The unbalance and bounds on the average waiting time for periodic routing to one queue

In this paper we introduce the combinatorial notion of unbalance for a periodic zero-one splitting sequence. Using this unbalance we derive an upper bound for the average expected waiting time of jobs which are routed to one queue according to a periodic zero-one splitting sequence. In the companion paper [16] the upper bound will be extended to the routing to N parallel queues.Acknowledgement.The authors would like to thank Bruno Gaujal for his hospitality during their visits to LORIA, Nancy. During one of the stimulating discussions with him the graph order was found. The authors thank Robert Tijdeman for his helpful comments.