An error bound for a continuous time approximation of a time-sharing queue

Performance characteristics of systems with discrete time are often approximated by similar characteristics of corresponding (in some sense) continuous time systems. Both from practical and theoretical points of view it is very important to estimate an error of such an approximation. In a recent paper N.M. van Dink and P.G. Taylor investigated this problem for the classic time-sharing system and obtained an error bound which is of the same order as the length of time slot. The present paper suggests another approach to the problem based on stochastic orderings. This approach can be applied to a wider class of performance characteristics and the present bound seems to be essentially better.