Packet arrival scheduling at a exponential server for min-max blocking

Consider a source using a high speed data link to transmit packets to a downstream buffer. It is argued that allocating finite buffer space to each source using the link encourages each source to regulate its packet arrival process to avoid packet blocking downstream. For bursty sources using high speed links, an entire burst might be transmitted to the downstream buffer before any feedback would be received. Regulating the packet transmission process to minimize packet blocking at the downstream link is formulated as a stochastic scheduling problem. For an exponential service facility with a service rate that is a nondecreasing function of queue occupancy, it is found that a type of threshold schedule minimizes the maximum packet blocking probability. Under light loading, these optimal threshold schedules exhibit a form of burstiness. In addition, these threshold schedules are then compared to a leaky bucket regulator