeneration process in which gingival fibroblasts may also participate, the aim of the work was to investigate the influence of hydroxyapatite-based biomaterials (allogeneic and xenogeneic) and biomaterials combined with enamel matrix derivative (Emdogain) on osteoblast and fibroblast redox balance in the context of osteoblast proliferation and differentiation.
The results showed that examined substitutes were not cytotoxic in vitro, but affected redox balance of osteoblasts and fibroblasts (ROS level increase and GSH level decrease) which led to oxidative stress (MDA and protein carbonyl groups level increase) resulting in an increase of the Nrf2 and NFκB expression. The consequence of these changes was partial inhibition of proliferation and osteoblast differentiation. Emdogain alone and combined with biomaterials decreased ROS generation and increased GSH level in both osteoblasts and fibroblasts leading to reduction of transcription factors expression especially proinflammatory NFκB, which promoted osteoblast differentiation and mineralization process.