Suppose customers aver fractionp should be allocqted to a single server queueing system by splitting a given inpvt stream, In this paper we first show that the regular splitting rule, proposed by Hajek [l], minimizes the waiting time of a reuted customeT ln the sense of convex stochastic ordering. However this arrival strearn of routed customers is not in general a renewal process, so it is difficult to eyaluate characteristics of the waiting time, Then we give upper and lower bounds foT the

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... ting time distribution by using approximated renewal sequences. At last an application of the above evaluating methocl to a simple network queueing system wil1 be dernonstrated, The OpeiationsReseaich Society of Japan