Cut-through switching, pipelining, and scheduling for network evacuation

A general model of a virtual circuit network consisting of a number of servers and a number of traffic classes is considered. A traffic class is identified by the sequence of servers that should be visited and the corresponding service rates before a message (customer) of the class leaves the network. The following cases are distinguished: (1) the messages need nonpreemptive service; (2) the service of a message can be preempted at any time; (3) pipelining of the service in a sequence of servers is allowed; and (4) pipelining is not allowed. All of these cases arise in different transmission switching techniques and scheduling schemes. A fluid model that emerges when both preemption and pipelining are allowed is considered. Scheduling schemes in the fluid model are compared with corresponding ones in the network with nonpreemptive service and no pipelining. The problem of evacuating the network from an initial backlog without further arrival is identified in the fluid model. Based on that, a policy with nearly optimal evacuation time is identified for the store-and-forward case. Finally, scheduling with deadlines is considered and it is shown that in the fluid model, the evacuation problem is equivalent to a linear programming problem. The evacuation times under different work-conserving policies are considered in specific examples.